A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 120 in. What dimensions will give a box with a square end the largest possible volume?

20 in, 40 in

Step-by-step explanation:

Let L is the length and W is the width.

Total distance around, P = 2 L + 2 W = 120

L + W = 60 (1)

Volume of box, V = W² x L

V = W² x (60 - W)             from equation (1)

V = 60 W² - W³

dV/dW = 120 W - 3W²

It is equal to zero for maxima and minima

120 W - 3 W² = 0

W = 40 in

L = 60 - 40 = 20 in

Thus, the dimensions of the box is L = 20 in, W = 40 in

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

answer: 8d

step-by-step explanation:

45+5= 50+5=55+5=60