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irina [24]
2 years ago
13

A solid has twelve more edges than faces. How many vertices does it have?

Mathematics
1 answer:
Nataly_w [17]2 years ago
8 0

Answer:

V=14

Step-by-step explanation:

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Find the measure of acute angle of a right angle triangle when one angle is 60°
Pachacha [2.7K]

Answer:

30 degrees.

Step-by-step explanation:

Let the acute angle be x.

Then as the 2 acute angles in a right triangle sum to 90 degrees,

x = 90 - 60

= 30.

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3 years ago
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At a local amusement park, 70% of the rides are made for kids who are 48 inches and taller. If there are 80 rides in total, how
Musya8 [376]

Answer:

56

Step-by-step explanation:

Basically you want to find out what is 70% of 80.

first you have to set up your problem

\frac{n}{80} = \frac{70}{100}

the first fraction would be the percent (70) over 100. (you always use 100)

The fraction to the left would be n over 80. the denominator (the number on the bottom) would be the whole amount. n would be the unknown number

To solve you would use the butterfly method. 80 x 70 and 100 x n. 80 x 70 is 5600 and 100 x n is 100n.

The final step is dividing. 5600 divided by 100 giving you 56

8 0
2 years ago
What is the median of 38,10,6, 23,26,38,14,23,20,11,27,33,20,13,14,31?
mixas84 [53]
Hope this helps!!! :)

7 0
3 years ago
Fifty-five percent of the pupils in a class are
tatyana61 [14]
Answer: it’s 55/100 percent
4 0
3 years ago
A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman
Yanka [14]

Answer:

W\approx 8.72 and L\approx 15.57.

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

2L+W+\frac{1}{2}(2\pi r)=38

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

2L+W+\frac{1}{2}(2r\pi)=38

2L+W+\frac{\pi}{2}W=38

Let us find area of window equation as:

\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)

\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})

\text{Area}=W\cdot L+\frac{\pi}{8}W^2

Now, we will solve for L is terms W from perimeter equation as:

L=38-(W+\frac{\pi }{2}W)

Substitute this value in area equation:

A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2

Since we need the area of window to maximize, so we need to optimize area equation.

A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2  

A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2  

Let us find derivative of area equation as:

A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W  

A'=38-2W-\pi W+\frac{\pi}{4}W    

A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W

A'=38-2W-\frac{3\pi W}{4}

To find maxima, we will equate first derivative equal to 0 as:

38-2W-\frac{3\pi W}{4}=0

-2W-\frac{3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}*4=-38*4

-8W-3\pi W=-152

8W+3\pi W=152

W(8+3\pi)=152

W=\frac{152}{8+3\pi}

W=8.723210

W\approx 8.72

Upon substituting W=8.723210 in equation L=38-(W+\frac{\pi }{2}W), we will get:

L=38-(8.723210+\frac{\pi }{2}8.723210)

L=38-(8.723210+\frac{8.723210\pi }{2})

L=38-(8.723210+\frac{27.40477245}{2})

L=38-(8.723210+13.70238622)

L=38-(22.42559622)

L=15.57440378

L\approx 15.57

Therefore, the dimensions of the window that will maximize the area would be W\approx 8.72 and L\approx 15.57.

8 0
3 years ago
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