# Calculus

posted by Deondre

1) If y = 2x3 - 4x and dx, dt equals 4 , find dy/ dt when x = 1.

2) The area A = πr^2 of a circular water ripple changes with the radius. At what rate does the area change with respect to the radius when r = 4ft?

3) A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x^2h cm^3. Find the rate at which the volume of the box is changing when the edge length of the base is 10 cm, the edge length of the base is increasing at a rate of 3 cm/min, the height of the box is 5 cm, and the height is decreasing at a rate of 1 cm/min.

4) The height of a cylinder with a fixed radius of 10 cm is increasing at the rate of 0.5 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 30cm.

1. Damon

Where are your attempts to do these? Where did you get stuck? I already took the subject, do not need practice. They are all really the same. For example the last one:
r = 10
V = pi r^2 h = 100pi h
100 pi is a constant so
dV/dt = 100 pi * dh/dt
or the second one (the first one has a typo)
dA/dt = dA/dr * dr/dt = 2 pi r * dr/dt
in other words the area increase is the circumference times dr

2. Writeacher

Deondre = James

=(

3. Damon

Never would have guessed :)

4. Writeacher

:D

## Similar Questions

1. ### Calculus - Related Rates

Bacteria are growing in a circular colony one bacterium thick. The bacteria are growing at a constant rate, thus making the area of the colony increase at a constant rate of 12 mm sq. per hour. Find an equation expressing the rate …
2. ### math

A stone dropped into water produces a circular ripple which increases in radius at a rate of 1.50 m/s. How fast is the area increasing within the ripple when its diameter is 6.00m?
3. ### Calculus

A pebble is dropped into a pond, causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate of 2 feet per second. When the radius is 10 feet, at what rate is the total area …
4. ### calculus

The area A = πr2 of a circular puddle changes with the radius. At what rate does the area change with respect to the radius when r = 5ft?
5. ### cauculus

The area A = πr2 of a circular puddle changes with the radius. At what rate does the area change with respect to the radius when r = 5ft?
6. ### math

The area A equals = πr^2 of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r equals= 3ft?
7. ### calculus

The area A = πr2 of a circular water ripple changes with the radius. At what rate does the area change with respect to the radius when r = 4ft?
8. ### Calc

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.6 ft/s. (a) How rapidly is the area enclosed by the ripple increasing when the radius is 4 feet?
9. ### Calculus

A stone is dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2 meters per second. How rapidly is the area enclosed by the ripple increasing at the end of 20 seconds?
10. ### Calculus

a pebble is dropped into a calm pond, causing ripples in the form of concentric circles. the radius r of the outer ripple is increasing at a constant rate of 1 root per second. When the radius is 4 feet, at what rate is the total area …

More Similar Questions