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
Answer:
36pi
Step-by-step explanation:
the volume of a sphere is equal to 4/3 x pi x r^3
the radius is half of the diameter
3^3=27
27x4/3=36
36pi
Answer:
-1,1
Step-by-step explanation:
because if you plot the points that is half.
2n-4=-12
Add 4 to both sides
2n=-8
Divide by 2 on both sides
n=-4
To do these types of questions do reverse PEMDAS. Do the opposite sign such as adding to undo subtraction.
Answer: it will take 5 months for both gyms to cost the same.
Step-by-step explanation:
Let x represent the number of months for which the total cost of gyms are the same.
Gym A charges a new member fee of $65 and $20 per month. This means that the cost of using gym A for x months would be
20x + 65
Gym B charges a new member fee of $25 and $35 per month but you get a discount of 20% monthly.
20% of 35 is 20/100 × 35 = 7
The monthly charge would be
35 - 7 = 28
This means that the cost of using gym A for x months would be
28x + 25
The number of months that it will take for the cost of both gyms to be the same would be
20x + 65 = 28x + 25
28x - 20x = 65 - 25
8x = 40
x = 40/8 = 5
