Answer:
Factor using the perfect square rule.
(
5
x + 2
)
^2
Step-by-step explanation:
I hope this helps! Have a nice day!
Answer:
![volume = 1536 m^3](https://tex.z-dn.net/?f=volume%20%3D%201536%20m%5E3)
Step-by-step explanation:
given data;
B = 16m
b =8 m
height H = 4 m
length L = 32 m
volume of any right cylinder = (Area of bottom) \times (length)
Volume = A* L
The area of a trapezoid is
![A=\frac{1}{2} H*(b+B)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20H%2A%28b%2BB%29)
![A =\frac{1}{2} 4*(8+16)](https://tex.z-dn.net/?f=A%20%3D%5Cfrac%7B1%7D%7B2%7D%204%2A%288%2B16%29)
![A = 48 m^2](https://tex.z-dn.net/?f=A%20%3D%2048%20m%5E2)
therefore volume is given as
volume = 48*32
![volume = 1536 m^3](https://tex.z-dn.net/?f=volume%20%3D%201536%20m%5E3)
Answer:
80
Step-by-step explanation:
First of all, before you do anything to compute the answer, you can see that there is (–13/100) on both sides of the equation. You can cancel them out, since they're the same thing.
Now, you're left with:
![0.8 = \frac{}{100}](https://tex.z-dn.net/?f=0.8%20%3D%20%5Cfrac%7B%7D%7B100%7D)
This is also read as 0.8 is the same thing as [how many] hundredths.
You should know that 0.8 = eight tenths.
So if you move the decimal point right once, you'll get:
0.80
Which is also eighty hundredths.
Your answer would be:
![0.8 = \frac{80}{100}](https://tex.z-dn.net/?f=0.8%20%3D%20%5Cfrac%7B80%7D%7B100%7D)
which is 80.
To check your answer, you can also do:
80/100
Because the fraction bar can also be read as "divided by."
You will get 0.8.
If you would like to solve the equation x/3 = x/2 - 2 for x, you can do this using the following steps:
<span>x/3 = x/2 - 2 /*6
</span>2x = 3x - 2 * 6
2x = 3x - 12
2x - 3x = -12
-x = -12
x = 12
The correct result would be x = 12.
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.