Answer:
This is the rate at which the radius of the balloon is changing when the volume is 300

Step-by-step explanation:
Let
be the radius and
the volume.
We know that the gas is escaping from a spherical balloon at the rate of
because the volume is decreasing, and we want to find 
The two variables are related by the equation

taking the derivative of the equation, we get

With the help of the formula for the volume of a sphere and the information given, we find
![V=\frac{4}{3}\pi r^3\\\\300=\frac{4}{3}\pi r^3\\\\r^3=\frac{225}{\pi }\\\\r=\sqrt[3]{\frac{225}{\pi }}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C%5C%5C300%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C%5C%5Cr%5E3%3D%5Cfrac%7B225%7D%7B%5Cpi%20%7D%5C%5C%5C%5Cr%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B225%7D%7B%5Cpi%20%7D%7D)
Substitute the values we know and solve for 
![\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=-\frac{12}{4\pi (\sqrt[3]{\frac{225}{\pi }})^2} \\\\\frac{dr}{dt}=-\frac{3}{\pi \left(\sqrt[3]{\frac{225}{\pi }}\right)^2}\\\\\frac{dr}{dt}=-\frac{3}{\pi \frac{225^{\frac{2}{3}}}{\pi ^{\frac{2}{3}}}}\\\\\frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \approx -0.05537 \:\frac{ft}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D4%5Cpi%20r%5E2%20%5Cfrac%7Bdr%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D%5Cfrac%7B%5Cfrac%7BdV%7D%7Bdt%7D%7D%7B4%5Cpi%20r%5E2%7D%20%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D-%5Cfrac%7B12%7D%7B4%5Cpi%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7B225%7D%7B%5Cpi%20%7D%7D%29%5E2%7D%20%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B%5Cpi%20%5Cleft%28%5Csqrt%5B3%5D%7B%5Cfrac%7B225%7D%7B%5Cpi%20%7D%7D%5Cright%29%5E2%7D%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B%5Cpi%20%5Cfrac%7B225%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7B%5Cpi%20%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7D%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B225%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Cpi%20%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%20%5Capprox%20-0.05537%20%5C%3A%5Cfrac%7Bft%7D%7Bh%7D)
You have to be very careful how you set this up. For every girl (who counts as 1) there are 3 boys (who count as 3). The total number in the proportion is 3 + 1 =4. You are given a total, but that is both boys and girls. That's why you need the 4.
3/4 = x / 236 Cross multiply
4x = 3 * 236
4x = 708 Divide by 4
x = 708/4
x = 177
There are 177 boys at the school and 236 - 177 = 59 girls.
Answer:
2(x + 3) <9
Step-by-step explanation:
<u>Two times</u> the <em>quantity of a number increased by 3</em> is <u>less than 9</u>
2 · (x + 3 ) < 9
= 2(x + 3) <9