The radius of a right circular cylinder is increasing at the rate of 3 ft/sec, while the height is decreasing at the rate of 6 ft/sec. at what rate is the volume of the cylinder changing when the radius is 15 ft and the height is 10 ft? remember to use the product rule when you find the expression for dv/dt. 30 ft3/sec −900 ft3/sec −450π ft3/sec −900π ft3/sec

Step-by-step explanation:

Let's assume

radius of cylinder as 'r'

height of cylinder as 'h'

so, we have

r=15ft

h=10ft

now, we can use volume of cylinder formula

we can find derivative with respect to t

now, we can plug values

now, we can simplify it

Step-by-step explanation:

First of all you have to put the zeros into factor form.

y1 = (x + 2)(x - 5)

Notice that the x changes sigh. You say that the zeros are -2 and  5. To get y1 to go to zero, you must make x the opposite sign of what you are given.

Now you have to expand the factored form to get the standard form

y = x^2 + 2x - 5x - 10

y = x^2 - 3x - 10

That's not the right answer.

f(0) = 30 but you have - 10 at the end so you have to multiply the factored form by - 3

-3(f(x)) = -3(x + 2)(x - 5)

-3(f(x)) = -3(x^2 - 3x - 10)

f(x) = -3x^2 + 9x + 30    

f(0) = -3(0)^2 + 9(0) + 30

f(0) = 30

The quadratic still has roots of (x +2)(x - 5) but that 3 makes the y intercept = 30.

See the graph below.