Answer:
20%
Step-by-step explanation:
To change a fraction to a percentage , multiply by 100%
× 100%
= 0.2 × 100%
= 20%
A person can pay $ 27 for a membership to the history museum and then go to the museum for just $1 per visit. What is the maximu
1 answer:
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The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
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Complete Question
(Image Attached)
Answer:
12.5%
Step-by-step explanation:
First we need to calculate the change in the area of Terry's room this is
108 ft2 - 96 ft2 = 12 ft2
Then we use a direct proportion in order to find the percentage
96 ft2 ----- 100%
12 ft2 ----- p?
Solvin for p we have that
p=12.5