Answer:
yes because a is the answer
Step-by-step explanation:
Plant's height after 31 months:82 centimeters
<h3>How to find the height of the plant</h3>
The equation that can be used to find the height of the plant is given as
h = 52 centimeters + 1m
We have that the plant grows at 1 centimeter every month hence we have 1m in the equation.
Then the number of periods is m, Now we are to find the height in this period of time
h = 52 + 1*31
= 51 + 31
= 82
Hence the height after 31 months is given as 82 centimeters.
Read more on height here:
brainly.com/question/73194
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Answer: 27,81
Step-by-step explanation:
First you do 3*3=9
9*3=27
27*3=81
So the sequence will be 3,9,27,81
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Answer:
5571.99
Step-by-step explanation:
We need to use the Pythagorean theorem to solve the problem.
The theorem indicates that,
![r^2+h^2=24^2 \\r^2+h^2=576\\r^2=576-h^2](https://tex.z-dn.net/?f=r%5E2%2Bh%5E2%3D24%5E2%20%5C%5Cr%5E2%2Bh%5E2%3D576%5C%5Cr%5E2%3D576-h%5E2)
Once this is defined, we proceed to define the volume of a cone,
![v=\frac{1}{3}\pi r^2 h](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h)
Substituting,
![v=\frac{1}{3} \pi (576-h^2)h\\v=\frac{1}{3} \pi (576h-h^3)](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%28576-h%5E2%29h%5C%5Cv%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%28576h-h%5E3%29)
We need to find the maximum height, so we proceed to calculate h, by means of its derivative and equalizing 0,
![\frac{dv}{dh} = \frac{1}{3} \pi (576-3h^2)](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdh%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%28576-3h%5E2%29)
then ![\rightarrow \frac{1}{3}\pi(576-3h^2)=0](https://tex.z-dn.net/?f=%5Crightarrow%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%28576-3h%5E2%29%3D0)
![h_1=-8\sqrt{3}\\h_2=8\sqrt{3}](https://tex.z-dn.net/?f=h_1%3D-8%5Csqrt%7B3%7D%5C%5Ch_2%3D8%5Csqrt%7B3%7D)
<em>We select the positiv value.</em>
We have then,
![r^2 = 576-(8\sqrt3)^2 = 384\\r=\sqrt{384}](https://tex.z-dn.net/?f=r%5E2%20%3D%20576-%288%5Csqrt3%29%5E2%20%3D%20384%5C%5Cr%3D%5Csqrt%7B384%7D)
We can now calculate the maximum volume,
![V_{max}= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (\sqrt{384})^2 (8\sqrt{3}) = 5571.99](https://tex.z-dn.net/?f=V_%7Bmax%7D%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28%5Csqrt%7B384%7D%29%5E2%20%288%5Csqrt%7B3%7D%29%20%3D%205571.99)