(30, 5)
(10, 1)
change of y / change of x
= (30 - 10) / (5 - 1)
= 20 /4
= 5
Answer:
Therefore the surface area of the balloon is increased at 4 cm³/s.
Explanation:
The balloon is being filled with air at a rate of 10 cm³/s
It means the volume of the balloon is increased at a rate 10 cm³/s.
i.e ![\frac{dv}{dt} =10 cm^3/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D10%20cm%5E3%2Fs)
Consider r be the radius of the balloon.
The volume of of a sphere is
![v=\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
Differentiate with respect to t
![\frac{dv}{dt} =\frac{4}{3} \pi \times 3r^2\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%5Ctimes%203r%5E2%5Cfrac%7Bdr%7D%7Bdt%7D)
![\Rightarrow 10 =4\pi r^2\frac{dr}{dt}](https://tex.z-dn.net/?f=%5CRightarrow%2010%20%3D4%5Cpi%20r%5E2%5Cfrac%7Bdr%7D%7Bdt%7D)
![\Rightarrow \frac{dr}{dt}=\frac{10}{4\pi r^2}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdr%7D%7Bdt%7D%3D%5Cfrac%7B10%7D%7B4%5Cpi%20r%5E2%7D)
The surface of area of the balloon is(S) = ![4\pi r^2](https://tex.z-dn.net/?f=4%5Cpi%20r%5E2)
![S=4\pi r^2](https://tex.z-dn.net/?f=S%3D4%5Cpi%20r%5E2)
Differentiate with respect to t
![\frac{dS}{dt} =4\pi\times2r\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdS%7D%7Bdt%7D%20%3D4%5Cpi%5Ctimes2r%5Cfrac%7Bdr%7D%7Bdt%7D)
![\Rightarrow \frac{dS}{dt} =8\pi r\frac{dr}{dt}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7BdS%7D%7Bdt%7D%20%3D8%5Cpi%20r%5Cfrac%7Bdr%7D%7Bdt%7D)
Putting the value of
![\Rightarrow \frac{dS}{dt} =8\pi r\times\frac{10}{4\pi r^2}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7BdS%7D%7Bdt%7D%20%3D8%5Cpi%20r%5Ctimes%5Cfrac%7B10%7D%7B4%5Cpi%20r%5E2%7D)
![\Rightarrow \frac{dS}{dt} =\frac{20}{ r}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7BdS%7D%7Bdt%7D%20%3D%5Cfrac%7B20%7D%7B%20r%7D)
Given that r = 5 cm
=4 cm³/s
Therefore the surface area of the balloon is increased at 4 cm³/s.
Answer:
Time required by boat 1 for the round trip is less than that of boat 2.
Hence, boat 1 wins.
Explanation:
Case 1: Boat 1
Speed of boat = ![\frac{distance of river}{time}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20of%20river%7D%7Btime%7D)
time = ![\frac{distance of river}{speed of boat}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20of%20river%7D%7Bspeed%20of%20boat%7D)
While going to another end
time = ![\frac{distance of river}{speed of boat}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20of%20river%7D%7Bspeed%20of%20boat%7D)
time = ![\frac{48}{48}](https://tex.z-dn.net/?f=%5Cfrac%7B48%7D%7B48%7D)
time = 1 hour
While going back,
time = ![\frac{distance of river}{speed of boat}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20of%20river%7D%7Bspeed%20of%20boat%7D)
time = ![\frac{48}{48}](https://tex.z-dn.net/?f=%5Cfrac%7B48%7D%7B48%7D)
time = 1 hour
Total time taken by boat 1 is,
Total time by boat 1 = 1 hour + 1 hour = 2 hour
Total time by boat 1 = 2 hour
Total time taken by boat 1 for the round trip is 2 hour.
Case 2: Boat 2
Speed of boat = ![\frac{distance of river}{time}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20of%20river%7D%7Btime%7D)
time = ![\frac{distance of river}{speed of boat}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20of%20river%7D%7Bspeed%20of%20boat%7D)
While going to another end
time = ![\frac{distance of river}{speed of boat}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20of%20river%7D%7Bspeed%20of%20boat%7D)
time = ![\frac{48}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B48%7D%7B24%7D)
time = 2 hour
While going back,
time = ![\frac{distance of river}{speed of boat}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20of%20river%7D%7Bspeed%20of%20boat%7D)
time = ![\frac{48}{72}](https://tex.z-dn.net/?f=%5Cfrac%7B48%7D%7B72%7D)
time = 0.66 hour
Total time taken by boat 2 is,
Total time by boat 1 = 2 hour + 0.66 hour
Total time by boat 1 = 2.66 hour
Total time taken by boat 2 for the round trip is 2.66 hour.
Time required by boat 1 for the round trip is less than that of boat 2.
Hence, boat 1 wins.
Answer:
Explanation:
The car is rolling without slipping so Vcm= R×ω = 0.325×49 = 16
Answer: what do you mean ''beyond certain temperature'', Do you mean ask in cooling the liquid down or heating the liquid up?
Explanation: