Calculus Help!!!?

Question

1) Find the rate of change of the distance between the origin and a moving pint on th egraph of y = sinx if dx/dt = 2 cm/second

2) All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is (a) 1 centimeter and (b) 10 centimeters.

3) All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the surface area changing when each edge is (a) 1 centimeter and (b) 10 centimeters

4) The formula for the volume of a cone is V = 1/3 pir^2h. Find the rate of change of the volume if dr/dt is 2 in per minute and h=3r when (a) r= 6 inches and (b) r =24 inches

Answer 1

It's all the Chain Rule, and plugging in known numbers.

For example, in 2

V = s^3. dV/dt = dV/ds * ds/dt = 3s^2 * ds/dt.

ds/dt is given to be 3, a constant. s is 1 in 2a and 10 in 2b. So plug the values in and you're done.

3 is exactly the same thing, except A = 6 s^2.

In 1, the distance from the origin is the square root of x^2 + y^2 = sqrt(x^2 + sin^2x). So take d/dt of that, which = 2 cm/sec times d/dx of it.

Answer 2

i might say shape is area of engineering meaning that a sturdy carry close on math is considerable, pre-cal is is like algebra to the subsequent point with the Pi chart and understanding approximately radians and perspective measures (which looks considerable) yet Calculus is the learn of derivatives, (the slope of a line at a definite factor) style of pointless no be counted what container of workd your going to, in case you inquire from me.