A cylindrical tank with radius 5 m is being filled with

Question

Brian Cruz's Quiz for Chapter 3-

1. Find the derivative of f((g(x)/h(x)) + x²) with respect to x.

2. Find g′(x) where g (x) = √(cos(sin² x)).

3. A particle moves on a line so that its coordinate at time t is y = -5t²+10t+√2, t ≥ 0. Find the velocity and acceleration functions.

4. Find the equations of the tangent line and the normal line to the curve y = x^{cos x} at x = 2π. Draw the lines in the picture of the graph below. Hint: to find dy/dx you can use logarithmic differentiation, or you can write y as e ^(something).

5. A cylindrical tank with radius 5 m is being filled with water at a rate of 3m³/min. How fast is the height of the water increasing? Remember to define your variables!

6. A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is poured into the cup at a rate of 2cm³/s, how fast is the water level rising when the water is 5 cm deep?

7. A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?