Aposter is to have an area of 180 in2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top. find the exact dimensions that will give the largest printed area.

x = 2√30

y= 3√30

Step-by-step explanation:

Area= 180in^2

For the larger shape,

Let the length be x and the width be y

A = x. y

x. y = =180

y= 180/x

For the smaller shape, lenght= x-2 while width = y-3

Area = (x-2)(y-3)

A(x) = (x-2)(y-3)

Put y= 180/x into A(x)

= (x-2)(180/x -3)

= 180 - 3x - 360/x + 6

Differentiate A(x) with respect to x

A'(x) = -3x+ 360/x^2

A'(x) = 0

0 = -3x + 360/x^2

3x = 360/x^2

3x^3 = 360

x^3 = 360/3

x^3 = 120

x = cuberoot 120

x = 2√30

Recall that y= 180/x

y = 180/2√30

y= 90/√30

By rationalizing the surd, we have

y = 90/√30 * √30/√30

y = (90√30) /30

y = 3√30

x = 2√30, y = 3√30

idk lol

step-by-step explanation:

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.