There are no variables, and you've included the answer already, so I'm not sure what you're asking for..
Answer:
Step-by-step explanation:
Let the length of one side of the square base be x
Let the height of the box by y
Volume of the box V = x²y
Since the box is opened at the top, the total surface area S = x² + 2xy + 2xy
S = x² + 4xy
Given
S = 7500sq in.
Substitute into the formula for calculating the total surface area
7500 = x² + 4xy
Make y the subject of the formula;
7500 - x² = 4xy
y = (7500-x²)/4x
Since V = x²y
V = x² (7500-x²)/4x
V = x(7500-x²)/4
V = 1/4(7500x-x³)
For us to maximize the volume, then dV/dx = 0
dV/dx = 1/4(7500-3x²)
1/4(7500-3x²) = 0
(7500-3x²) = 0
7500 = 3x²
x² = 7500/3
x² = 2500
x = √2500
x = 50in
Since y = (7500-x²)/4x
y = 7500-2500/4(50)
y = 5000/200
y = 25in
Hence the dimensions of the box that will maximize its volume is 50in by 50in by 25in.
The Volume of the box V = 50²*25
V = 2500*25
V= 62,500in³
Hence the maximum volume is 62,500in³
Answer:
1 
Step-by-step explanation:
1/4cake=1/3cup
Now times both sides by 4
x 
=1 cake
x =
which equals 1
Answer:
B) 
x units
Step-by-step explanation:
Let quadrilateral KMPT be a rectangle with dimensions 12 units by 8 units. Then its perimeter would be equal to:
Perimeter of a rectangle = 2 (l + b)
where: l is the length = 12 units and b is the breadth = 8 units. So that:
Perimeter of KMPT = 2 (12 + 8)
= 40 units
Dilating KMPT by a scale factor of would create K'M'P'T' of dimensions; × 12 units by × 8 units. Thus, the dimensions of K'M'P'T' would be 9 units by 6 units.
Perimeter of K'M'P'T' = 2 (l + b)
= 2(9 + 6)
= 30 units
Comparing the perimeters of KMPT and K'M'P'T', the perimeter of K'M'P'T' would be × perimeter of KMPT.
Therefore, if the perimeter of KMPT is x units, then;
perimeter of K'M'P'T' = * x units
= x units
Answer:
The different winning scores possible are 25 (from 28 to 52).
Step-by-step explanation:
- The minimum score obtained by a player will be 28.
since, we divide 1-7 numbered to one and 8-14 to the other player such that one receives the maximum and the other receives the minimum.
the least minimum possibility is :28 as one get the card as(1,2,3,4,5,6,7).
while the other player gets 77 sum and loses.
- for increasing this score now we give the number 1,2,3,4,5,6,8 to one of the player so that they sum upto 29 and will get the minimum score and wins while the other player gets 76 sum with the help of numbers{9,10,11,12,13,14,7} and loses.
- next possible minimum sum to win will be 30 by assigning 1,2,3,4,5,6,9 whereas the other gets the sum 75 and loses.
- continuing in the same way we see that the minimum sum obtained to win will be 52( by assigning 2,3,6,7,9,12,13) while the other gets the sum 53 and loses.
Hence, there are total 25 winning scores possible. (from 28 to 52 i.e. 52-28=25).
