Derivatives and Rate of Change : Calculate the rate a shadow is moving up a wall.

I need to determine how fast a shadow is moving up a wall. Given the heigth of the wall the height if the object that cast the shadow. The length of the wire the object moves on, and the height of the light that casts the shadow. I have worked out the
first sections in an Excel 2000 spreadsheet but I need a push in the right direction in calculating the derivatives on the last section.

1.Water is poured into a conical funnel at a rate of 1 cm3/s. The radius of the top of the funnel is 10 cm andthe height of the funnel is 20 cm. Find therate at which the water level is rising when it is 5 cm from the top of the funnel.
I know that I am suppose to use the volume of the cone
V=1pi r2h
3
2.A ligh

A tightrope is stretched 30 ft above the ground between Building 1(at point A) and Building 2( point B), which are 50 ft apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A.
a) how far from point A is the tightrope walker when

1.) A fugitive is running along a wall at 4.0m/s. A searchlight 20m from the wall is trained on him. How fast is the searchlight rotating at the instant when he is 10m from the point on the wall nearest the searching?
2.) A balloon is rising from the ground at therate of 6.0m/s from a point 100m from an observer, also on the

41) Suppose that the average yearly cost per item for producing x items of a business product is C(x)=10+(100/x) . if the current production is x=10 and production is increasing at a rate of 2 items per year, find therate of change of the average cost.
45) Suppose a 6ft tall person is 12 ft away from a 18-ft tall lamppost. i

Please assist me with understanding the following questions:
1. A glider is flying along the line y = - (1/3)x + 100. Its horizontal shadow is moving at 10 m/s. How fast is the glider approaching the origin (0,0) at the time when it is located at (-30, 110)?
2. Boyle's Law states that when a sample of gas is compressed a

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t)
To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t.
a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get therate of change of

Water is running out of a conical funnel at therate of 1 cubic inch per second. If the radius of the top of the funnel is 4 inches andthe height is 8 inches, find therate at which the water level is dropping when it is 2 inches from the top.

(1.) A particle moves along the x-axis so that at any time that t is greater than or equal to zero, its position is given by x(t)= t^3-12t+5.
a.) Find the velocity of the particle at any time t.
b.) Find the acceleration of the particle at any time t.
c.) Find all values of t for which the particle is at rest.
d.) Find the s