Question 1

A. To solve this part of the problem take the integral of the equation

over the interval 0 to 30 (you can do this in your calculator easily).

The answer is 2474.0775 and this is rounded to the nearest whole number.

= 2474 cars in the 30 minute time period

B. You can tell if a function is increasing or decreasing at a certain point by looking at it's derivative so.....

Then plug in t=7 and it's F'(t) = -1.8729

F'(t) is negative, so F(t) is decreasing

C. Average Value Theorem --->

Plug in the domain (a=10 b=15) and solve.

= 81.899 cars/minute

D. Use the Average Value Theorem again, but for rates.

The integral becomes invalid because you are taking the integral of a derivative.

Plug in your numbers again (a=10 b=15) to make

=1.518 (cars/mins)/mins

A. Area should be the integral of f(x) - g(x) on the interval zero to one.

= 1.133

B. Use the washer theorem to solve this, it's really quite easy.

= 16.179

C.

= 15

A.

= 7.133

B. You need to find the dx/dt value so that you can find the m (slope).

dx/dt = 3 + cos(4).

m =

so the line is...

=

C. The equation for speed is

Plug it in!

= 7.383

D. d²y/dt² = d/dt[(2t + 1)dx/dt]

so d²y/dt² =

plug it in and you get.. 24.814 for d²y/dt²

plug in t for dx²/dt² and you get 2.303

so the acceleration vector is

= (2.303 , 24.814)