calc

posted by .

Assume that a rectangle with sides x and y is expanding with time. Let y = 2x and x(t)=2t+5. What is the rate of change of the area when t=2?

• calc -

The area A = x*y
We already know that y = 2x, so we can substitute that in:

A = x*2x = 2x^2

We were given that x(t) = 2t+5

A = 2x^2 = 2(2t +5)^2
A = 2(4t^2 + 10t + 25)
A(t) = 8t^2 + 20t + 25

The rate of change of the area with respect to time is dA/dt

dA/dt = 16t + 20

When t=2, dA/dt = 36

Similar Questions

1. calculus

Determine the rate at which the surface area is changing with respect to time at t=2 min, assuming that r = 3 at t = 0 Assume that the radius r of a sphere is expanding at a rate of 14 in / min. Its surface area is 4(pi)r^2 Ds/dt= …

For each right triangle, draw the rectangle made by drawing sides opposite the two shorter sides in the triangle. Find the area of each rectangle. 9cm height 4cm width How does the area of each rectangle relate to the area of either …
3. calculus

The length l of a rectangle is decrasing at a rate of 5 cm/sec while the width w is increasing at a rate of 2 cm/sec. When l = 15 cm and w = 7 cm, find the following rates of change: The rate of change of the area: Answer = cm^2/sec. …
4. calc -rates

assume a circle is expanding with time where r= t+3. What is the formula for rate of change of an area of the circle with reswpect to time?
5. Calculus

Assume the dimensions of a rectangle are continuously changing in a way so that the area, A, of the rectangle remains constant. If the base of the rectangle is increasing at a rate of 3 inches per second, at what rate is the height …
6. Calculus-Math

The length of a rectangle is given by 2t + 2 and its height is √t, where t is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time. A'(t)=
7. Calculus

A rectangle has area 64 m2. Express the perimeter of the rectangle as a function of the length L of one of its sides. State the domain of P. (Assume the length of the rectangle is larger than its width. Enter your answer using interval …
8. Calc

Rope and wire are arranged in the shape of a rectangle. Two parallel sides of the rectangle are made from the rope which costs \$2.00 per foot. The other two sides are made from the wire which costs \$3.00 per foot. Find the dimensions …
9. Math

A rectangle has sides of length x cm and 2x - 4cm and the length x cm at time t seconds is given by x = 2 + 3t, (t>=0) . Show that the area, A cm^2 , the rectangle, in terms of t is A =12t + 18t^2 . Hence find the rate of change …
10. Math

A rectangle has sides of length x cm and 2x - 4cm and the length x cm at time t seconds is given by x = 2 + 3t, (t >=0) . Show that the area, Acm2 , the rectangle, in terms of t is A =12t + 18t^2 . Hence find the rate of change …

More Similar Questions