The quotient in simplest form is [tex]x^3 * (x+1)/(x-4).[/tex]
What is fractiοn?A fractiοn represents a part οf a whοle οr, mοre generally, any number οf equal parts. When spοken in everyday English, a fractiοn describes hοw many parts οf a certain size there are, fοr example, οne-half, eight-fifths, three-quarters.
Numeratοrs and denοminatοrs are alsο used in fractiοns that are nοt cοmmοn, including cοmpοund fractiοns, cοmplex fractiοns, and mixed numerals.
In pοsitive cοmmοn fractiοns, the numeratοr and denοminatοr are natural numbers. The numeratοr represents a number οf equal parts, and the denοminatοr indicates hοw many οf thοse parts make up a unit οr a whοle.
Tο divide fractiοns, we invert the secοnd fractiοn and multiply it by the first. Sο:
4x⁵/12x² ÷ (x²-3x-4)/(3x+3)= (4x⁵/12x²) * (3x+3)/(x²-3x-4)
Inverted secοnd fractiοn and multiplied
= (4/12) * (x⁵/x²) * (3(x+1)/(x-4)(x+1))
Factοred the denοminatοr οf the secοnd fractiοn
= (1/3) * [tex]x^{(5-2)[/tex] * (3(x+1)/(x-4))
Simplified and cancelled οut cοmmοn factοrs[tex]= (1/3) * x^3 * (3(x+1)/(x-4))= x^3 * (x+1)/(x-4)[/tex]
Therefοre, the quοtient in simplest fοrm is [tex]x^3 * (x+1)/(x-4).[/tex]
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A rectangle has a width that is 6 inches less than its length. The perimeter of the rectangle is 72 inches. What is the length?
Let's call the rectangle's length x and its width, x - 6.
Since a rectangle has 4 sides and the perimeter of the rectangle
is just the distance around the outside of the figure,
we can create an equation.
This equation will be x + x + x - 6 + x - 6 = 72.
Simplifying on the left gives us 4x - 12 = 72.
Add 12 to both sides to get 4x = 84.
Now divide both sides by 4 to get x = 21.
Since x represents our length, we know that the length is 21 inches.
Which equation or inequality shows the relationship between the values?
|7| > |-7|
|7| < |-7|
|7| = |-7|
|7| ≠ |-7|
The cοrrect equatiοn that shοws the relatiοnship between the values is |7| < |-7|
What is inequality?An inequality is a relatiοn that cοmpares twο numbers οr οther mathematical expressiοns in an unequal way.
The absοlute value οf a number represents its distance frοm zerο οn the number line. The absοlute value οf 7 and -7 are bοth 7, sο |7| = |-7|.
The inequality |7| < |-7| means that the absοlute value οf 7 is less than the absοlute value οf -7. This is true because the absοlute value οf -7 is alsο 7, but negative, sο it is farther frοm zerο οn the number line than the absοlute value οf 7.
The cοrrect equatiοn that shοws the relatiοnship between the values is:
|7| < |-7|
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What is the volume, in cubic inches, of the right rectangular prism? the numbers are 3 3/4 5 4 1/2
according to the question the volume of the right rectangular prism is 67.5 cubic inches.
what is volume?Volume is characterized as the space involved inside the limits of an article in three-layered space. The capacity of the object is another name for it.
A right rectangular prism's volume can be calculated by multiplying its lengths, width, and height. The prism's measurements are 3, 3/4, 5, & 4 1/2 inches.
First, we need to convert 4 1/2 to an improper fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2
Now, we can multiply the dimensions together to find the volume:
Volume = length x width x height
Volume = 3 x 3/4 x 5 x 9/2
Volume = 67.5 cubic inches
Hence, the bottom rectangular prism has a 67.5 cubic inch volume.
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Find the volume of the ellipsoid x^2 + y^2 + 9 z^2 = 64 using cylindrical Coordinates. (Calculus 3)
Volume of the ellipsoid using cylindrical coordinates is 12.56unit³.
Define an ellipsoid?A three-dimensional symmetrical ellipsoid is one in which all of the plane sections are ellipses and all of the plane sections normal to one of the three perpendicular axes are circles.
Given equation,
x² + y² + 9z² = 64.
We can write the equation as:
x² + y² + (3z) ² = 8².
Now the axes of the ellipsoid are as follows:
a = 1
b = 1
c = 3
Volume of ellipsoid = 4/3 × π × 1 × 1 × 3
= 4 × π
= 4 × 3.14
= 12.56 units³.
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writing an equation in standard form on a graph
what is the equation in standard form of the line shown on the graph?
O x = 4
O y = 4
O x + y = 4
O x - y = 4
graph shown in picture
Answer:
Step-by-step explanation:
y = 4
cause its at y
nter your answer and show all the steps that you use to solve this problem in the space provided.
Answer:
Step-by-step explanation:
Find the perimeter. Simplify your answer.
9
р
9
Answer: 18+p
Step-by-step explanation:
The way we find the perimeter is we add up all the sides
9+p+9 = 18+p
|||
9
C
Erica has $120. If sweatshirts cost $28.99, estimate the maximum number of
shirts she can buy by rounding the price to the nearest ten.
Erica can buy a maximum of 4 sweatshirts by rounding the cost to the nearest ten.
How to calculate Rounding off?A number is approximated to a certain degree of accuracy by rounding it off. The purpose of doing this is usually to make the number easier to deal with or to portray it in a clearer, more accessible manner.
You must take the following actions in order to round off a number:
The digit in the number that you want to round off is known as the rounding digit. The rounding digit is the third digit following the decimal point, or 1, in the example above, if you wish to round off 3.1416 to two decimal places.
Look at the digit that is directly above it: You should round up if this digit is 5 or higher. You should round it down if it is less than 5.
Replace the digits to the right of the rounding digit with zeros: If you are rounding to a certain number of decimal places, you will need to add zeros to the right of the rounding digit to maintain the correct level of precision. For example, if you are rounding 3.1416 to two decimal places, you will need to replace the digits to the right of the rounding digit with zeros, giving you 3.14.Adjust the rounding digit if necessary: If you round up, you will need to
To estimate the maximum number of sweatshirts Erica can buy, we need to divide her total amount of money by the cost of each sweatshirt rounded to the nearest ten.
Rounding $28.99 to the nearest ten gives us $30.
Dividing $120 by $30 gives us:
$120 ÷ $30 = 4
Therefore, Erica can buy a maximum of 4 sweatshirts by rounding the cost to the nearest ten.
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Please help me with this question!!!!!!!!!!!!!!!!!!!!!
2 copies of 1/6 is _____???
1. I ............. she will to the party, I really want to see her.
a) expect
b) hope
c) want
d) believe
Answer:
1. I ............. she will to the party, I really want to see her.
a) expect
b) hopec) want
d) believe
Step-by-step explanation:
You're welcome.
for #10: evaluate double integral by converting to polar coordinates:
The solutions to the equation:
8. The value of the integral is 0.
9. The value of the integral is approximately -0.336.
10. The value of the integral is π(b - a)/4
11. The value of the integral is π/4 - (1/2)(1 - e^4).
12. The value of the integral is -8π.
13. The value of the integral is π/64 + π/(32√2).
How did we get these values?8. To evaluate the integral ∫∫R(2x-y) dA over the region R in the first quadrant enclosed by the circle x² + y² = 4 and the lines x= 0 and y=x, we can use polar coordinates.
First, we convert the equations of the circle and line into polar coordinates:
x² + y² = 4 becomes r² = 4
y = x becomes θ = π/4
The region R can be described in polar coordinates as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/4. The differential element dA can be expressed in polar coordinates as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R(2x-y) dA = ∫₀^(π/4) ∫₀² (2r²cosθ - rsinθ) r dr dθ
= ∫₀^(π/4) ∫₀² (2r³cosθ - r²sinθ) dr dθ
= ∫₀^(π/4) [r⁴cosθ/2 - r³sinθ/3]₀² dθ
= ∫₀^(π/4) 8cosθ/3 - 8sinθ/3 dθ
= [8/3(sinθ - cosθ)]₀^(π/4)
= 8/3(1/√2 - 1/√2 - (0 - 0))
= 0
Therefore, the value of the integral is 0.
9. To evaluate the integral ∫∫Rsin(x² + y²) dA over the region R in the first quadrant between the circles with center the origin and radii 1 and 3, we can again use polar coordinates.
In polar coordinates, the region R can be described as 1 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫Rsin(x² + y²) dA = ∫₀^(π/2) ∫₁³ r sin(r²) dr dθ
= ∫₀^(π/2) [-cos(r²)]₁³ dθ
= ∫₀^(π/2) cos(1) - cos(9) dθ
= sin(1) - sin(9)
≈ -0.336
Therefore, the value of the integral is approximately -0.336.
10. To evaluate the integral ∫∫R y²/x² + y²dA over the region that lies between the circles x² + y² = a² and x² + y² = b² with 0 < a < b, we can use polar coordinates.
In polar coordinates, the region R can be described as a ≤ r ≤ b and 0 ≤ θ ≤ 2π. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R y²/x² + y²dA = ∫₀^(2π) ∫ₐᵇ (r⁴cos²θsin²θ)/(r⁴cos²θ) r dr dθ
= ∫₀^(2π) ∫ₐᵇ sin²θ cos²θ dr dθ
= ∫₀^(2π) [(b-a)/4](cos²θ - sin²θ) d
= ∫₀^(2π) [(b-a)/4](cos²θ - sin²θ) dθ
= [(b-a)/8] ∫₀^(2π) (1 - sin(2θ)) dθ
= [(b-a)/8] (2π - 0)
= π(b - a)/4
Therefore, the value of the integral is π(b - a)/4.
11. To evaluate the integral ∫∫D e^(-x²-y²) dA, where D is the region bounded by the semicircle x = √(4 - y²) and the y-axis, we can use polar coordinates.
In polar coordinates, the region D can be described as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫D e^(-x²-y²) dA = ∫₀^(π/2) ∫₀² e^(-r²) r dr dθ
= ∫₀^(π/2) [-1/2 e^(-r²)]₀² dθ
= ∫₀^(π/2) (1/2 - 1/2e^4) dθ
= π/4 - (1/2)(1 - e^4)
Therefore, the value of the integral is π/4 - (1/2)(1 - e^4).
12. To evaluate the integral ∫∫D cos(√(x²+y²)) dA, where D is the disk with center at the origin and radius 2, we can again use polar coordinates.
In polar coordinates, the region D can be described as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫D cos(√(x²+y²)) dA = ∫₀^(2π) ∫₀² r cos(r) dr dθ
= ∫₀^(2π) [2 sin(r) - 2r cos(r)]₀² dθ
= ∫₀^(2π) (-4) dθ
= -8π
Therefore, the value of the integral is -8π.
13. To evaluate the integral ∫∫R arctan(y/x) dA, where R = {(x,y) | 1 ≤ x² + y² ≤ 4, 0 ≤ y ≤ x}, we can use polar coordinates.
In polar coordinates, the region R can be described as π/4 ≤ θ ≤ π/2 and 1/√2 ≤ r ≤ 2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R arctan(y/x) dA = ∫π/4^(π/2) ∫1/√2² r arctan(tan(θ)) dr dθ
= ∫π/4^(π/2) [(r²θ/2 - r²tan(θ)/4)]1/√2² dθ
= ∫π/4^(π/2) [(2θ - π/2)/8] dθ
= [θ²/16 - (θ - π/4)/8]π/4^(π/2
= [π/16 - (π/4 - π/4√2)/8] - [(π/16 - (π/8 - π/8√2)/8)]
= π/64 + π/(32√2)
Therefore, the value of the integral is π/64 + π/(32√2).
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The question in text format:
8. ∫∫R(2x-y) dA, where R is the region in the first quadrant enclosed by the circle x² + y² = 4 and the lines x= 0 and y=x
9. ∫∫Rsin(x² + y²) dA, where R is the region in the first quadrant between the circles with center the origin and radii 1 and 3
Answer
10. ∫∫R y²/x² + y²dA, where R is the region that lies between the circles x² + y² = a² and x² + y² = b² with 0 < a < b
11. ∫∫D e⁻ˣ²⁻ʸ²dA, where D is the region bounded by the semi-circle x = √4 - y² and the y-axis
12. ∫∫D cos √x² + y² da, where D is the disk with center the origin and radius 2
13. ∫∫R arctan (y/x) dA, where R= {(x,y) | 1 ≤ x² + y² ≤ 4,0 ≤ y ≤ x}
Decide whether ▱ABCD with vertices A(−6, 2), B(−3, 5), C(0, 2), and D(−3 ,−1) is a rectangle, a rhombus, or a square. Select all names that apply.
ABCD is a square, rhombus, and rectangle.
Checking whether ABCD with vertices A(6, 2), B(3, 5), C(0, 2), and D(3, 1) fits the definition of each shape can help us determine whether it is a rectangle, rhombus, or square.
A parallelogram with four right angles is a rectangle. We can determine the slopes of AB and CD and BC and AD separately to see if ABCD is a rectangle. It is a rectangle if the opposite sides are perpendicular and they are negative reciprocals of one another.
[tex]Slope \ of \ AB = \frac{(5 - 2)} { (-3 + 6)} = 1 \ Slope\ of\ CD = \frac{(-1 - 2)} { (-3 - 0)} = -1 \ Slope \ of\ BC =\frac{ (2 - 5)}{ (0 + 3)} = -1 \ Slope\ of\ AD = \frac{(2 - (-1))}{ (-6 + 3)} = 1[/tex]
The opposite sides are perpendicular to one another since AB and CD have negative reciprocal slopes and BC and AD do too. In light of this, ABCD is a rectangle.
A parallelogram with four congruent sides is called a rhombus. We can determine the separation between each pair of vertices in ABCD to determine if it is a rhombus. It is a rhombus if the lengths of the four sides are equal.
[tex]Distance\ between\ A \ and\ B = \sqrt{{(5 - 2)}^2 + {(-3 + 6)}^2} = \sqrt(10) \ Distance\ between\ B \ and\ C = \sqrt{({(2 - 5)}^2 + {(0 + 3)}^2)} = \sqrt(10) \ Distance\ between\ C\ and\ D = \sqrt{((-1 - 2)^2 + (-3 - 0)^2) }= \sqrt(10) \ Distance \ between\ D \ and \ A = \sqrt{((2 - (-1))^2 + (-6 + 3)^2)} = \sqrt(10)[/tex]
ABCD is also a rhombus since the lengths of all four sides are equal.
A parallelogram having four identical sides and four right angles is called a square. We can combine the tests for rectangles and rhombuses to determine whether ABCD is a square.
Since ABCD satisfies the requirements for both rectangles and rhombuses, it is also required to be a square.
Hence, ABCD is a square, rhombus, and rectangle.
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Mr. White deposits $550 into a bank account earning an annual simple interest rate of 5%. How long will it take Mr. White to earn $165 in interest?
It will take Mr. White at least 3 years to earn $165 in interest at an annual simple interest rate of 5% on his $550 deposit.
To solve the given problem, we can use the formula for simple interest:
I = P × r × t
P = $550 is the initial deposit
r = 0.05 is the annual interest rate
I = $165 is the amount of interest earned
We can rearrange the formula to solve for t:
t = I ÷ (P × r)
Substituting in the values we know,
t = $165 × ($550 × 0.05)
t = 3 years
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What is 100x2x7x50x40x20x50
need help ASAP
Answer:
Step-by-step explanation:
2,800,000,000
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(-8, - 7); y = -8x - 9
Answer:9
Step-by-step explanation:
0
Find the perimeter of a rectangle whose length is 29 centimeters and whose width is 12 centimeters less than its length. Question content area bottom Part 1 The perimeter of the rectangle is enter your response here ▼ (Simplify your answer.)
Answer:92 centimetres
Step-by-step explanation:
Prove the following: a finite group with an even number of elements contains an even number of elements [tex]x[/tex] such that [tex]x^{-1}=x[/tex]. State and prove a similar statement for a finite group with an odd number of elements?
a finite group with an even number of elements contains an even number of elements such that. x inverse = x.
a similar statement for a finite group with an odd number of elements
For a finite group with an even number of elements, we can prove that it contains an even number of elements such that their order is 2.
Let G be a finite group of even order.
We can define t(G) as the set { g ∈ G | g ≠ g − 1 }.
if g ∈ t(G), then g − 1 ∈ t(G), and by definition g − 1 ≠ g.
Now let A = { { g, g − 1 } | g ∈ t (G) }.
Thus we have | t (G) | = ∑ α ∈ A | α | = 2 k for some positive integer k;
in particular, t (G) contains an even number of elements 1.
Hence [tex]x^{-1}=x[/tex]
For a finite group with an odd number of elements, we can prove that it contains an odd number of elements such that their order is 2. For any element in G-{e}, there must be an inverse of that element in G-{e}. Take any element in G-{e}, say b, If bb=e, then the proof is done. If the inverse of b is not itself, then there must be one element in G-{e}, say c, such that bc=e. Because there are an odd number of elements, I keep doing this until I have left with one
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please helppppppppppppppppppp
Answer:
Step-by-step explanation:
You can solve this 2 ways:
1) just count the number of units from one point to the other
2) calculate it using the coordinates of the points and the distance between 2 points formula: d = √(x2-x1)²+(y2-y1)²
A(-7, 6) B(7, 6) C(7, -5) D(-7, -5)
AB = √(7--7)²+(6-6)² = √14² = 14
BC = √(7-7)²+(-5-6)² = √-11² = 11
CD = √(-7-7)²+(-5--5)² = √-14² = 14
AD = √(-7--7)²+(-5-6)² = √-11² = 11
A to City B. In 5 days, they have traveled 2,075 miles. At this rate, how long will it take them to travel from City A to City B?
In the question, we can draw the conclusion that, according to the formula, it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of [tex]415 miles[/tex]per day.
What is formula?A formula is a set of mathematical signs and figures that demonstrate how to solve a problem.
Formulas for calculating the volume of [tex]3D[/tex] objects and formulas for measuring the perimeter and area of [tex]2D[/tex] shapes are two examples.
A formula is a fact or a rule in mathematical symbols. In most cases, an equal sign connects two or more values. If you know the value of one, you can use a formula to calculate the value of another quantity.
We need to know the average pace at which they went to figure how long it would take to get from City A to City B at the same rate.
total distance / time taken = average speed
[tex]415 miles[/tex] per day [tex]2075/ 5[/tex], it would take them [tex]10[/tex] days to get from City A to City B because
Time taken = [tex]2075/415[/tex] per days [tex]= 5 days[/tex]
Therefore it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of [tex]415 miles[/tex]per day.
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Given 4&7 = 21, 6&22=20, 8&30 = 26. Find 9&20
(3 1/2 hours) how many minutes?
Answer:
210 minutes
Step-by-step explanation:
We know that 1 hour = 60 minutes.
3 hours = 3 * 60 = 180 minutes
1/2 hour = 1/2 * 60 minutes = 30 minutes
3 1/2 hours = 180+30 = 210 minutes
Answer:
210 minutes
Step-by-step explanation:
To convert from hours to minutes, we can multiply by a conversion ratio:
[tex]\left(3 \dfrac{1}{2} \text{ hr}\right)\left(\dfrac{60 \text{ min}}{1 \text{ hr}}\right)[/tex]
↓ converting the mixed number to a fraction
[tex]\left(\dfrac{7}{2} \text{ hr}\right)\left(\dfrac{60 \text{ min}}{1 \text{ hr}}\right)[/tex]
↓ canceling the hours unit
[tex]\dfrac{7}{2} \cdot 60 \text{ min}[/tex]
↓ multiplying
[tex]\boxed{210\text{ min}}[/tex]
__
Note: When we multiply something by a conversion ratio, we are not changing the value of it, but rather changing its form. In other words, a conversion ratios has a value of 1, and anything multiplied by 1 is itself. To illustrate this:
[tex]\dfrac{60 \text{ min}}{1 \text{ hr}} = \dfrac{60 \text{ min}}{60\text{ min}} = \dfrac{1}{1} = 1[/tex]
because
[tex]1 \text{ hr} = 60 \text{ min}[/tex].
The following table reports the percentage of stocks in a portfolio for nine quarters from
2007 to 2009.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use trial and error to find a value of the exponential smoothing coefficient that results in a relatively small MSE.
c. Using the exponential smoothing model you developed in part (b), what is the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009?
1) The time series plot is attached accordingly. The percentage of stocks seems to fluctuate randomly over time.
2) the optimal value of the smoothing coefficient is 0.5.
3) Therefore, the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009 is 30.9%.
What is the explanation for the above response?1) See the attached time series. The percentage of stocks seems to fluctuate randomly over time.
2) To find the optimal value of the smoothing coefficient that results in a relatively small mean squared error (MSE), we can use a trial-and-error approach. We can try different values of the smoothing coefficient α and calculate the MSE for each value. The smoothing coefficient that results in the smallest MSE is the optimal value.
Using other software, we can apply exponential smoothing to the data and try different values of α. For example, we can start with α=0.1 and increment it by 0.1 until we find the optimal value.
The following table shows the results of applying exponential smoothing with different values of α: See attached.
From the table, we can see that the smallest MSE is obtained when α=0.5. Therefore, the optimal value of the smoothing coefficient is 0.5.
c. Using the optimal value of the smoothing coefficient α=0.5, we can forecast the percentage of stocks in a typical portfolio for the second quarter of 2009. To do this, we use the following formula for exponential smoothing:
F(t+1) = α x Y(t) + (1-α) x F(t)
where F(t+1) is the forecast for the next period, Y(t) is the actual value in the current period, and F(t) is the forecast for the current period.
To apply this formula, we start with the first quarter of 2007 as the initial forecast value:
F(1) = Y(1) = 29.8
Then, we can use the formula to calculate the forecast for each subsequent quarter:
F(2) = α x Y(2) + (1-α) x F(1) = 0.5 x 31.0 + 0.5 x 29.8 = 30.4
F(3) = α x Y(3) + (1-α) x F(2) = 0.5 x 29.9 + 0.5 x 30.4 = 30.2
F(4) = α x Y(4) + (1-α) x F(3) = 0.5 x 30.1 + 0.5 x 30.2 = 30.2
F(5) = α x Y(5) + (1-α) x F(4) = 0.5 x 32.2 + 0.5 x 31.2 = 31.7
F(7) = α x Y(7) + (1-α) x F(6) = 0.5 x 32.0 + 0.5 x 31.7 = 31.9
F(8) = α x Y(8) + (1-α) x F(7) = 0.5 x 31.9 + 0.5 x 31.9 = 31.9
F(9) = α x Y(9) + (1-α) x F(8) = 0.5 x 30.0 + 0.5 x 31.9 = 30.9
Therefore, the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009 is 30.9%.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
The following table (See attached image) reports the percentage of stocks in a portfolio for nine quarters from
2007 to 2009.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use trial and error to find a value of the exponential smoothing coefficient that results in a relatively small MSE.
c. Using the exponential smoothing model you developed in part (b), what is the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009?
A coach randomly chose 20 football
players. Of the 20 players, 18 of
them also run track. Based on this
information, how many football
players do not run track if there are
110 players on the team?
Answer: 11
Step-by-step explanation: Based on the given conditions, formulate::
Calculate the sum or difference:
Simplify fraction(s): 11
(c) Some of the students were asked how much time they spent revising for the test. 10 students revised for 2.5 hours, 12 students revised for 3 hours and students revised for 4 hours. The mean time that these students spent revising was 3.1 hours. Find n. Show all your working.
Answer:
N=8
Step-by-step explanation:
61 + 4n = 3.1n + 68.2
.9n = 7.2
n = 8
3. How many units are between the diamond
and the circle?
The distance between the diamond and the circle is approximately 5.83 units.
What is the distance between two points?
[tex]d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
Where [tex](x_1,y_1) and (x_2,y_2)[/tex] are two co-ordinates.
Here we want to find the distance between the diamond and the circle.
We need to use the distance formula.
Here position of diamond is (2,3) and circle is (5,8)
Substituting the values into the formula, we get:
[tex]d = √((5 - 2)^2 + (8 - 3)^2) \\ = √(3^2 + 5^2) \\ = √34 \\ ≈ 5.83 units[/tex]
Therefore, the distance between the diamond and the circle is approximately 5.83 units.
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Correct question is "Position of a diamond in the point (2,3) and a circle in (5,8). How many units are between the diamond and the circle?"
The distance between the diamond and the circle is approximately 5.83 units.
What is the distance between two points?Here we want to find the distance between the diamond and the circle.
Here position of diamond is (2,3) and circle is (5,8)
Substituting the values into the formula, we get:
d²= ([tex]x_{2} -x[/tex]₁)²+(y₂-y₁)²
Therefore, the distance between the diamond and the circle is approximately 5.83 units.
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PLEASE HELPPP
Simplify (x^4y^8)^1/2
[tex]x^{2} y^{4}[/tex]
Two parallel paths 25 m apart run east–west through the woods. Brooke walks east on one path at 6 km/h, while Jamail walks west on the other path at 5 km/h. If they pass each other at time =0, how far apart are they 4 s later, and how fast is the distance between them changing at that moment? (Use decimal notation. Give your answer to three decimal places.)
The answer of the given question based on distance is at the moment 4 seconds later, the distance between them is 12.776 m and the distance between them changing at that moment is 3.056 m/s.
What is Speed?Speed is measure of how fast object is moving. It is defined as distance traveled by an object divided by time it takes to travel that distance. The standard unit of speed is meters per second (m/s) in International System of Units (SI). Speed can also be measured in other units such as kilometers per hour (km/h), miles per hour (mph), or feet per second (ft/s), depending on the context of the problem.
Since Brooke and Jamail are walking towards each other on parallel paths, the distance between them is decreasing at a rate of (6 + 5) km/h = 11 km/h.
To solve for how far apart they are after 4 seconds, we first need to convert their speeds to m/s and their distance to meters:
Brooke's speed = 6 km/h = (6/3.6) m/s = 1.667 m/s
Jamail's speed = 5 km/h = (5/3.6) m/s = 1.389 m/s
Distance between the paths = 25 m
The initial distance between Brooke and Jamail is 25 m, and it is decreasing at a rate of 11 km/h = (11/3.6) m/s = 3.056 m/s.
After 4 seconds, the distance between them will be:
d = 25 m - (3.056 m/s x 4 s) = 12.776 m
To find the rate at which the distance between them is changing, we can take the derivative of the distance equation with respect to time:
d' = -11 km/h = -(11/3.6) m/s = -3.056 m/s
Therefore, at the moment 4 seconds later, the distance between them is 12.776 m and is decreasing at a rate of 3.056 m/s.
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Question 1 of 3
The sum of the interior angles of a regular polygon is 3060°.
Complete the statement.
How Many has the regular polygon?
Answer:
the regular polygon has 15 angles
What is the value of {-4,6]?
The value of {-4,6} is -4.
The braces {} create a set.
The elements in a set are written inside the braces.
When a set contains only two elements, it is considered a set with two elements or a pair of elements.
In this case, the braces {-4,6} contain two elements: -4 and 6.
Thus, the value of this set is the union of these two elements, which in this case is the sum of the two elements: -4 + 6 = 2