Answer:
57 mph
Step-by-step explanation:
Let b represent Bob's speed on the trip. Then his time is ...
time = distance/speed
Bob's time = 230/b
Then John's speed is b+8, and his time is ...
John's time = 230/(b+8)
The difference of their times is 1/2 hour:
Bob's time - John's time = 1/2
230/b -230/(b+8) = 1/2 . . . substitute the expressions for time
460(b+8 -b) = b(b+8) . . . . . multiply by 2b(b+8)
b^2 +8b -3680 = 0 . . . . . . .put in standard form
(b +4)^2 -3696 = 0 . . . . . . . add 16-16 to complete the square
b = -4 +√3696 ≈ 56.795 . . . solve for positive b
Bob's drove about 57 mph on the trip.
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)
Answer:
n + 10
Step-by-step explanation:
The product of 7 and 50 is = 350
Improper Fraction
12/7 = 1 5/7