Answer:
Not a function
Step-by-step explanation:
This is not a function because there are different outputs for the same input.
There are 12! ways to line 12 people up. That is 12 factorial (the name for the exclamation point
12! means 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Using a scientific calculator to compute 12!, we get 479,001,600 ways to line up 12 people. I know it sounds amazing but here is a chart.
People Ways
3 6
4 24 (Notice that if you multiply 6 x 4 you get 24)
5 120 (Notice that if you muliply 24 x 5 you get 120 etc.)
6 720
7 5040
8 40,320
9 362,880
10 3,628,880
11 39,916,800
12 479,001,600
1 cup = 8 fluid oz
8 × 8 = 64
So Joshua drinks 64 fluid ounces a day
Hope this helped. Have a great day!
Answer:
Step-by-step explanation:
Represent the length of one side of the base be s and the height by h. Then the volume of the box is V = s^2*h; this is to be maximized.
The constraints are as follows: 2s + h = 114 in. Solving for h, we get 114 - 2s = h.
Substituting 114 - 2s for h in the volume formula, we obtain:
V = s^2*(114 - 2s), or V = 114s^2 - 2s^3, or V = 2*(s^2)(57 - s)
This is to be maximized. To accomplish this, find the first derivative of this formula for V, set the result equal to 0 and solve for s:
dV
----- = 2[(s^2)(-1) + (57 - s)(2s)] = 0 = 2s^2(-1) + 114s - 2s^2
ds
Simplifying this, we get dV/ds = -4s^2 + 114s = 0. Then either s = 28.5 or s = 0.
Then the area of the base is 28.5^2 in^2 and the height is 114 - 2(28.5) = 57 in
and the volume is V = s^2(h) = 46,298.25 in^3
