Velocity word problem

All work must be shown step by step, any answers given without proper justification will not be accepted. Keep track of units and use proper notation. An object is dropped from a tall building, If the air resistance is proportional to the square of the velocity, then (dv/dt)=-32(ft/sec^2)+kv^2 where k is a constant. Show th ...continues

How long will it be before the radius has decreased to one-half its initial value? How long before the mothball disappears completely?

A mothball loses mass by evaporation at a rate proportional to its instantaneous surface area. If half the mass is lost in 100 days, how long will it be before the radius has decreased to one-half its initial value? How long before the mothball disappears completely?

Integrals

Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by: y= x^4 y= 125x about the x-axis. I am more concerned with understanding than the answer. Thanks for your help.

For OTA 103997 or 103877 only/Calculus Help

1. The position equation for the movement of a particle is given by when s is measured in feet and t is measured in seconds. Find the acceleration at two seconds. 2. Find the derivative: . 3. Find if . 4. The radius of a circle is increasing at the rate of 5 inches per minute. At what rate is the area increasing when ...continues

Evaluating integrals

evaluate the integral from 0 to infinity of (sin (xy))^2 / x^2 dx

Integration

Find the volume of the solid obtained by rotating the region bounded by the given curves: y=1/x^6, y=0, x=4, x=8 about the "y" axis

Evaluating integrals

evaluate the integral from 0 to infinity of (e^(-at) - e^(-bt))/t dt for a,b > 0

Integration

See attached for Diagram The base of a certain solid is the area bounded above by the graph of y=f(x)=16 and below by the graph of y=(gx=36*. Cross sections perpendicular to the x-axis are squares. See picture above. Use formula (see attachment) to find the volume of the solid.

Integrals

Show that the integral from 0 to infinity of (t^n e^-t dt) = n!

Rotation of integrals

Find the volume of a solid generated by revolving about the x-axis the region bounded by the upper half of the ellipse *See attached for equation* and the x-axis and thus find the volume of a prolate spheroid. Here a and b are positive constants, with a ...continues