Answer:
Step-by-step explanation:
From the initial condition,
So we have that 
At the bottom of the motion: The potential energy of the spring is at a maximum since the spring is stretched at its maximum extension. The potential energy due to gravity is at a minimum, since the mass is lifted the least amount above ground.
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.
Step-by-step explanation:
288÷60(60 minutes in an hour) = 4.8
is this what you asked for?
Answer:
P = 300
r = 0.15
n = 12
A(t) = 300(1.0125)^12t
Step-by-step explanation:
Given that:
Total credit taken for book purchase = $300
Annual Interest rate = 15% compounded monthly
Time or period = 4 years
P(1 + r/n)^nt
P in the expression above means the principal amount which is the total credit spent on book purchase = $300
r = annual interest rate on Emma's account = 15% = 15/100 = 0.15
n = number of compounding times per period ; loan which compounds monthly = number of months in a year = 12
Hence,
P = $300 ; r = 0.15 ; n = 12
Substituting into the equation :
P(1 + r/n)^nt
Simplified expression written in terms of t:
Final amount, A after t years
A(t) = 300(1 + 0.15/12)^12t
A(t) = 300(1 + 0.0125)^12t
A(t) = 300(1.0125)^12t
