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Dovator [93]
3 years ago
11

A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the

Mathematics
1 answer:
creativ13 [48]3 years ago
6 0

Answer:

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

2r+s=18

s=r \theta

2r+r \theta=18

solve for r

r=\frac{18}{2+\theta}

step 2

Find the value of s

s=r \theta

substitute the value of r

s=\frac{18}{2+\theta}\theta

step 3

we know that

The area of complete circle is equal to

A=\pi r^{2}

The complete circle subtends a central angle of 2π radians

so

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}

substitute the value of r

A=\frac{(\frac{18}{2+\theta})^2\theta}{2}

A=\frac{162 \theta}{(\theta+2)^2}

Convert to function notation

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

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Lady_Fox [76]
5/6 = 83% 
1/6= 16%

83% of the apple pie was left from dinner. 
Victor is gonna eat 16% of the pie tomorrow 
You have to subtract 16% from 83%
In other words 5/6-1/6


The denominators are same so you don't have to do anything to them  
5/6 - 1/6 

5-1=4

4/6 of the pie would be left 
In simplest form it would be 

4/6     <span> ÷2</span>
=2/3

2/3 is in simplest form 

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Unit 4: Congruent Triangles Homework 2: Angles of Triangles
garri49 [273]

The value of the third angle that can be found in the information given about the congruent triangles will be 45°.

<h3>How to solve the triangle?</h3>

From the complete information, the angles that are given in the triangle are 76° and 59°.

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For the following paired data, (1) Calculate the correlation coefficient, r, and (2) at the 0.05 significance level, determine w
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Answer:

Linear correlation exists

Step-by-step explanation:

Given the data :

X : | 2 4 5 6

Y : | 6 9 8 10

Using technology to fit the data and obtain the correlation Coefficient of the regression model,

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To test if there exists a linear correlation :

Test statistic :

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α = 0.05

Pvalue > α ; We reject the null and conclude that linear correlation exists

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3 years ago
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