Pls help

Math 141 - Algebra with Applications Name: Graded Class Activity 8B: Power Functions Sections Chapters 7 **Show all work for full credit and box in your final answers. ** 1. The volume, V, of a pyramid in cubic inches is directly proportional to the height, h, and the area of the base, B, given in inches. a. Write an equation to express the proportionality relationship above, using k as the constant of proportionality. b. Suppose the volume is 700 cubic inches when the height is 10 inches and the area of the base is 210 inches squared. Determine the constant of proportionality, k. C. Suppose the height of the pyramid is doubled to 20 inches and the area of the base is 150 inches squared. Determine the volume of the new pyramid. Round to the nearest tenth 2. The centripetal force, F, measured in Newtons acting on an object varies directly as the square of the speed, v, in meters per second (m/s) and inversely to the radius, r, of its path in meters. a. Write an equation to express the proportionality relationship above, using k as the constant of proportionality. b. If the centripetal force is 100 Newtons when the object is traveling 20 m/s in a path or radius of 2 m, determine the constant of proportionality, k. Round to the nearest tenth. c. Suppose the speed increases to 30 m/s and the path's radius is now 4 m. Determine the centripetal force acting on the object. Round to the nearest tenth. 3793. Consider the function f(x) = kx , where p is an odd, negative integer. Assume k > 0. Sketch the graph of f(x).And In a. Using interval notation, state the domain and range of f (x). Domain: Range: Is this function symmetric with respect to the x-axis, y-axis, origin, or none of these? oidio Ook aromalo c. Determine the equations for any horizontal or vertical asymptotes. If none exist , write DNE. d. Fill in the blanks for f(x). As x- - co, f(x)- As x-+0o, f (x) -_ pi 4. Consider the function f(x) = kx for each of the following graphs. Create a function that could represent the following graphs. b. a. 380