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2 years ago

Given the arc length of a circle is 127π centimeters and the subtended angle is 60˚. Find the Circumference of the circle.

Mathematics

1 answer:

Mumz [18]2 years ago

4 0

The circumference of the circle is 762π cm.

<h3>What is length of arc of a circle?</h3>

The length of arc a circle can is determined with the radius and central angle of the arc.

The radius of the circle is calculated as follows;

$L = \pi r \times \frac{ \theta }{180} \\\\
\pi r \theta = 180 L\\\\
\pi r = \frac{180 L}{\theta}$

The circumference of the circle is calculated as follows;

$C = 2\pi r\\\\
C = 2(\pi r)\\\\
C = 2(\frac{180 \ L}{\theta } )\\\\
C = 2(\frac{180 \times 127\pi}{60 } )\\\\
C = 762 \pi \ cm$

Learn more about circumference of a circle here: brainly.com/question/9782777

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The cereal box shown below is a rectangular prism. Find the surface area of the cereal box.

aksik [14]

Answer:

Surface area is found:

Surface Area = 1700 cm²

Step-by-step explanation:

(The cereal box is shown in the ATTACHMENT)

The surface area of a rectangular prism can be found by added the areas of all 6 sides of the rectangular prism.

L = length = 20 cm

H = height = 30 cm

W = Width = 5 cm

A(1) = L×H

A(1) = 20×30

A(1) = 600 cm²

As the measurements of the side at the back of side 1 has the same measurement of side 1. then:

A(2) = 600 cm²

A(3) = L×W

A(3) = 20×5

A(3) = 100 cm²

As the measurements of the side at the back of side 4 has the same measurement of side 4. then:

A(4) = 100 cm²

A(5) = H×W

A(5) = 30×5

A(5) = 150 cm²

As the measurements of the side at the back of side 5 has the same measurement of side 5. then:

A(6) = 150 cm²

<h3>Surface Area:</h3>

Adding areas of all the sides

A(1) + A(2) + A(3) +A(4) + A(5) + A(6) = 600 + 600 + 100 +100 + 150 +150

Surface Area = 1700 cm²

8 0

4 years ago

Read 2 more answers

The height of a sunflower plant varies directly with it's age.Once it has sprouted from the ground,when a sunflower is 2 week ol

yKpoI14uk [10]

<span> (38/2) x 3 1/2 or (114/6) x 3 1/2=66.5

so your answer is 66.5</span>

7 0

3 years ago

Rewrite each equation in vertex form by completing the square. Then identify the vertex.

ioda

ANSWER

Vertex form;

$y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}$

Vertex

$V( - \frac{3}{2} , - \frac{35}{4} )$

EXPLANATION

Given:

$f(x) = 3 {x}^{2} + 9x - 2$

We complete the square as follows:

$y = 3( {x}^{2} + 3x) - 2$

$y = 3( {x}^{2} + 3x + \frac{9}{4} ) - 2 - 3 \times \frac{9}{4}$

The vertex form is:

$y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}$

The vertex is

$V( - \frac{3}{2} , - \frac{35}{4} )$

6 0

4 years ago

Read 2 more answers

Lucy is raising money for a school trip by selling lollipops and bags of

sukhopar [10]

<h3>16 lollipops and 9 bags of chips are sold</h3>

<em><u>Solution:</u></em>

Let "x" be the number of lollipops sold

Let "y" be the number of bags of chips sold

Cost of 1 lollipop = $ 1.50

Cost of 1 bag of chip = $ 1.75

<em><u>Yesterday Lucy made $39.75 from selling a total of 25 lollipops and bags of chips</u></em>

Therefore,

x + y = 25

y = 25 - x -------- eqn 1

<em><u>Yesterday Lucy made $39.75</u></em>

Therefore,

number of lollipops sold x Cost of 1 lollipop + number of bags of chips sold x Cost of 1 bag of chip = 39.75

$x \times 1.50 + y \times 1.75 = 39.75$

1.5x + 1.75y = 39.75 -------- eqn 2

<em><u>Substitute eqn 1 in eqn 2</u></em>

1.5x + 1.75(25 - x) = 39.75

1.5x + 43.75 - 1.75x = 39.75

0.25x = 4

<em><u>Substitute x = 16 in eqn 1</u></em>

y = 25 - 16

Thus 16 lollipops and 9 bags of chips are sold

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3 years ago

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Kaylis [27]

Answer:

option d

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7 0

3 years ago