Ppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 108 in. What are the dimensions and volume of a square based box with the greatest volume under theses conditions

dimensions are 36 x 36 x 36

Volume= 46656 inch³

Step-by-step explanation:

Supposing the dimensions x , x and y as the base is a square base.

So, their sum is : x + x +  y= 108

2x + y= 108

y= 108 - 2x --> eq(1)

Also, they are lengths, x,y >0

Next is to determine the maximum volume, the function is

V(x,y)= x.x.y => x²y

By subsitituing value of y from eq(1) in above equation

V(x)=x²(108-2x)

V(x)= 108x² - 2x³

In order to find critical point, take the derivative and set it to zero

V'(x)=  216 x - 6x² = 0

36 - x =0

x = 36 in

Plugging the value of 'x' in eq(1)

(1)=> y = 108 - 2(36)

y= 36 in

Therefore, the  volume of a square based box will be

V= x²y = 36² . 36

V=46656 in³

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: