Alan

Since area is \(A=\pi r^2\)  then  \(\frac{dA}{dt} = 2\pi r\frac{dr}{dt}\)

So the rate of change of area is \(2\pi r\) times the rate of change of radius.

I'll leave you to plug in the numbers.

Let c = number of cheesburgers and p = number of potatoes.

Then

c + p = 10

8.99*c + 7.49*p = 85.4

You now have two equations for the two unknowns.  Can you take it from here?

Google translation:

An equal number of boys and girls attended the art exhibition. When 40 boys and 85 girls left, there were six times as many boys as girls. How many girls went to the art exhibition first?

b = g   number of boys = number of girls

b-  40 = 6*(g - 85)

Use first eqn in second eqn
 

g - 40 = 6g - 510

Can you finish it from there?

f(n) = 3*f(n-1) + 4*n         f(1) = 2

n = 2:   f(2) = 3*f(1) + 4*2

n = 3:  f(3) = 3*f(2) + 4*3

Can you take it from here?

If \(f(x) = x^2-3x+4\)  then \(f(2x)=(2x)^2-3(2x)+4\)  which, when simplified is \(4x^2-6x+4\)

This diagram should help

.

Use similar triangles to find where the line crosses the x-axis.

The mean of a binomial distribution is given by np

Tha variance of a binomial distribution is given by np(1-p)

Hence:  n*p = 2

             n*p*(1 - p) = 1.5

You now have two equations in two unknowns.  Can you take it from here?

Here is (b)

Can you now do (c)?

As follows:

"The polynomial of degree 3, P(x), has a root of multiplicity 2 at x= 3 and a root of multiplicity 1 at x= - 4. The y-intercept is y = - 28.8.Find a formula for P(x)."