Show that if n is a positive integer, then (2n n) = 2(n 2) + n^2 using a)combinatorial argument b)algebraic manipulation

Water flows from the bottom of a storage tank at a rate of r(t) liters per minute. Find the amount of water R that flows from the tank during the first 35 minutes.

(x .y + z) + (x+y+z) +(x+y+z)

what is 5015 devided by 59?

If an open box has a square base and a volume of 104 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. (Round your answers to two decimal places.)

The winning team's scores in 9 high school basketball games were recorded. If the sample mean is 9.8 points and the sample standard deviation is 0.15 points, find the 98% confidence interval of the true mean.

Triangles FGH and MNO are similar. The length of the sides of FGH are 105, 126, and 231. The length of the smallest side of MNO is 150, what is the length of the longest side of MNO?

f. Choose some real numbers and show how this equation provides an answer to the husband s apparent problem. What does this equation suggest about the relationship between velocity and area?

A cylindrical drill with radius 1 is used to bore a hole throught the center of a sphere of radius 4. Find the volume of the ring shaped solid that remains.

Let f be defined on R: f(x) = 0, when x=0 f(x) = (x^n)*sin(1/x) when x !=0 For what values of n in N is f(x) differentiable at x=0? And for what values of n is f continuously differentiable on R? Prove the answers.