The volume of a box is 120 cubic feet, the width and length are equal to x, the height is y. Find the dimensions that use the least amount of material. V=x^2 * y

The answer is below

Step-by-step explanation:

The volume of box = width * length * height

120 = x * x * y

120 = x²y

y=120/x²

The surface area (SA) = sum of the area of all faces side

SA = x² + x² + xy + xy + xy + xy

SA = 2x² + 4xy

substitute y =120/x²

SA = 2x² + 4x(120/x²)

SA = 2x² + 480/x

Taking the derivative:

SA' = 4x - 480/x²

making SA' = 0:

0 = 4x - 480/x²

480/x² = 4x

4x³ = 480

x³ = 120

x = 4.93 feet

y = 120 / x² = 120 / 4.93² = 4.93

Hence the width, length and height is 4.93 feet.

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100%   is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

16

retail price is $16.

answer

a) the midrange of the data set shown is 85.5

step by step explanation

let's find the midrange.

the midrange is nothing but add the greatest value and the least value, then divide it by 2.

here the greatest value = 99

the least value = 72

midrange = (99 + 72)/2

= 171/2

midrange = 85.5

you.