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.
Measurements of weight can be converted quite easily! However, you may need some extra information if you are converting from things like pounds to kilograms.
For conversions like pounds to kilograms, you will need a conversion factor. Most of the time, a quick Google search will find you this factor. For example with pounds and kilograms, 2.205 pounds is equal to 1 kilogram. To find the number of kilograms in a pound, you would divide the number of pounds by 2.205. To find the number of pounds in a kilogram, you would multiply the number of kilograms by 2.205.
For other conversions, like kilograms to grams, you would need to remember your prefixes. For example, kilo means 1000. Grams is the single unit, so that means 1000 grams is equal to 1 kilogram. To find the number of grams in a kilogram, you would multiply the number of kilograms by 1000. To find the number of kilograms in a number of grams, you would divide the number of grams by 1000.
Hope this helps!! :)
Answer:
5.4'
Step-by-step explanation:
See diagram attached.
The 8' wire is the hypotenuse of the triangle, with a base angle of 42°.
Hence the height is the length of the hypotenuse multiplied by sin(42°)
H = 8sin(42°) = 8 *0.6691 = 5.353'
Answer:
6x + 1
Step-by-step explanation:
Distribute
3 + 2 ( x- 1 ) + 4x
3 + 2x - 2 + 4x
Subtract
3 + 2x - 2 + 4x
1 + 2x + 4x
Like terms
1 + 2x + 4x
1 + 6x
Rearrange
6x + 1
Assuming your "x" is a multiplication symbol, you can divide the equation by 6 to get
10 + s = 17
Subtract 10 from both sides of the equation to find the value of s.
s = 7
