Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and four sides of the box costs $1/ft2; the material for the base costs $2/ft2. Find the dimensions of the box of greatest possible volume if you are allowed to spend $144 for the material to make it. List largest to smallest.

height = 14.5 ft

width = length = 3.2 ft

Step-by-step explanation:

Let the side of the square base is a and the height of the box is h.

The material required to make the box is equal to the total surface area of the box.

Area of base = a²

Cost of square base is $ 2 per ft²

So, the cost of making base = 2a²

Area of four walls + area of top = 2 (a² + ah + ah) + a² =  3a² + 2ah

Cost of making walls and the top is $ 1 per ft²

So, the cost of making walls and the top = 1 x ( 3a² + 2ah)

Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah

According to the question

144 = 5a² + 2ah

    .... (1)

The volume of the box is V = length x width x height

V = a x a x h

V = 72 a - 2.5 a³     from equation (1)

Differentiate both sides with respect to a.

dV/da = 72 - 7.5 a²

Put, it equal to zero for maxima and minima

7.5 a² = 72

a = 3.2 ft

Put in equation (1)

h = 14.5 ft

So, the dimensions of the box are

height = 14.5 ft

width = length = 3.2 ft

76%

step-by-step explanation:

24% are dogs and the remaining is 76% because 100-24=76

the above table 1 will calculate the population size (n) after a certain length of time (t). all you need to do is plug in the initial population number (no), the growth rate (r) and the length of time (t). the constant (e) is already entered into the equation. it stands for the base of the natural logarithms (approximately 2.71828). growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. for humans, population growth rate is based on one year. if a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent.

step-by-step explanation: