Answer:
A) A[p(t)] = 36πt²
B) 7234.56 square units
Step-by-step explanation:
<u>Given functions</u>:
<u>Part A</u>
To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):
![\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%28p%29%20%26%20%3D%20%5Cpi%20p%5E2%5C%5C%5C%5C%20%5Cimplies%20A%5Bp%28t%29%5D%20%26%20%3D%20%5Cpi%20%5Bp%28t%29%5D%5E2%5C%5C%26%20%3D%20%5Cpi%20%286t%29%5E2%5C%5C%26%20%3D%20%5Cpi%206%5E2%20t%5E2%5C%5C%26%20%3D%2036%5Cpi%20t%5E2%5Cend%7Baligned%7D)
<u>Part B</u>
Given
Substitute the given values into the equation for A[p(t)} found in part A:
![\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%5Bp%288%29%5D%20%26%20%3D%2036%5Cpi%20t%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%208%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%2064%5C%5C%26%20%3D%20113.04%20%5Ccdot%2064%5C%5C%26%20%3D%207234.56%5C%3A%5C%3A%20%5Csf%20square%5C%3Aunits%5Cend%7Baligned%7D)
Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.
Answer:
A. $58.50
B. $80
C. No. The markup was 33 1/3%
Step-by-step explanation:
You are expected to know the relevant relationship is ...
cost + markup = selling price . . . . also called "store price" in this problem
___
A. The markup is 30% × $45 = $13.50, so the store price is ...
$45 + 13.50 = $58.50
___
B. When the 30% markup is added to the 100% cost, the selling price is 130% of the cost, or 1.30 times the cost. Here you have ...
$104 = 1.30 × cost
$104/1.3 = cost = $80 . . . . . divide by the coefficient of cost
___
C. The markup is $100 -75 = $25, so the markup percentage based on cost is ...
$25/$75 × 100% = 33 1/3%
This is not 30%.
Step-by-step explanation:
Which box plot represents the data? 43, 48, 52, 61, 74, 81, 40, 42, 56, 77, 81, 43?
frutty [35]
The box plot for the set of data
<span>43, 48, 52, 61, 74, 81, 40, 42, 56, 77, 81, 43
</span>will be found by rewriting the data in ascending data, then plotting it. This will give us the box plot in the attached figure.
Set up a proportion to describe this relationship. So, for every 2 cats, there is five dogs. Therefore, “c” can represent your unknown quantity for every 35 animals.
2/5 = c/35
Cross multiply, multiplying the numerator/top number of the first fraction/ratio, by the denominator/bottom number in the second fraction/ratio.
2 • 35 = 70
Then, Cross multiply, multiplying the numerator/top number of the second fraction/ratio, by the denominator/bottom number in the first fraction/ratio.
C • 5 = 5c
So, now the problem shows both products as equal to each other.
70 = 5c
To solve for the variable, “c”, you must isolate the variable, by performing the opposite/inverse operation of multiplication, since that will undo the multiplication, for the variable to stand alone. Therefore, divide both sides of the equation by 5.
70/5 = 5c/5
14 = c
So, there is 14 cats out of 35 animals.
