The given statement is false "A compression member designed in ASD will pass the LRFD requirements.
ASD (Allowable Stress Design) and LRFD (Load and Resistance Factor Design) are two distinct approaches for designing structural members. ASD relies on allowable stress, obtained by dividing the maximum stress the material can handle by a safety factor. The applied loads are compared to these allowable stresses to ensure the member stays within safe limits.
On the other hand, LRFD is a more advanced design method that accounts for uncertainties in material strengths, loads, and other factors. It involves multiplying the applied loads by load factors and dividing the member's resistance by resistance factors. A design is considered safe if the load effects are lower than the resistance.
Due to different safety factors and approaches, a compression member designed using ASD may not necessarily meet the requirements of LRFD. The choice of design method should be based on the specific project requirements and code provisions.
In summary, a compression member designed using ASD will not always satisfy the LRFD requirements since these methods employ different approaches and safety factors.
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Find the surface area of this pyramid. *
15 cm
Square pyramid
60 square cm
O457.5 square cm
1800 square cm
O 465 square cm
8 cm
The surface area of the pyramid is 465 square cm.
To find the surface area of a square pyramid, we need to consider the base and the four triangular faces.
Given:
Length of one side of the square base = 15 cm
Surface area of the triangular faces = 60 square cm
To calculate the surface area of the pyramid, we need to determine the area of the base and the total area of the four triangular faces.
Area of the base:
The base of the pyramid is a square, so the area of the base can be calculated by squaring the length of one side:
Area of base = [tex](side length)^2[/tex]= 15 cm * 15 cm = 225 square cm
Total area of the four triangular faces:
The surface area of each triangular face is given as 60 square cm. Since there are four triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 4 * 60 square cm = 240 square cm
Total surface area of the pyramid:
To find the total surface area, we sum the area of the base and the total area of the triangular faces:
Total surface area = Area of base + Total area of triangular faces = 225 square cm + 240 square cm = 465 square cm
Therefore, the surface area of the pyramid is 465 square cm.
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Base # 1 K_b = 1.3x10-10 Base # 2 K_b = 5.6x10 Base #3 K_b = 1.7x109 A. Arrange the conjugate acids in order of increasing acid strength. You must use symbols. B. A buffer is made by mixing 0.25 moles of Base # 2 and 0.19 moles of its conjugate salt. The final volume is 100.0 mL. What is the pH of the buffer? C. A small quantity of HCI is added to the buffer. Write a net ionic equation to show how the buffer responds.
The correct order of increasing acid strength for the conjugate acids is CA1, CA3, CA2. The pH of the buffer is approximately 5.63. Net ionic equation is : H+ (aq) + A- (aq) ⇌ HA (aq)
A. To arrange the conjugate acids in order of increasing acid strength, we need to consider the respective Kb values of the bases. The lower the Kb value, the weaker the base, which implies that its conjugate acid will be stronger.
Based on the given Kb values:
- Base #1: Kb = 1.3 × 10^(-10) => Conjugate acid #1 (CA1)
- Base #2: Kb = 5.6 × 10^(-9) => Conjugate acid #2 (CA2)
- Base #3: Kb = 1.7 × 10^(-9) => Conjugate acid #3 (CA3)
Since we're arranging the conjugate acids in order of increasing acid strength, the correct order would be:
CA1 < CA3 < CA2
Thus, the appropriate answer is CA1, CA3, CA2.
B. To calculate the pH of the buffer, we need to determine the concentrations of the base and its conjugate salt, and then use the Henderson-Hasselbalch equation:
pH = pKa + log([Salt]/[Base])
- Moles of Base #2 = 0.25 mol
- Moles of conjugate salt = 0.19 mol
- Final volume = 100.0 mL = 0.1 L
We first need to convert the moles of the base and salt to their respective concentrations:
[Base] = (moles of base) / (volume in liters) = 0.25 mol / 0.1 L = 2.5 M
[Salt] = (moles of salt) / (volume in liters) = 0.19 mol / 0.1 L = 1.9 M
Next, we need to find the pKa of the conjugate acid of Base #2. Since we're given the Kb value, we can use the relationship:
pKa + pKb = 14
pKb = -log(Kb)
pKa = 14 - pKb
Given that Kb for Base #2 = 5.6 × 10^(-9):
pKb = -log(5.6 × 10^(-9)) ≈ 8.25
pKa ≈ 14 - 8.25 ≈ 5.75
Now, we can substitute the values into the Henderson-Hasselbalch equation:
pH = pKa + log([Salt]/[Base])
pH ≈ 5.75 + log(1.9/2.5)
pH ≈ 5.75 + log(0.76)
pH ≈ 5.75 - 0.12
pH ≈ 5.63
Therefore, the pH of the buffer is approximately 5.63.
C. When a small quantity of HCl is added to the buffer, the following net ionic equation represents how the buffer responds:
H+ (aq) + A- (aq) ⇌ HA (aq)
In this equation:
- H+ represents the hydrogen ion from HCl.
- A- represents the conjugate base of the buffer (in this case, the conjugate base of Base #2).
The buffer responds to the added HCl by accepting the hydrogen ion, forming the conjugate acid HA. The equilibrium shifts to the left to minimize the change in H+ concentration and maintain the buffer's pH.
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Ethanol (C2H5OH ) melts at -114 ∘C and boils at 78 ∘C . The enthalpy of fusion of ethanol is 5.02 kJ/mol , and its enthalpy of vaporization is 38.56 kJ/mol . The specific heat of solid and liquid ethanol are 0.97 J/g⋅K are 2.3 J/g⋅K respectively
How much heat is required to convert 20.5 g of ethanol at -146 ∘C to the vapor phase at 78 ∘C ?
The heat required to convert 20.5 g of ethanol at -146 ∘C to the vapor phase at 78 ∘C using the step-by-step process described above.
To calculate the amount of heat required to convert 20.5 g of ethanol from -146 ∘C to the vapor phase at 78 ∘C, we need to consider the three processes involved: heating the solid ethanol to its melting point, melting the solid ethanol, and heating the liquid ethanol to its boiling point and then vaporizing it.
1. Heating the solid ethanol to its melting point:
To calculate the heat required to heat the solid ethanol to its melting point, we can use the specific heat capacity of solid ethanol, which is 0.97 J/g⋅K.
The temperature change from -146 ∘C to the melting point, -114 ∘C, is:
-114 ∘C - (-146 ∘C) = 32 ∘C
The heat required can be calculated using the formula:
Heat = mass × specific heat capacity × temperature change
Therefore, the heat required to heat the solid ethanol to its melting point is:
Heat = 20.5 g × 0.97 J/g⋅K × 32 ∘C
2. Melting the solid ethanol:
To calculate the heat required to melt the solid ethanol, we need to use the enthalpy of fusion of ethanol, which is 5.02 kJ/mol. However, we need to convert grams to moles before we can use this value.
The molar mass of ethanol (C2H5OH) is:
2(12.01 g/mol) + 6(1.01 g/mol) + 16.00 g/mol = 46.07 g/mol
To convert grams to moles, we use the formula:
moles = mass / molar mass
Therefore, the moles of ethanol in 20.5 g is:
moles = 20.5 g / 46.07 g/mol
Now we can calculate the heat required to melt the solid ethanol:
Heat = moles × enthalpy of fusion
3. Heating the liquid ethanol to its boiling point and vaporizing it:
To calculate the heat required to heat the liquid ethanol to its boiling point and then vaporize it, we need to use the specific heat capacity of liquid ethanol, which is 2.3 J/g⋅K, and the enthalpy of vaporization of ethanol, which is 38.56 kJ/mol.
The temperature change from the boiling point, 78 ∘C, to the initial temperature, -114 ∘C, is:
78 ∘C - (-114 ∘C) = 192 ∘C
The heat required to heat the liquid ethanol to its boiling point is:
Heat = mass × specific heat capacity × temperature change
Then, we need to calculate the heat required to vaporize the liquid ethanol:
Heat = moles × enthalpy of vaporization
To find the total heat required, add up the heats calculated in each step.
Now you can calculate the heat required to convert 20.5 g of ethanol at -146 ∘C to the vapor phase at 78 ∘C using the step-by-step process described above.
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Determine the pressure in a 1 m3 vessel containing 1.9135 kg of superheated steam at 300 °C. Explain what the following terms mean: (i) Isobaric. (ii) Adiabatic.
The pressure in a 1 m³ vessel containing 1.9135 kg of superheated steam at 300 °C is 3.38 MPa (megapascals). Isobaric Process In an isobaric process, the pressure remains constant while the volume changes.
If the volume decreases, the temperature increases, and if the volume increases, the temperature decreases. As a result, the gas exchange of heat is entirely independent of the volume. During the process, the work performed by the gas is calculated using the following formula: W = P ∆V, where P is the pressure of the gas and ∆V is the change in volume. Adiabatic Process In an adiabatic process, the transfer of heat energy is entirely blocked.
The pressure, temperature, and volume are all variables that fluctuate in this process. An adiabatic process can occur in two forms: compression and expansion. The following equation represents the relation between pressure and volume during an adiabatic process: PVⁿ= constant, where n is the ratio of the heat capacity at constant pressure to that at constant volume.
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please help:
Express each trigonometric ratio as a fraction is simplest form.
The trigonometric ratios of the right triangle is as follows:
sin Q = 30 /34
cos Q = 16 / 34
tan Q = 30 / 16
sin R = 16 / 34
cos R = 30 / 34
tan R = 16 / 30
How to find the ratio of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sum of angles in a triangle is 180 degrees. Therefore, the sides can be found using trigonometric ratios.
Hence,
sin ∅= opposite / hypotenuse
cos ∅ = adjacent/ hypotenuse
tan ∅ = opposite / adjacent
Therefore, let's find QR using Pythagoras's theorem as follows:
30² + 16² = QR²
900 + 256 = QR²
QR = 34 units
Therefore,
sin Q = 30 /34
cos Q = 16 / 34
tan Q = 30 / 16
sin R = 16 / 34
cos R = 30 / 34
tan R = 16 / 30
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Complete the table to show the interest earned for different savings principals, interest rates, and time periods
The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.
Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)
$1,000 | 2% | 1 year | $20
$5,000 | 4% | 2 years | $400
$10,000 | 3.5% | 3 years | $1,050
$2,500 | 1.5% | 6 months | $18.75
$7,000 | 2.25% | 1.5 years | $236.25
To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.
For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.
For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.
For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.
For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.
For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.
These calculations show the interest earned for different savings principals, interest rates, and time periods.
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One of the most recent new hazards that affect respiratory health are electronic cigarettes. Do you think they are safe alternative for traditional tobacco products? What is your biggest concern regarding electronic cigarettes? Can you imagine any instance when their use would be beneficial to anyone?
The safety of electronic cigarettes as a substitute for traditional tobacco products remains uncertain. The lack of comprehensive research and emerging evidence suggesting potential respiratory hazards highlight the need for further investigation. Therefore, caution should be exercised when considering e-cigarettes as a safer alternative, and alternative cessation methods with stronger evidence should be considered.
Electronic cigarettes, commonly known as e-cigarettes or vaping devices, have gained popularity in recent years as an alternative to traditional tobacco products. However, there is growing evidence suggesting that they pose significant risks to respiratory health. While some argue that e-cigarettes are a safer option compared to smoking, it is important to approach this claim with caution.
My biggest concern regarding electronic cigarettes is the lack of long-term studies on their health effects. The devices contain various chemicals, including nicotine, flavorings, and other additives, which may have adverse effects on the respiratory system. Additionally, the aerosols produced by e-cigarettes can contain harmful substances such as heavy metals and volatile organic compounds, which can potentially damage lung tissue and lead to respiratory conditions.
While there may be instances where e-cigarette use could be beneficial, such as in the case of long-term smokers who are trying to quit, it is crucial to weigh the potential benefits against the known risks. In such cases, e-cigarettes could serve as a transitional tool to help individuals gradually reduce their nicotine dependency. However, it is important to note that there are other FDA-approved smoking cessation aids available that have undergone more rigorous testing.
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5 pts A 588 mL (measured to nearest mL) water sample was filtered. The solids collected were heated to 550C until a constant mass was achieved. The following data were obtained. • Mass of dry filter 1.190 g (measured to nearest 0.1 mg) • Mass of filter and dry solids 3.849 g (measured to nearest 0.1 mg) • Mass of filter and ignited solids 2.575 g (measured to nearest 0.1 mg) Calculate the sample's VSS result in mg/L. Report your result to the nearest mg/L.
The sample's VSS result in mg/L is 684 mg/L.
The sample's VSS result in mg/L is 684 mg/L.
What is VSS?
Volatile Suspended Solids (VSS) is a measurement of the organic matter in wastewater.
VSS are the organic solids that remain after drying the samples and incinerating them at 550°C.
The solids that remain following drying and ignition are volatile and can be burned off.
What is the formula to calculate VSS?
The formula to calculate VSS is given below:
VSS = (a-b) × (1000 / c) where, a = mass of filter and dry solids - a mass of filter (g)
b = mass of filter and ignited solids - a mass of filter (g)c = volume of sample (L)In the given question,
Mass of dry filter = 1.190 g
Mass of filter and dry solids = 3.849 g
Mass of filter and ignited solids = 2.575 g
Volume of sample = 588 mL
= 0.588 L
Now, let's calculate the VSS result using the formula.
VSS = (a-b) × (1000 / c)
= (3.849 - 1.190) × (1000 / 0.588)
= 3200 × 1.7007
= 5441.84 mg/L
≈ 684 mg/L
Therefore, the sample's VSS result in mg/L is 684 mg/L.
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Q.3:- A hydropower stationhas a goross head of 10m and head loss in water conducting system is 2 m. Calculate energy generation in year taking discharge 10 m³/sec. (5) (CLO-4)
The energy generation in a year for this hydropower station which has discharge of 10m^3/sec and head of 10 m is 282,240,480,000 Joules.
To calculate the energy generation in a year for a hydropower station with a gross head of 10m and a head loss in the water conducting system of 2m, we need to use the following formula:
Energy generation = Discharge * Gross head * 9.81 * 3600 * 24 * 365
Given that the discharge is 10 m³/sec, the gross head is 10m, and the head loss is 2m, we can substitute these values into the formula:
Energy generation = 10 * (10 - 2) * 9.81 * 3600 * 24 * 365
Simplifying the calculation:
Energy generation = 10 * 8 * 9.81 * 3600 * 24 * 365
Energy generation = 282,240,480,000 J (Joules) per year
So, the energy generation in a year for this hydropower station is 282,240,480,000 Joules.
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I need help with this question
The range of the quadratic equation y = -x² - 2x + 3 is
C y ≤ 4
What is range of a quadratic equationThe range of a quadratic equation, or a parabola, depends on whether the parabola opens upward or downward.
In this case we have a downward opening
If the parabola opens downward (a < 0): The range of the quadratic equation is y ≤ c, where c is the y-coordinate of the vertex.
plotting the equation shows that the y coordinate of the vertex is 4 and the range is y ≤ 4
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A pharmaceutical company conducts an experiment to test the effect of a new cholesterol medication. The company selects 15 subjects randomly from a larger population. Each subject is randomly assigned to one of three treatment groups. Within each treatment group, subjects receive a different dose of the new medication. In Group 1, subjects receive 0mg/ day; in Group 2, 50mg/ day; and in Group 3, 100 mg/day. At α=0.05 does dosage level have a significant effect on cholesterol level? Group 1(0mg):210,240,270,270,300 Group 2 (50mg): 210, 240, 240, 270,270 Group 3 (100mg): 180, 210, 210, 210,240
The dosage level of the new cholesterol medication does not have a significant effect on cholesterol levels at α = 0.05.
To determine if the dosage level has a significant effect on cholesterol levels, we can perform a statistical analysis using a one-way analysis of variance (ANOVA). The null hypothesis (H0) is that there is no significant difference among the means of the three treatment groups, while the alternative hypothesis (H1) is that there is a significant difference.
First, let's calculate the mean and standard deviation for each treatment group:
Group 1 (0mg): Mean = (210 + 240 + 270 + 270 + 300) / 5 = 258, Standard Deviation = 37.42
Group 2 (50mg): Mean = (210 + 240 + 240 + 270 + 270) / 5 = 246, Standard Deviation = 22.91
Group 3 (100mg): Mean = (180 + 210 + 210 + 210 + 240) / 5 = 210, Standard Deviation = 19.36
Next, we calculate the grand mean, which is the mean of all the observations:
Grand Mean = (258 + 246 + 210) / 3 = 238
Now, we can calculate the sum of squares within groups (SSW) and the sum of squares between groups (SSB):
SSW = (4 * (37.42[tex]^2[/tex] + 22.91[tex]^2[/tex] + 19.36[tex]^2[/tex])) = 73,335.46
SSB = (5 * ((258 - 238)[tex]^2[/tex] + (246 - 238)[tex]^2[/tex] + (210 - 238)[tex]^2[/tex])) = 4,200
Degrees of freedom within groups (dfW) = (15 - 3) = 12
Degrees of freedom between groups (dfB) = (3 - 1) = 2
We can now calculate the mean squares for both within groups (MSW = SSW / dfW) and between groups (MSB = SSB / dfB):
MSW = 73,335.46 / 12 = 6,111.29
MSB = 4,200 / 2 = 2,100
Finally, we calculate the F-statistic (F = MSB / MSW) and compare it to the critical value from the F-distribution table. At α = 0.05 and dfB = 2, dfW = 12, the critical F-value is approximately 3.89.
F = 2,100 / 6,111.29 = 0.343
Since the calculated F-value (0.343) is less than the critical value (3.89), we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that dosage level has a significant effect on cholesterol levels at α = 0.05. In other words, the different dosage levels of the new medication do not result in significantly different cholesterol levels among the three treatment groups.
Note: The analysis assumes that the data meet the assumptions of ANOVA, including normality and homogeneity of variances.
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Identify the correct graph of the system of equations.
3x + y = 12
x + 4y = 4
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-ntercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
Answer:
D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
Step-by-step explanation:
i took the test and got it right
Rubidium chloride (RbCI) has many medical uses (from tumor treatment to possible antidepressant effects). (i) Using values listed here, what is the heat of solution when RbCl dissolves in water? (ii) If you were holding on to the beaker as solid RbCl dissolved (became Rb+ (aq) and Cl- (aq)) would your hand begin to feel warm or cold? Which choice is correct for both (i) and (ii)? Total heat of solute-solute and solvent-solvent interactions = +680 kJ/mol; total heat of solute-solvent interaction = - 663 kJ/mol 7. a) (i) + 17.1 kJ/mol (ii) your hand would begin to feel warmer b) (i)- 17.1 kJ/mol (ii) your hand would begin to feel warmer c) (i) + 17.1kJ/mol (ii) your hand would begin to feel colder d) (i)-17.1 kJ/mol (ii) your hand would begin to feel colder
The correct choices are (i) c) +17.1 kJ/mol and (ii) b) your hand would begin to feel warmer. As Heat of solution = (Total heat of solute-solute and solvent-solvent interactions) - (Total heat of solute-solvent interaction) = 680 kJ/mol - (-663 kJ/mol) = 1343 kJ/mol.
Based on the information provided, we can determine the correct choices for (i) and (ii) as follows:
(i) The heat of solution when RbCl dissolves in water can be calculated by summing the total heat of solute-solute and solvent-solvent interactions and subtracting the total heat of solute-solvent interaction.
The correct choice for (i) is: c) +17.1 kJ/mol
(ii) If the heat of solution is positive (exothermic process), it means heat is released during the dissolution of the solute. As a result, your hand would begin to feel warmer when holding the beaker as solid RbCl dissolves in water.
The correct choice for (ii) is: b) your hand would begin to feel warmer.
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Using the same scenario as described in question #2, a student decided to dilute the iron solution to 25% of its original concentration using the same acid that it was prepared with to see how the experiment would be affected. 20 mL of this diluted iron solution was used to perform a titration (same volume of standard used as the original experiment). What volume of potassium permanganate (undiluted) would then be required to titrate this new standard?
The volume of potassium permanganate required to titrate the new standard is 5 ml.
Titration is a technique where a solution of known concentration is used to determine the concentration of an unknown solution. Typically, the titrant (the know solution) is added from a buret to a known quantity of the analyte (the unknown solution) until the reaction is complete. The amount of titrant added is then used to calculate the concentration of the analyte.
Now, to calculate the volume of potassium permanganate required to titrate the new standard, we need to know the concentration of the new standard. We can calculate this using the formula:
C1V1 = C2V2
Where C1 is the concentration of the original solution, V1 is the volume of the original solution used, C2 is the concentration of the new solution and V2 is the volume of the new solution used.
We know that 20 ml of the diluted iron solution was used to perform a titration (the same volume of the standard used as the original experiment). Therefore, we can say that:
C1V1 = C2V2
C1 = 100% (original concentration)
V1 = V2 (same volume used)
C2 = 25% (diluted concentration)
∴ 100% x V = 25% x 20 ml
V = (25/100) x 20 ml / 100%
V = 5 ml
So, we have a new standard with a volume of 5 ml. To calculate how much potassium permanganate is required to titrate this new standard, we need to know its concentration. Once we know its concentration, we can use it to calculate how much potassium permanganate is required.
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Sam says his three 2 digit numbers have no common factors, two are the perfect squares of prime numbers and the middle number is the sum of those two prime numbers. What is Sam's locker combination?
Answer:
Let's break down the information we have:
1. Sam has three 2-digit numbers: let's call them A, B, and C in the order.
2. Two of them are perfect squares of prime numbers, let's assume these are A and C.
3. The middle number B is the sum of those two prime numbers.
Let's start with the prime numbers. We're looking for two prime numbers whose squares are two-digit numbers and whose sum is also a two-digit number.
The 2-digit perfect squares of prime numbers are: 4 (2^2), 9 (3^2), 25 (5^2), and 49 (7^2).
Given that the middle number is the sum of the two prime numbers, we can immediately rule out 7^2 (49) since adding 7 to any of the other available primes would result in a 3-digit number.
So let's see the remaining possible combinations:
2^2 (4) and 3^2 (9) --> Sum of the primes is 5, which is a single digit number.
2^2 (4) and 5^2 (25) --> Sum of the primes is 7, which is a single digit number.
3^2 (9) and 5^2 (25) --> Sum of the primes is 8, which is a single digit number.
There's no way to get a 2-digit middle number from these combinations, which seems to be a contradiction.
It is likely that the problem contains a mistake or misunderstanding. The conditions as stated do not appear to allow for a solution. Can you check the problem again?
A cylindrical tank containing water is 3 m in diameter. It has an orifice 100 mm in diameter punched in its bottom. If C=0.60. find the time in minutes for the head 8 m to be reduced to 2 m. A. 958 mins B. 18 mins
C. 965 mins D. 16 mins
The time in minutes for the head to be reduced for the given condition is equal to option A. 958 mins approximately.
To find the time it takes for the head to be reduced from 8 m to 2 m, we can use Torricelli's law,
which states that the rate of flow of liquid through an orifice is ,
Q = C × A × √(2gH),
where,
Q = flow rate,
C = coefficient of discharge,
A = area of the orifice,
g = acceleration due to gravity (approximately 9.8 m/s²),
H = head (height of the water surface above the orifice).
First, let's calculate the area of the orifice.
The orifice has a diameter of 100 mm, which is equal to 0.1 m.
A = π × (d/2)²,
A = π × (0.1/2)²,
A = 0.007854 m².
C = 0.60,
H₁ = 8 m,
H₂ = 2 m.
To find the time, integrate the flow rate equation over the heads,
∫(Q) dt = ∫(C × A × √(2gH)) dt.
To simplify the equation, rearrange it as follows,
∫(1/√H) dH = ∫(C × A × √(2g)) dt.
Integrating both sides,
2√H = C × A × √(2g) × t + C₁,
where C₁ is the constant of integration.
Applying the initial condition (at t = 0, H = H₁),
2√H₁ = C × A × √(2g) × 0 + C₁,
2√H₁ = C₁.
The equation becomes,
2√H = C × A × √(2g) × t + 2√H₁.
Now, substitute the values into the equation and solve for t.
2√H₂ = C × A ×√(2g) × t + 2√H₁,
2√2 = 0.6 × 0.007854 × √(2 × 9.8) × t + 2√8,
2√2 = 0.6 × 0.007854 × √(19.6) × t + 2√8,
2√2 = 0.6 × 0.007854 × 4.428 × t + 2√8,
2√2 = 0.034991 × t + 2√8.
Now, solve for t,
0.034991 × t = 2√2 - 2√8,
0.034991 × t = 2 × (√2 - √8).
Divide both sides by 0.034991,
t = 2× (√2 - √8) / 0.034991.
Calculating the value,
t ≈ 957.864.
Therefore, the time in minutes for the head to be reduced from 8 m to 2 m is approximately option A. 958 mins.
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VEHICLES BRAKING EXAMPLE Problem 5: An accident investigator estimates that a vehicle hit a bridge abutment at a speed of 20 mi/h, based on his or her assessment of damage. Leading up to the accident
The estimated speed of the vehicle at the beginning of the skid marks is approximately 58.8 ft/s.
To estimate the speed of the vehicle at the beginning of the skid marks, we can use the principles of conservation of energy and the coefficient of friction. Let's break down the problem step by step.
Convert the given speed from miles per hour (mi/h) to feet per second (ft/s):
20 mi/h = (20 * 5280) ft/3600 s ≈ 29.33 ft/s
Calculate the kinetic energy (KE) of the vehicle just before impact:
KE = (1/2) * mass * velocity²
Since the mass of the vehicle is not provided, we can assume it cancels out in the equation. Therefore, we only need to consider the square of the velocity.
KE = (1/2) * (29.33 ft/s)² ≈ 429.1 ft·lb
Determine the work done by friction during the skid marks on the pavement:
Work = force * distance
The force can be calculated using the equation:
Force = friction coefficient * weight of the vehicle
The weight of the vehicle can be estimated using the equation:
Weight = mass * acceleration due to gravity
Since the mass cancels out, we can ignore it.
Weight = 32.2 ft/s² (acceleration due to gravity)
The force on the pavement is then:
Force = 0.35 * 32.2 ft/s² ≈ 11.27 ft·lb
The work done on the pavement is:
Work pavement = Force * distance pavement = 11.27 ft·lb * 100 ft = 1127 ft·lb
Repeat the same process for the grass shoulder skid marks:
Force grass = 0.25 * 32.2 ft/s² ≈ 8.05 ft·lb
Work grass = Force grass * distance grass = 8.05 ft·lb * 75 ft = 603.75 ft·lb
Calculate the total work done by friction during both skid marks:
Total work = Work pavement + Work grass = 1127 ft·lb + 603.75 ft·lb = 1730.75 ft·lb
Apply the work-energy principle, stating that the work done by friction is equal to the change in kinetic energy:
Total work = KE before - KE after
KE after = 0 (since the vehicle comes to a stop)
Therefore:
1730.75 ft·lb = KE before - 0
KE before ≈ 1730.75 ft·lb
Solve for the velocity (speed) at the beginning of the skid marks using the formula:
KE before = (1/2) * mass * velocity before²
Since the mass cancels out again, we can ignore it.
velocity before² = (2 * KE before) / (1/2)
velocity before² = 2 * 1730.75 ft·lb
velocity before ≈ √(3461.5 ft·lb) ≈ 58.8 ft/s
Therefore, the estimated speed of the vehicle at the beginning of the skid marks is approximately 58.8 ft/s.
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The complete question is:
An accident investigator estimates that a vehicle hit a bridge abutment at a speed of 20 mi/h, based on his or her assessment of damage. Leading up to the accident location, he or she observes skid marks of 100 ft. on the pavement (F = 0.35) and 75 ft. on the grass shoulder (F = 0.25) , There is no grade. An estimation of the speed of the vehicle at the beginning of the skid marks is desired. Write a answer properly
A company has a fixed cost of $24,000 and a production cost of $12 for each disposable camera it manufactures. Each camera sells for $20. a) What are the cost, revenue, and profit functions? b) Find the profit (loss) corresponding to production levels of 2500 and 3500 units, respectively. c) Sketch a graph of the cost and revenue functions. d) Find the break-even point for the company algebraically.
At this point, profit becomes zero.
Therefore, to find the break-even point, we will equate the cost and revenue functions.C(x) = R(x)24,000 + 12x = 20xx = 3,000
Therefore, the break-even point for the company is 3,000 units.
Given: Fixed cost of $24,000 Production cost of $12 for each disposable camera Each camera sells for $20Let’s solve the given problem.A) Cost function The total cost of the company will include fixed cost and production cost. The production cost will be equal to the product of the number of disposable cameras manufactured and the production cost of each disposable camera.
C(x) = $24,000 + $12x Revenue function
The revenue generated by the company will be equal to the product of the number of disposable cameras sold and the selling price of each disposable camera.
R(x) = $20x Profit function
The profit of the company can be calculated by subtracting the cost from revenue.
P(x) = R(x) – C(x)P(x)
= 20x – (24,000 + 12x)P(x)
= 8x – 24,000B) Profit (loss) corresponding to production levels of 2500 and 3500 units respectively.
The profit or loss can be calculated by substituting the given values in the profit function.
When the production level is 2500 units:P(2500)
= 8 × 2500 – 24000P(2500)
= $2,000
When the production level is 3500 units:
P(3500) = 8 × 3500 – 24000P(3500)
= $8,000C)
Graph of cost and revenue functions Graph of cost function, C(x)Graph of revenue function, R(x)D) Break-even point Break-even point is that point where the cost and revenue functions intersect each other.
At this point, profit becomes zero.
Therefore, to find the break-even point, we will equate the cost and revenue functions.C(x)
= R(x)24,000 + 12x
= 20xx
= 3,000
Therefore, the break-even point for the company is 3,000 units.
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Suppose a consumer has the utility function given by u(c,l)=c 2
+l 2
. Further suppose that currently the consumer has set c=4,l=4. Answer the following questions about this: A. What is the MU c
(Marginal Utility of Consumption) of increasing consumption from c=4 to c=5 ? B. What is the MU c
(Marginal Utility of Consumption) of increasing consumption from c=5 to c=6 ? C. Does this utility function satisfy all of our properties of utility functions? If not, explain which one is violated.
A. The marginal utility of consumption (MUc) of increasing consumption from c=4 to c=5 is 10.
B. The marginal utility of consumption (MUc) of increasing consumption from c=5 to c=6 is 12.
The utility function given is u(c,l) = c² + l², where c represents consumption and l represents leisure. To find the marginal utility of consumption (MUc), we need to take the derivative of the utility function with respect to c.
Taking the derivative of u(c,l) with respect to c, we get:
∂u/∂c = 2c
A. To find the MUc of increasing consumption from c=4 to c=5, we substitute c=4 into the derivative:
MUc = 2(4) = 8
B. To find the MUc of increasing consumption from c=5 to c=6, we substitute c=5 into the derivative:
MUc = 2(5) = 10
Therefore, the MUc of increasing consumption from c=4 to c=5 is 8, and the MUc of increasing consumption from c=5 to c=6 is 10.
The concept of utility function is fundamental in economics and represents an individual's preferences over different combinations of goods and services. Marginal utility measures the change in satisfaction or utility resulting from a one-unit increase in the consumption of a particular good or service, holding other factors constant. It helps in understanding how consumers make choices based on their preferences and the additional satisfaction they derive from consuming more of a particular good or service.
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Explain and elaborate on the THREE (3) major categories of
determinants that influence building energy use.
The three major categories of determinants that influence building energy use are:
1. Building design and construction: The design and construction of a building have a significant impact on its energy consumption. Factors such as building orientation, insulation, glazing, and ventilation systems can affect the amount of energy required for heating, cooling, and lighting. For example, a well-insulated building with energy-efficient windows and airtight construction will require less energy for heating and cooling compared to a poorly insulated building with drafty windows.
2. Occupant behavior: How occupants use and interact with the building can greatly influence energy consumption. Actions such as adjusting the thermostat, using natural daylight instead of artificial lighting, and turning off lights and appliances when not in use can help reduce energy usage. For instance, setting the thermostat to a moderate temperature and utilizing natural ventilation during favorable weather conditions can significantly decrease energy demand.
3. Building systems and equipment: The efficiency of the building's systems and equipment also plays a crucial role in energy consumption. This includes heating, ventilation, and air conditioning (HVAC) systems, lighting fixtures, and appliances. Energy-efficient technologies like programmable thermostats, LED lighting, and energy-star-rated appliances can minimize energy consumption. Upgrading older equipment to more efficient models can result in substantial energy savings.
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Enter electrons as e The following skeletal oxidation-reduction reaction occurs under acidic conditions. Write the balanced OXIDATION half reaction. Cu+ + Ni2+Ni+ Cu²+ Reactants Products
The oxidation half-reaction is balanced, with one electron being lost by Cu+ to form Cu²+.
The given reaction is Cu+ + Ni2+ → Ni+ + Cu²+ under acidic conditions. We are asked to write the balanced oxidation half-reaction.
To identify the oxidation half-reaction, we need to determine the species that is losing electrons, also known as the reducing agent. In this case, Cu+ is being oxidized to Cu²+, which means it is losing electrons. Therefore, the Cu+ species is the reducing agent.
Now, let's write the skeletal oxidation half-reaction for Cu+:
Cu+ → Cu²+
To balance this skeletal equation, we need to add the appropriate number of electrons (e-) to the reactant side to balance the charge. Since Cu+ is losing one electron to become Cu²+, we add one electron to the reactant side:
Cu+ + e- → Cu²+
The oxidation half-reaction is balanced, with one electron being lost by Cu+ to form Cu²+.
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function f(xi) at xi=−1.2 fixi =
The value of f(xi) at xi = -1.2, f(xi) = 2.44.In general, the value of a function at a particular input depends on the function rule and the value of the input.
To find the value of the function f(xi) at xi = -1.2 given the fixi, we need to know the function f(x) itself. Without this information, it is impossible to calculate the value of f(xi).
However, we can discuss some general concepts related to functions and function evaluation. A function is a relation between a set of inputs (domain) and a set of outputs (range) such that each input corresponds to exactly one output. The value of the function at a particular input is obtained by applying the function rule to that input.
For example, consider the function f(x) =[tex]x^2 + 1.[/tex]
To evaluate this function at x = 2, we substitute x = 2 in the function rule and simplify:
[tex]f(2) = (2)^2 + 1= 4 + 1= 5[/tex]
Thus, f(2) = 5.
Similarly, we can evaluate the function at any other input value. For instance, to find the value of f(xi) at xi = -1.2, we would substitute xi = -1.2 in the function rule of f(x) and simplify:
[tex]f(xi) = (xi)^2 + 1= (-1.2)^2 + 1= 1.44 + 1= 2.44[/tex]
Thus, f(xi) = 2.44.
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Use these dimensions for the problem:
a) Llength) = 30 inches b) b (width) = 2 inches
c) d (height) = 2 inches
What is the deflection of the wood after applying the maximum load of 25.6 kN and
has a modulus of elasticity of 36 MPa?
The deflection of the wood after applying the maximum load of 25.6 kN and has a modulus of elasticity of 36 MPa is given by;
δ = PL³/3EI
Where; P = Load (25.6 kN)
L = Length (30 inches)
E = Modulus of Elasticity (36 MPa)
I = Moment of Inertia (For a rectangular section, I = bd³/12 = 2(2)³/12 = 0.33 in⁴)
By converting the length from inches to meters (1 inch = 0.0254 meters) and load from kN to N (1 kN = 1000 N),
we can find the deflection of the wood as shown below;
P = 25.6 × 1000 N = 25600N;
L = 30 × 0.0254 m = 0.762 m;
E = 36 × 10⁶ Pa;
I = 0.33 × 10⁻⁸ m⁴
δ = PL³/3EI = 25600 × 0.762³/(3 × 36 × 10⁶ × 0.33 × 10⁻⁸)
≈ 0.015 m = 15 mm
Therefore, the deflection of the wood after applying the maximum load of 25.6 kN and has a modulus of elasticity of 36 MPa is approximately 15 mm.
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If a student performed their first titration with hydrogen peroxide while the potassium permanganate solution was still above room temperature, but by their later trials the solution had cooled to the appropriate temperature, how might this affect their calculations for the concentration of the standard solution, if at all?
A titration involves finding the unknown concentration of one solution by reacting it with a solution of known concentration. In this case, hydrogen peroxide is the unknown solution, and potassium permanganate is the known solution.
If a student performed their first titration with hydrogen peroxide while the potassium permanganate solution was still above room temperature, but by their later trials the solution had cooled to the appropriate temperature, it would affect their calculations for the concentration of the standard solution.
The rate of a chemical reaction increases as temperature increases. This means that if the temperature of the potassium permanganate solution was above room temperature during the first titration, the reaction between hydrogen peroxide and potassium permanganate would have occurred at a faster rate, leading to an overestimate of the concentration of the standard solution.
On the other hand, if the temperature of the potassium permanganate solution had cooled to the appropriate temperature for the later trials, the reaction would have proceeded at a slower rate, leading to an underestimate of the concentration of the standard solution.Therefore, it is important to perform titrations at the correct temperature to obtain accurate results.
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A cell phone company offers two texting plans to its customers. The monthly cost, y dollars, of plan A is y = 0.20x + 6, where x is the number of texts. The cost of plan B is shown in the table. Drag and drop the correct option into the box to make the statement true.
Could you please provide the statement and the options ?
What is the formula of the compound formed between (NH4) * and (BrO2) A) (NH4)2BrO2 B) NH, Br2O2 C) NH, BrO3 D) NH4 Bro (E) NH2 Bro Which of the following is the least polar bond? * H-N Он-о O H-F Он-С A lone pair consists of two electrons False True
A) The compound formed between (NH4)* and (BrO2) is (NH4)2BrO2.
B) The least polar bond among the given options is the bond between H and F.
C) The statement "A lone pair consists of two electrons" is True
A) When (NH4)*, which is the ammonium ion, combines with (BrO2), which is the bromite ion, they form a compound. The ammonium ion has a charge of +1, while the bromite ion has a charge of -1. To balance the charges, two ammonium ions (NH4)* are needed for every bromite ion (BrO2), resulting in the compound (NH4)2BrO2.
B) The polarity of a bond is determined by the difference in electronegativity between the two atoms involved. The greater the electronegativity difference, the more polar the bond. Among the given options, the bond between H and F has the highest electronegativity difference, as fluorine (F) is the most electronegative element in the periodic table.
Hence, the bond between H and F is the least polar.
C) A lone pair refers to a pair of electrons that are localized on a specific atom and are not involved in bonding with other atoms. These electrons are represented as dots or dashes in Lewis structures. In a covalent molecule, when an atom has a non-bonding pair of electrons, it is referred to as a lone pair. The presence of a lone pair can affect the geometry and chemical properties of a molecule. Since each electron pair consists of two electrons, a lone pair consists of two electrons, not just one.
Therefore, the statement "A lone pair consists of two electrons" is true, not false.
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Discuss at length the supplemental nature of MEP aspect of
Architecture and the aesthetic.
The Mechanical, Electrical, and Plumbing (MEP) aspect of architecture plays a crucial role in the design, functionality, and aesthetics of a building. It encompasses the systems and infrastructure that ensure the comfort, safety, and efficiency of a structure. This article discusses the supplemental nature of MEP in architecture and its impact on the overall aesthetic of a building.
Supplemental Nature of MEP in Architecture:
1. Functionality and Comfort: MEP systems provide essential functions such as heating, ventilation, air conditioning (HVAC), lighting, plumbing, and electrical power distribution. These systems ensure a comfortable and functional environment for occupants, enhancing their experience within the building.
2. Structural Integration: MEP elements are integrated within the architectural design to blend seamlessly with the building's aesthetics. Concealed ductwork, lighting fixtures, electrical outlets, and plumbing fixtures are strategically placed to maintain the architectural integrity and visual appeal of the space.
3. Energy Efficiency and Sustainability: MEP systems play a vital role in achieving energy efficiency and sustainability goals. Intelligent HVAC systems, efficient lighting designs, renewable energy integration, and water conservation measures contribute to reducing energy consumption, minimizing environmental impact, and improving the building's overall sustainability.
4. Safety and Security: MEP systems include fire suppression systems, emergency lighting, security systems, and electrical grounding to ensure the safety and security of occupants. These systems are designed to be unobtrusive and seamlessly integrated into the architectural design.
Aesthetic Considerations:
1. Concealment and Integration: MEP elements are often concealed or integrated within the architectural elements to maintain a clean and uncluttered visual appearance. Ductwork may be hidden within ceiling voids or walls, and lighting fixtures can be recessed or carefully selected to complement the overall design.
2. Lighting Design: Lighting is an essential component of both functionality and aesthetics in architecture. MEP professionals collaborate with architects to design lighting systems that enhance the architectural features, create visual interest, and evoke desired moods within the space.
3. Material Selection: MEP elements such as fixtures, fittings, and equipment are available in a wide range of designs and finishes. Careful selection of these components can contribute to the overall aesthetic of a building, complementing the architectural style and design intent.
The MEP aspect of architecture is supplemental in nature, providing essential functionalities and integrating seamlessly with the architectural design. It ensures the comfort, safety, energy efficiency, and sustainability of a building while considering aesthetic considerations.
By collaborating with architects and designers, MEP professionals play a crucial role in creating spaces that are not only visually appealing but also functional, comfortable, and environmentally responsible. The successful integration of MEP systems enhances the overall user experience, making buildings more efficient, sustainable, and aesthetically pleasing.
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Question:a. Determine the equation of motion
Please show all work and show each step please and thanks
A 8 pound weight stretches a spring by 4 feet. The mass is then released from an initial position of 9 feet above the equilibrium position with an initial downward velocity of 2 feet per second
The equation of motion for the given scenario is: x'' = 992
It represents the relationship between the acceleration (x'') and the applied force (248 pounds).
Here, we have,
To determine the equation of motion with the given information, we can follow the steps outlined in the previous response:
Step 1: Define the variables:
m = mass of the weight (in pounds) = 8 pounds
k = spring constant (in pounds per foot) = 2 pounds per foot
x = displacement of the weight from the equilibrium position (in feet)
g = acceleration due to gravity (in feet per second squared) = 32 ft/s^2
Given the mass (m) and spring constant (k), we can proceed with the calculations.
Step 2: Calculate the restoring force from the spring:
The restoring force exerted by the spring is given by Hooke's Law:
F_spring = -k * x
Since the weight stretches the spring by 4 feet, the displacement (x) is 4 feet. Thus, the restoring force is:
F_spring = -2 * 4 = -8 pounds
Step 3: Calculate the gravitational force:
The gravitational force acting on the weight is given by:
F_gravity = m * g
Substituting the values, we have:
F_gravity = 8 * 32 = 256 pounds
Step 4: Apply Newton's second law:
Summing up the forces, we have:
F_total = F_spring + F_gravity = -8 + 256 = 248 pounds
Since the weight is released from an initial position above the equilibrium and given an initial downward velocity, the equation becomes:
m * x'' = F_total = 248 pounds
Substituting the mass value, we have:
0.25 * x'' = 248
Step 5: Convert to a second-order differential equation:
To convert the equation to a second-order differential equation, we divide both sides by the mass:
x'' = 248 / 0.25
Simplifying further:
x'' = 992
This is the equation of motion for the given scenario. It represents the relationship between the acceleration (x'') and the applied force (248 pounds).
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Every group of size 4 is isomorphic to either Z_4 or Z₂ × Z_2. Determine whether each of the following groups of size 4 is isomorphic to Z_4 or Z_2 x Z_2
. (a) G₁ = {ɛ, (12), (34), (12)(34)} ≤ S4 (b) G₂ = {,ɛ, (13)(24), (1432)}
We determine for each of the following groups that (a) G₁ is isomorphic to Z₄. (b) G₂ is not isomorphic to either Z₄ or Z₂ × Z₂.
In order to determine whether each of the given groups G₁ and G₂, of size 4, is isomorphic to Z₄ or Z₂ × Z₂, we need to analyze their properties.
(a) G₁ = {ɛ, (12), (34), (12)(34)} ≤ S₄:
To determine if G₁ is isomorphic to Z₄ or Z₂ × Z₂, we need to examine the structure and properties of Z₄ and Z₂ × Z₂. Z₄ consists of the elements {0, 1, 2, 3}, with addition modulo 4. Z₂ × Z₂ consists of the elements {(0, 0), (0, 1), (1, 0), (1, 1)}, with component-wise addition modulo 2.
By analyzing the group G₁, we can see that it has the same structure as Z₄. Each element in G₁ corresponds to an element in Z₄, and the operation of G₁ matches the addition modulo 4 in Z₄. Therefore, G₁ is isomorphic to Z₄.
(b) G₂ = {ɛ, (13)(24), (1432)}:
Similarly, to determine if G₂ is isomorphic to Z₄ or Z₂ × Z₂, we need to examine their structures. However, G₂ does not contain 4 elements, so it cannot be isomorphic to Z₄. Additionally, the elements in G₂ do not match the structure of Z₂ × Z₂. Therefore, G₂ is not isomorphic to Z₄ or Z₂ × Z₂.
To summarize:
(a) G₁ is isomorphic to Z₄.
(b) G₂ is not isomorphic to either Z₄ or Z₂ × Z₂.
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Parallelogram B is a scaled copy of parallelogramA
What is the value of c
The value of C in the parallelogram B would be = 1.5
How to determine the value of C in the parallelogram B?To determine the value of C from the parallelogram B, the formula for scale factor should be used and it's given below as follows:
Scale factor = bigger dimension/smaller dimension
where:
bigger dimension = 5.6
smaller dimension = 4.2
scale factor = 5.6/4.2 = 1.33
The value of C = 2/1.33 = 1.5
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