Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
The rate of change of surface area is 524.02 square kilometers per minutes.
what is surface area of square prism?The total space occupied by a three-dimensional square prism is called surface area.
What is the rate of change of surface area of the prism?
Given, the decreasing rate of the base side with respect to time, ds/dt = 7 km/min
the increasing rate of height with respect to time, dh/dt = 10 km/min
At a time, t, base side, s = 4 km
and height, h = 9 km
we need to determine the rate of change of surface area with respect to time, d A/dt
from the differentiation chain rule, d A/ dt = d A /dt × ds /ds
d A /dt = d A/ ds × ds /dt ... equation 1
we know that the surface area for prism, A = 2s² + 4sh
if we differentiate with respect to s then we find d A /ds
d/ds (A) = d/ ds (2s² + 4sh)
d A /ds = 4s + 4h +4s dh/ds ...... equation 2
now dh /ds = dh /ds × dt /dt [ using differentiation chain rule]
dh/ds = dh/ dt× dt/ds
d h/ ds = dh/dt × 1/ ds/dt
it stated earlier that dh/ dt = 10 and ds /dt = 7
dh / ds = 10/7
putting this value in equation 2, we get
d A /ds = 4s +4h + 4s ×10/7
as we know at time t, s= 4 and h = 9
d A /ds = 4 × 4 + 4 ×9 +4×4 ×10 /7
d A /ds = 74.86
putting the value d A /ds in equation 1, we get
d A /dt = d A /ds × ds/ dt
d A/ dt = 74.86 × 7
d A /dt = 524.02 km² / min
hence, the rate of change of surface area = 524.02 square kilometers per minutes
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in the past year, a veterinarian finds a 35% of animals she treats are cats. Assuming the pets are brought to the vet randomly, what is the probability that exactly 2 of the next 5 animals brought in will be cats?
ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.
What is an equation?There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.
X now has 300 mg of sodium in it.
[tex]x = 300[/tex]
Y also has 450 mg of sodium in it.
[tex]y = 450[/tex]
Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.
Let the number of frozen dinners be "b," and the number of soup cans be "a."
ax + by = 6000
a(300) + b(450) = 6000 .
Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation
[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]
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What is the major theme and minor theme in “Arachne and the weaving contest”
The central theme of Arachne is human limitation and hubris.The center of the ellipse is located midway between the foci .
What is major axis ?The center of the ellipse is located midway between the foci. The minor axis is the line segment going through the center and perpendicular to the major axis, with both endpoints on the ellipse. The length of the ellipse's major axis is equal to the bigger of 2a or 2b, while the length of its minor axis is equal to the smaller. The major axis, which is the largest distance between any two points on the ellipse, is the line that connects both foci and runs from one end to the other. The minor axis, which is the shortest path between two points on the ellipse, is the line that passes through the center of the major axis in a perpendicular direction.
given
The central theme of Arachne is human limitation and hubris. Arachne, a young girl who is a remarkably gifted weaver, thrives on the adulation of her customers.
As a result of her youth and inexperience as well as her awareness of her exceptional talents, Arachne eventually boasts that her weaving is even greater than Athena's.
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14% of a certain food is fat. Out of 400 total grams, how many grams are not fat?
Answer:
344 grams are not fat
Step-by-step explanation:
400 x (100% - 14%) =
400 x 86% = 344
Hope that helps! :)
-Aphrodite
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 38 randomly selected people who train in groups, and finds that they run a mean of 49.5 miles per week. Assume that the population standard deviation for group runners is known to be 1.1 miles per week. She also interviews a random sample of 33 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 2.6 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2.
Required:
Draw a conclusion and interpret the decision.
Answer:
conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.
Step-by-step explanation:
H0 : μ1 = μ2
H0 : μ1 ≠ μ2
The test statistic :
(x1 - x2) / √(s1²/n1) + (s2²/n2)
(49.5 - 48.5) / √(1.1²/38) + (2.6²/33)
1 / √0.2366905
Test statistic = 2.055
Using the Pvalue from Tstatistic calculator :
df = (smaller sample - 1) = 33 - 1 = 32
Pvalue from Test score calculator = 0.048
Pvalue > α ; Fail to reject the null ;
Hence, conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.
what is the value of the expression 3.5 + (1 + 4) x (6.5 + 1.5)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3.5 + (1 + 4)\times (6.5 + 1.5)}\\\mathsf{1 + 4 = \bf 5}\\\mathsf{6.5+1.5=\bf 8}\\\mathsf{3.5+5\times8}\\\mathsf{5\times8=\bf 40}\\\mathsf{3.5+40}\\\large\text{= \bf 43.5}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf 43.5}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
One root of the equation 4x² + 12x + k = 0, k = Z and x = R, is five times the other root.
Find the value of k.
We found the value of K is 5 and the root of equation is x = -1/2 and x = -5/2
What is quadratic equation?An equation of second order polynomial having one variable is called quadratic equation. Second order means the highest power used with variable is 2.
How to determine the value of k in the question?We are given, 4x²+ 12x +k =0, k =Z and x = R
the quadratic equation is 4x²+12x+k =0
we know the roots of a quadratic equation is x = - b ± √ (b² - 4ac) / 2a
when the quadratic equation is ax²+bx+ c= 0
Hence, roots of the equation given in question will be,
x = - 12 ±√ (12² - 4×4×k) / 2×4
x = - 12 ± √(144-16k) / 8
as per the condition given in question, one root of this equation is 5 times the other root.
hence, - 12 -12 √(144-16k) / 8 = [- 12 + √(144-16k) / 8] × 5
multiplying both sides by 8
- 12 - √(144-16k) = [-12 + √(144-16k)] ×5
- 12 - √(144-16k) = - 60 + 5√(144-16k)
- 12 + 60 = 6√(144-16k)
48 = 6√(144-16k)
8 = √(144-16k)
64 = 144 -16k
16k = 80
k = 5
the value of k =5
by putting the value of k =5
x = -12 ± √ (144 - 80) / 8 = (-12 ± 8) /8
x = -1/2 and x = -5/2
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Write 49D2
in the base-ten system.
Each position in base 10 is worth ten times the place to its right, and there are ten numbers (0–9). 49D2 in the base-ten system is equal to 204064.
What does base-10 value 2 have?When you come to "two," you discover that there isn't a single digit in base-two math that stands for "two." Instead, you enter a "1" for "1 two" and a "0" for "0 ones" in the twos and units columns, respectively.
[tex]49D2 in the base-ten system is 4916^3 + 1316^2 + 216^1 \\\\= (494096) + (13256) + (216) \\\\= 200704 + 3328 + 32\\ \\= 204064[/tex]
Binary has a basis of 2 or 10.A binary counting system simply employs the numerals 0 and 1 in each place. Base 2 is another name for binary. In binary, a second place is required to represent a number greater than 1.
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(7/8 x 14) / (3/8 x 6) + 2 1/5
Answer:
7/8 x 14= 12.25 or 49/4 or 12 1/4
(3/8 x 6) + 2 1/5= 4.45
(hope this helps I probably wasn't fully understanding)
How many 2/3 Tablespoons are in a half Tablespoon
Therefore , the solution of the given question of equation come out to be
x = 1/3 tablespoon .
Define equation.Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.
Here,
Given : 2/3 cup Tablespoons
We have to find the half Tablespoons
So,
In order to find the half Tablespoons
Thus,
=> 1 Tablespoon = 2/3Tablespoons + x
where x is the half Tablespoons
=> x = 1/3 tablespoon
Therefore , the solution of the given question of equation come out to be
x = 1/3 tablespoon .
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What is the value of 7/8+ (-2/3) - (-4)?
The value of fraction will be;
⇒ 101/24
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The expression is,
⇒ 7/8+ (-2/3) - (-4)
Now,
Since, The expression is,
⇒ 7/8+ (-2/3) - (-4)
Simplify as;
⇒ 7/8 - 2/3 + 4
⇒ (21 - 16)/24 + 4
⇒ 5/24 + 4
⇒ (5 + 96) / 24
⇒ 101/24
Thus, The solution is,
⇒ 101/24
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Based on information from a large insurance company, 67% of all damage liability claims are made by single people under the age of 25. A random sample of 52 claims showed that 43 were made by single people under the age of 25. Does this indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company
Answer:
Yes. This indicates that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company.
Step-by-step explanation:
Damage liability claims by single people under the age of 25 = 67%
Sample size = 52 claims
Claims made by single people under the age of 25 from the sample = 43 out of 52 claims
In percentage terms, the claims made by single people under the age of 25 from the sample = 43/52 = 83%
Since 83% > 67% (with a difference of 16%)
Bananas FOR $1.00 Oranges - 6 FOR $1.50 Peaches - 4 for $1.28 Frankie mother tells Him that they need 5 Bananas 15 Oranges. And 10 peaches For the Salad. Determine the total cost of the amount of fruit that " FRAnkie needs.
Answer:
Mizuki is here to help! The answer will be $11.95
Step-by-step explanation:
Ok so... Frankie wants 5 bananas, 15 oranges, and 10 peaches for the salad right?
First, let's find the price of the 5 bananas. We multiply 1 by 5 and get 5, so $5 is the cost for the bananas he is going to spend.
Next, let's find the price for 15 oranges. First, we will divide 15 by 6, which will end up with 2.5. Then, we multiply 1.5 by 2.5 which will be 3.75. The price for the oranges he is going to buy is $3.75.
Then, let's find the price of the 10 peaches. The step is similar from the way we solved the price of oranges. We divide 10 by 4 and get 2.5. Next, we will multiply 1.28 by 2.5 and get 3.2. The price for peaches is $3.2.
Finally, let's add up 5, 3.75, and 3.2! The total should be 11.95! That will be your answer!
Pls help no files pls
9514 1404 393
Answer:
x = -1x = -2Step-by-step explanation:
1) Divide both sides by the coefficient of x.
x = (7.2/(-14/9))/((-108/35)/(-2/3))
x = -1
__
2) Multiply both sides by the factor x is being divided by.
x = (-3.18/5.3)/((-20/3)/(-2))
x = -2
_____
Your calculator can help you with this.
Draw a diagram of x + 2 and a separate diagram of 3x when x is 2.
The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.
The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.
What is diagram in mathematics?In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.
For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).
A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.
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The height h (in feet) of a fireworks shell shot vertically upward as a function of time t (in s) is h(t)=-16t^2+144t+4 . How long should the fuse last so that the shell explodes at the top of its trajectory?
Answer:
Step-by-step explanation:
h(t)=16t²+144t +4
=16(t²+9t+(9/2)²)-16(9/2)²+4
check your problem statement.
Find the slope of the line that has an equation of 4x-2y=6
4x - 2y = 6
2y = 4x - 6
y = (4x - 6)/2
y = 2x - 3
1/4(10-3+5)2 pls help
Answer:
6
Step-by-step explanation:
Joe decided to track the temperature in his town for five consecutive days. On Monday, the temperature was 23°C. On Tuesday, it decreased by 9°C and then increased by 7°C on Wednesday. On Thursday, the temperature rose 4°C and then decreased by 5°C on Friday. What was the overall temperature change over those five days?
Using a subtraction operation, the overall temperature change over those five days that Joe tracked the temperature in his town was a decrease of 3°C.
How is the temperature change computed?The temperature change can be computed by determining the differences in temperature from one day to the next and summing the differences.
The temperature change can also be computed by finding the difference between the ending period's temperature and the beginning period's temperature.
Days Temperature Change
Monday 23°C 0
Tuesday 14°C (23 - 9) -9
Wednesday 21°C (14 + 7) +7
Thursday 25°C (21 + 4) +4
Friday 20°C (25 - 5) -5
Overall change = -3°C
= 20°C - 23°C = -3°C
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What is the probability that the student selected at random preferred bananas or grapes? 26 58 42 34
Answer:
I do not know.
Step-by-step explanation:
if you answer the question Correctly I will give you brainliest.
Answer:
6982 ft squared
Step-by-step explanation:
The area of the trapezoid is 10000 feet square and the area of the square building is 3072 square feet. In order to find the area of the lawn, you need to subtract the area of the building from the area of the trapezoid, which is 6982 feet squared.
Answer:
6982 ft squared
Step-by-step explanation:
Angela has 24 golf balls and 18 golf clubs. She wants to sell packages of balls and clubs bundles together. What is the greatest number of packages she can sell with no leftover balls or clubs? Do not include units.
Answer:
GCF of 18 and 24 is 6. So she can sell 6 packages with 4golf balls and 3 golf clubs
Step-by-step explanation:
Give brainliest please
If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
Answer:
If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
Match each modification to its effect on an ecosystem.
Many desert regions in the West were transformed
into lush urban areas and farmlands.
Water bodies in the Owens Valley and its
surrounding areas began to dry up.
Runoff containing disease-carrying organisms
contaminated soil and caused water pollution.
construction of the Los Angeles aqueduct
arrowRight
construction of large highways
arrowRight
damming of the Colorado River
The modifications and their effects on the ecosystem include:
construction of the Los Angeles aqueduct - Many desert regions in the West were transformed into lush urban areas and farmlands.construction of large highways - Runoff containing disease-carrying organismsdamming of the Colorado River - Water bodies in the Owens Valley and its surrounding areas began to dry up.What were the effects of some man made feats in the west ?With the construction of the Los Angeles aqueduct, water was transported to the west such that many desert regions there became lush urban areas and farmlands.
Large high ways and the damming of the Colorado River did not have such a good impact however, as they both led to runoff and to water bodies in the Owen valley drying up.
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Solve: 2x - 5 = 4x + 3
Important: No spaces in your answer
(any spaces within the answer can get the whole answer wrong)
How many times will Anna need to fill the measuring cup to measure 78 7 8 cup of turnips? If Anna divides the ingredients equally into 4 pots, how many cups of onions will she need in each pot?
Answer:
Step-by-step explanation:
3 너 도넛
There are approximately 3.6 million deaths per year in Nigeria. Express this quantity as deaths per minute
Answer:
6.84931507 = 6-7 deaths
Step-by-step explanation:
3,600,000 / 525600 (minutes in a year) = 6.84931507
If Nayesha pumps 9.4 gallons of gas in her gas tank and each gallon costs $2.98, how much money will she spend? QUCIKLY
Answer:
28.012
Step-by-step explanation:
9.4*2.98 = 28.012
In ΔRST, sin T = 1/5, m∠R = 30, and r = 15. What is the length of t?
Answer:
t = 6Step-by-step explanation:
Given ΔRST with:
sin ∠T = 1/5m ∠R = 30°r = 15t = ?Solution
We know t is opposite ∠T and r is opposite ∠R.
Use the law of sines to find the missing value of t.
r / sin ∠R = t / sin ∠TSubstitute the known values and solve for t:
15 / sin (30°) = t / (1/5)15 / (1/2) = 5t30 = 5tt = 30/5t = 6Answer:
t = 6
Step-by-step explanation:
In ΔRST:
Angle R is opposite side r.Angle S is opposite side s.Angle T is opposite side t.Sine Rule
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Given:
sin T = ¹/₅R = 30°r = 15Substitute the given values into the Sine Rule formula and solve for t:
[tex]\implies \sf \dfrac{r}{\sin R}=\dfrac{s}{\sin S}=\dfrac{t}{\sin T}[/tex]
[tex]\implies \sf \dfrac{15}{\sin 30^{\circ}}=\dfrac{t}{\frac{1}{5}}[/tex]
[tex]\implies \sf \dfrac{15}{\sin 30^{\circ}}=5t[/tex]
[tex]\implies \sf t=\dfrac{15}{5 \sin 30^{\circ}}[/tex]
[tex]\implies \sf t=\dfrac{15}{5 \cdot \frac{1}{2}}[/tex]
[tex]\implies \sf t=\dfrac{15}{\frac{5}{2}}[/tex]
[tex]\implies \sf t=15 \cdot \dfrac{2}{5}[/tex]
[tex]\implies \sf t=\dfrac{30}{5}[/tex]
[tex]\implies \sf t=6[/tex]
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the following sample data are from a normal population : 10,8,12,,15,13,11,6,5