An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. If the volume V of the box is a function of the length x of the side of the square cut from each corner, for what value of x is V the largest

x=4 Inch

Step-by-step explanation:

Length of the Square = 24 Inches

If a Square of Length x cm is cut out from each corner

Length of the Box = 24-x-x=(24-2x) Inches

Width of the Box =24-x-x=(24-2x) Inches

Height of the box = x inches

Volume of a Cuboid = Length X Width X Height

V(x)= x(24-2x)(24-2x)

Simplifying

V(x)=4x(12-x)(12-x)

To determine the value of x at which V is largest, we take the derivative of V(x) and solve for the critical points.

V(x)=4x(12-x)(12-x)

Set the derivative equal to zero to obtain the critical points

x cannot be equal to 12 as it divides the length of the square cardboard into exactly two equal parts.

When x=4

V(4)=4*4(12-4)(12-4)=16*8*8=1024 Cubic Inches

When x=4 Inch, the volume, V of the open box is largest.

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.

nothjing

step-by-step explanation: