Related Rate Again..
1. Let http://webwork1.math.utah.edu/webwor...0fcdd79cd1.png be the area of a circle with radius http://webwork1.math.utah.edu/webwor...79cb7891c1.png. If http://webwork1.math.utah.edu/webwor...985d565591.png, find http://webwork1.math.utah.edu/webwor...375c713261.png when http://webwork1.math.utah.edu/webwor...c95730d941.png.
2. The radius of a right circular cone is increasing at a rate of 4 inches per second and its height is decreasing at a rate of 3 inches per second. At what rate is the volume of the cone changing when the radius is 50 inches and the height is 20 inches?
3. At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 22 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
4. The top of a 28 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 7 feet away from the base of the wall?
Lets take a look at #1 and #2
Area of a circle:
Then, by implicit differentiation,
And we know and r = 1, so we can get
Volume of a right circular cone:
Then, again by implicit differentiation,
and this time we know , , r = 50, h = 20
Sorry but just dont do number 4..i got the answer already :)