Question

answer following question​

Answer 1

Answer:

Step-by-step explanation:

A. x must be > 0, <12

B. If you cut x inches square from four corners of 12 x 18 inch sheet

Length of box = 18-2x inches

Width of box = 12-2x inches

Height of box = x inches

Volume V = (18-2x)(12-2x)(x) = 4x3 - 60x2 + 216x

C. To find max of this function put dV/dx = 0

12x2 - 120x + 216 = 0

Solve this quadratic equation

x = (120 + √(14400 - 10368))/24 = (120 + 63.5)/24 = 2.35 or 7.65

max volume = 228 cubic inch or - 68 cubic inch. Since volume cant be -ve so x = 2.35 inch for max volume

D. 4x3 - 60x2 + 216x > 80

=> Factorize

=> x(x-9)(x-6) > 80

x = 11 inches

Answer 2

I can't see the image to answer