The volume of the balloon is ![2352\pi cc/min](https://tex.z-dn.net/?f=2352%5Cpi%20cc%2Fmin)
Explanation:
The radius of the balloon is increasing at a rate of 3 cm/min.
To determine the volume of the balloon when the radius is 14 cm, we shall use the formula ![V=\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
The rate of change of r with respect to time t is given by,
![\frac{d}{d t}(r)=3 \mathrm{cm} / \mathrm{minute}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bd%20t%7D%28r%29%3D3%20%5Cmathrm%7Bcm%7D%20%2F%20%5Cmathrm%7Bminute%7D)
Now, we shall determine the
![\begin{aligned}\frac{d}{d t}(V) &=\frac{d}{d t}\left(\frac{4}{3} \pi r^{3}\right) \\&=\frac{4}{3} \pi\left(3 r^{2}\right)\frac{d}{d t}(r) \\&=4 \pi r^{2}\frac{d}{d t}(r)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cfrac%7Bd%7D%7Bd%20t%7D%28V%29%20%26%3D%5Cfrac%7Bd%7D%7Bd%20t%7D%5Cleft%28%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D%5Cright%29%20%5C%5C%26%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%5Cleft%283%20r%5E%7B2%7D%5Cright%29%5Cfrac%7Bd%7D%7Bd%20t%7D%28r%29%20%5C%5C%26%3D4%20%5Cpi%20r%5E%7B2%7D%5Cfrac%7Bd%7D%7Bd%20t%7D%28r%29%5Cend%7Baligned%7D)
Now, we shall determine the
at
and substituting
, we get,
![\begin{aligned}\left(\frac{d V}{d t}\right)_{r=14} &=4 \pi r^{2} \frac{d}{d t}(r)\\&=4 \pi(14)^{2} (3)\\&=4 \pi 196 (3)\\&=2352\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cleft%28%5Cfrac%7Bd%20V%7D%7Bd%20t%7D%5Cright%29_%7Br%3D14%7D%20%26%3D4%20%5Cpi%20r%5E%7B2%7D%20%5Cfrac%7Bd%7D%7Bd%20t%7D%28r%29%5C%5C%26%3D4%20%5Cpi%2814%29%5E%7B2%7D%20%283%29%5C%5C%26%3D4%20%5Cpi%20196%20%283%29%5C%5C%26%3D2352%5Cend%7Baligned%7D)
Thus, The volume of the balloon is ![2352\pi cc/min](https://tex.z-dn.net/?f=2352%5Cpi%20cc%2Fmin)
Answer:
6 cups of water
Step-by-step explanation:
A recipe calls for 3 cups of sugar and 9 cups of water. How many should be used with 2 cups of sugar?
The question above, is solved below:
3 cups of sugar = 9 cups of water
2 cups of sugar = x
Cross Multiply
3x = 9 × 2
x = 18/3
x = 6
Hence, 2 cups of sugar = 6 cups of water
Answer:
3 ounces
Step-by-step explanation:
$8.75 you just divide 5 by four and you get 1.25 and add up however much you need.
Hope this helps. :)
Answer:
you want a specific place as an answer? or the mileage?