2. a box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. find the largest volume of the box

Step-by-step explanation:

We are given that

Side of square shaped piece= 3ft

Let  square of side x cut from each corner of square piece cardboard.

Length of box=

Breadth of box=

Height of box= x

We have to find the largest volume of box.

Volume of box is given by

Differentiate w.r.t x

Substitute

Again differentiate w.r.t x

Substitute

Substitute

Therefore, at

Hence, the volume is maximum at

Substitute the value then we get

step-by-step explanation:

*calories burned = (weight)(calorie factor)*

calories burned = 180 (0.65)

calories burned = 117

the calories he used up is 117, which is 65% of his weight.