The material for the base of an open box costs 1.5 times as much per unit area as the material for constructing the sides.

use lagrange multipliers to find the dimensions of the box of largest volume that can be made for a fixed cot c.
(maximize v = xyz subject to 1.5xy + 2xz + 2yz = c.)

Using the side-splitter theorem, daniel wrote a proportion for the segment formed by luke segment de. what is ec?

The median am of triangle ∆abc is half the length of the side towards which it is drawn, bc . prove that triangle ∆abc is a right triangle, and find angle mac and abm

Johnny rode his bike to a friends house 4 blocks down the street in his neighborhood. he immediately rode back home once he realized his friend was unable to play. what was his displacement for the total bike ride trip? what could you use as a reference point ? show the steps to solve this problem.