If a cylinder’s radius and height are each shrunk down to a third of the original size, what would be the formula to find the modified surface area?

We let

r1 = the original radius of the cylinder

r2 = the new radius of the cylinder

h1 = the original height of the cylinder

h2 = the new height of the cylinder

SA = surface are of the cylinder

the radius and the height are shrunk down to a third of their value therefore

r2 = r1/3

h2 = h1/3

 SA = 2(PI)r^2 + 2(PI)rh

SA = 2(PI)[(r1^2)/9] +2(PI)(r1/3)(h1/3)

Simplifying

SA = [2(PI)r]/9 * (r1 + h1)

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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