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Sedbober [7]
3 years ago
15

Length: 1/2 width: 1/2 height: 3/4 what is the volume?

Mathematics
2 answers:
slava [35]3 years ago
8 0

Answer:

The volume is 3/16 cubic units.

Step-by-step explanation:

Given

Length l = 1/2

Width w = 1/2

Height h = 3/4

To determine

Volume = ?

The volume can be determined using the formula

Volume = l × w × h

substitute l = 1/2, w = 1/2, and h = 3/4

Volume = 1/2 × 1/2 × 3/4

Volume = 1/4 × 3/4

Volume = 3/16 cubic units

Therefore, the volume is 3/16 cubic units.

makvit [3.9K]3 years ago
5 0

Answer:

3/16

Step-by-step explanation:

The formula for Volume is V = L * W * H

The given are L = 1/2, W = 1/2, H = 3/4

Substituting the values -

V = 1/2 * 1/2 * 3/4

  = 3/16

  = 3/16 divide by the Greatest Common Factor (GCF) of 3 and 16 to get the lowest term

 = 3/16

Therefore, the volume of the box in 3/16.

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A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen
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Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}

The restriction is that the perimeter have to be 12 ft at most:

P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12

We can express b in function of a as:

2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a

Then, the area become:

A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2

To maximize the area, we derive and equal to zero:

\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36

Then, b is:

b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68

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3 years ago
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Step-by-step explanation:

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b=-2a+P

Which is your final answer.
b = -2a+P.
Hope that helped! =)
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