2. For a certain font, the scale factor is 1.414 and one of the scale sizes is 1.999. What is the next larger scale size?

3. For a certain font, the scale factor is 1.42 and one of the scale sizes is 2.863.

What is the next smaller scale size?

5. Adan has 20 ft of fence with which to build a rectangular dog run.

What is the maximum area he can enclose?

2. We are given the first scale size which is 1.414. The second scale size is 1.999. The next larger scale size would be

1.414 (1.999/1.414) ^3 = 2.826

3. We are given the first scale size of 1.42 and the second scale size is 2.863. The next larger scale size would be (doing the same thing as 2)

1.142 (2.863/1.142) ^2 = 5.77

4. The perimeter is

P = 2L + 2W = 20

The area is

A = LW

Substituting

A = L (10 - L)

Differentiating and equating to 0

dA = L (-1) + (10 - L)

L = 5

and

W = 5

The maximum area is

A = 5 (5)

A = 25