Answer:
Cubed root of 9
Step-by-step explanation:
3^(2/3)
=³√3²
= ³√9
Answer:
A = 1, B = 0, C = 7
Step-by-step explanation:
The egg follows the path x = 7, so the equation is ...
1x +0y = 7
A = 1, B = 0, C = 7
![sin= \frac{opp}{hyp} \\\\sin (20) = \frac{10000}{hyp}\\\\hyp= \frac{10000}{sin(20)} \\\\hyp= 29238 ft](https://tex.z-dn.net/?f=sin%3D%20%5Cfrac%7Bopp%7D%7Bhyp%7D%20%5C%5C%5C%5Csin%20%2820%29%20%3D%20%5Cfrac%7B10000%7D%7Bhyp%7D%5C%5C%5C%5Chyp%3D%20%5Cfrac%7B10000%7D%7Bsin%2820%29%7D%20%5C%5C%5C%5Chyp%3D%2029238%20ft)
The aircraft is 29238 ft from the ship
//
Note: this is based on my assumption that we are looking for the hypotenuse.
If we are looking for the adjacent side, then the answer would be 27475 ft.
Answer:
A) A[p(t)] = 36πt²
B) 7234.56 square units
Step-by-step explanation:
<u>Given functions</u>:
![\begin{cases}p(t)=6t \\ A(p)=\pi p^2 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dp%28t%29%3D6t%20%5C%5C%20A%28p%29%3D%5Cpi%20p%5E2%20%5Cend%7Bcases%7D)
<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.