Calculate the AR% from the information provided.

Evaluate the integral. ​   given, , , , . ​

Write the limit , as a definite integral on the interval [0, 8] where ci is any point in the ith subinterval. ​

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​ ​

Find the x- and y-intercepts of f.f(x) = (x + 5)(x – 4)(x + 4)

Find the slope of the graph of the function  at x = 5. ​

Find the cubic function of the form where and the coefficients a, b, c, d are real numbers, which satisfies the conditions given below. ​ Relative maximum: Relative minimum: Inflection point: ​

For the given functions f and g, find the requested composite function value.f(x) = 7x + 8, g(x) = -1/x;Find (g ∘ f)(3).

A population of 640 bacteria is introduced into a culture and grows in number according to the equation , where t is measured in hours. Find the rate at which the population is growing when t = 6. Round your answer to two decimal places. ​

Solve the problem.A box with an open top is formed by cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides. If x represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 14 inches by 13 inches, what size square must be cut if the volume of the box is to be 168 cubic inches?