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JulsSmile [24]
3 years ago
12

A pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle. Is the perimeter of the

pentagon greater than 26 centimeters?(1) The area of the circle is 16π square centimeters.(2) The length of each diagonal of the pentagon is less than 8 centimeters.
Mathematics
1 answer:
sweet [91]3 years ago
3 0

Answer:

Step-by-step explanation:

Given that a pentagon with 5  sides of equal length and 5 interior angles of equal measure is inscribed in a circle

The circle has area of 16 pi sq cm.

Hence radius of circle = 4 cm

The pengagon each side would be a chord of equal length subtending angle 72 at the centre.

visualize the triangle made by one side of pentagon with centre.  This is isosceles with angles 72, 54 and 54

Use sine angle for this triangle.

\frac{R}{sin 54} =\frac{s}{sin 72}, where R = radius =4 and s = side of pentagon.

s= 4.702

Perimeter = 5s = 23.5114 cm

Perimeter not greater than 26 cm.

If origin is at the centre then two vertices would be (4,0) (4cos 72, 4sin72),(4cos 144, 4 sin 144) and so on.

Longest diagonal = distance between (4,0) and (4cos 144, 4 sin 144)

= (-3.236, 2.351) and (4,0)

=7.608

Yes less than 8 cm

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Which number line represents the solution set for the inequality –4(x + 3) ≤ –2 – 2x?
Yuliya22 [10]
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>>.....-4x -12 </span>≤ -2 -2x

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2 years ago
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A cylinder has a radius of 6 inches and a height of 15 inches. What is the surface area of the cylinder? Express the answer in t
shutvik [7]

Answer:

The surface area for this cylinder is 252*pi square inches.

Step-by-step explanation:

The surface area of a cylinder can be calculated by using the following formula:

surface area = 2*pi*r² + 2*pi*r*h

Applying the data from the problem, we have:

surface area = 2*pi*(6)² + 2*pi*(6)*15

surface area = 2*pi*36 + 180*pi

surface area = 72*pi + 180*pi

surface area = 252*pi

The surface area for this cylinder is 252*pi square inches.

4 0
2 years ago
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a utility worker is 5.5 feet tall and is casting a shadow 4 feet long at the same time a nearby utility pole casts a shadow 20 f
Assoli18 [71]

So this is essentially a proportion problem. They want you to be able to recognize a relationship between the two. The easiest way to go about this is to draw a picture (I have included one). What you want to do is notice that you are given both shadow lengths. This is essentially going to be your first step to creating the proportion.


Understanding that we know the shadow lengths, we can turn these into a fraction such as so:


4ft/20ft.


Now that we know that, we need to look at are unknown. Our unknown is the height of the utility pole. We can solve this by substituting for X since we know the utility worker is 5.5 ft tall.


Your fraction for that would look like:


5.5ft/X


Make sure to always make your top to top match, such as since I put the utility worker's shadow on top, I need to put his height on top.

Now we can solve.

4ft/20ft =5.5ft/X


We need to cross multiply to get an equation we can work with. If we cross multiply, Your equation will look like:


4x = 110ft


This is a simple one step equation. Divide both sides by 4 to get your answer.

x= 27.5ft.

This means your Utility pole's height is 27.5ft.

6 0
3 years ago
4A.
antoniya [11.8K]

The number of paychecks Jalen will have to save until he can purchase the laptop is 6

<h3>How many paychecks will Jalen have to save until he can purchase the laptop? </h3>

<u>Define your variable</u>

To do this, we use the following variables

  • x represents the number of paychecks
  • y represents the cost of the laptop

<u>Set up an equation, and solve it.</u>

In (a), we have:

  • x represents the number of paychecks
  • y represents the cost of the laptop

Using the above variables, the equation is:

y = 200 + 50x

The cost of the laptop is $500.

So, we have:

200 + 50x = 500

Evaluate the like terms

50x = 300

Divide by 50

x = 6

Hence, the number of paychecks Jalen will have to save until he can purchase the laptop is 6

Read more about linear equations at:

brainly.com/question/14323743

#SPJ1

4 0
1 year ago
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