Physics, 03.03.2020 00:46 andybiersack154

The radius r of a sphere is increasing at a rate of 8 inches per minute. (a) Find the rate of change of the volume when r = 8 inches. in.3/min (b) Find the rate of change of the volume when r = 38 inches. in.3/min

Answers: 3

Show answers

Answers

Answer from: challenggirl

a) 2421.743 in³/ min , b) 54437.52 in³/ min

Explanation: The formulae for the volume of a sphere is given below as

V = (4π/3) ×r³ where V =volume of sphere and r = radius of sphere.

By taking the time derivative of the formulae, we have the rate of change of volume with time (we do so by using implicit diffrenciation) , hence we have that

dV/dt = (4π/3) × 3r²×dr/dt

Where dV/dt = rate of change of volume and dr/dt= rate of change of radius.

r = 8 inches, dr/dt = 3 in/min

By substituting this into the formulae, we have that

dV/dt = (4π/3) × 3r²×dr/dt

dV/dt = (4π/3) × 3(8)² × 3

dV/dt = (4π/3) × 576

dV/dt = 2421.743 in³/ min

r = 38 inches, dr/dt = 3 in/min

By substituting this into the formulae, we have that

dV/dt = (4π/3) × 3r²×dr/dt

dV/dt = (4π/3) × 3(38)² × 3

dV/dt = (4π/3) × 12996

dV/dt = 54437.52 in³/ min

Answer from: Quest

Less force and energy was applied

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

Another question on Physics

Physics, 22.06.2019 11:00

If angle "a" is 25°, angle "b" is: a) equal to angle c b) less than angle c c) greater than angle c

Answers: 1

Answer

Physics, 22.06.2019 13:00

Acertain radio station broadcasts radio waves that have a wavelength of 298cm what is its broadcast frequency?

Answers: 3

Answer

Physics, 22.06.2019 14:30

An electromagnet is a device in which moving electric chargers in a coil of wire create a magnet.whats one advantage of using electromagnetic in devices

Answers: 1

Answer

Physics, 23.06.2019 00:00

What is the difference between mass density and weight density?

Answers: 1

Answer

You know the right answer?

The radius r of a sphere is increasing at a rate of 8 inches per minute. (a) Find the rate of change...

Questions