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.
Okay, so all the angles of the triangle will add up to 180
You know one side is 104 and the other two are equal to each other.
180-104= 76
76 is both of the angles together so divide it by two to get 38
X=38
:)
It will be 52 as you know when looking at a triangle with 3 angles they must all add up to 180 so you simply do 56+72 then subtract 180 from it and you get 52.
Answer:
6 over 1/24
Step-by-step explanation:
You can find the quotient of 9 2/3 divided by 1 3/5 by first making the two terms into improper fractions.
To make the improper fractions, you can turn 9 2/3 into 29/3 by multiiplying 9 by the denominator (bottom number in fractions) and adding that to the numerator of 2 which gives 29.
1 3/5 can turn into 8/5.
Then you can divide using a simple trick of first organizing the data.
Currentlly it should be
29/3 divided by 8/5
Then you can flip the second fraction over.
29/3 divided by 5/8
Then you change the sign into multiplication.
29/3 times 5/8
Then you multiply like normal.
29 times 5 over 3 times 8
145 over 24
You can simplify now
6 over 1/24
Hope this helps!
You would start by 6÷3. This would tell you that for every proud of hamburger you pay $2.
Therefore multiply 10×2 and that equals 20.
Therefore, your answer is $20.
