Euler found the sum of the p-series with p = 4: ζ(4) = [infinity] 1 n4 = π4 90 n = 1 use euler's result to find the sum of the series. (a) [infinity] 2 n 4 n = 1 (b) [infinity] 1 (k − 3)4 k = 6

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.

Grace paid $1.70 for 5 ounces of candy. how much did she pay for 24 ounces?