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
Circumference: 2πr C=18 so r= 18/2π= 9π
Arc length = rθ 6=(9π)θ θ=6/9π
Convert to degrees by multiplying by 180/π
6/9π x 180/π = 120 degrees
Answer:
?
Step-by-step explanation:
Answer:
Step-by-step explanatinon:
percent is per hundred
4 dimes is 40 cents or $0.40 or 40/100 of a dollar which is40%
1 nickel and 3 pennies or 8 cents or $0.08 Or 8/100 or 8%
5 quarters and one dime is 135/100 or $1.35 or 135/100 which is 135%
-40) No
0) No
-5) No
13) Yes
21)Yes