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lukranit [14]
3 years ago
7

If the diameter of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?

Mathematics
2 answers:
m_a_m_a [10]3 years ago
3 0
C = πD = π6in

Arc = D * 70°/360° = 3.1416*6*7/36=3.67 in
Leya [2.2K]3 years ago
3 0

Answer:

Length of arc of a circle is given by:

L = r \cdot \theta     .....[1]

where

L is the length of an arc

r is the radius of  the circle.

As per the statement:

Diameter of the circle(D) = 6 inches.

we know that:

D  =2r

6 = 2r

Divide both sides by 2 we get;

3 = r

or

r = 3 inches

We have to find the long arc arc subtended by an angle measuring 70°.

Substitute the value of r = 3 inches and \theta = 70^{\circ} in [1] we have;

L =3 \cdot 70

Simplify:

L = 210 inches

Therefore, 210 inches long is the arc subtended by an angle measuring 70 degree.

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Step-by-step explanation:

Part 1) we have

2x^{2} -12x+1=0

Convert to vertex form

step 1  

Factor the leading coefficient and complete the square

2(x^{2} -6x)+1=0

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step 2

2(x^{2} -6x+9)+1-18=0

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step 3

Rewrite as perfect squares

2(x-3)^{2}-17=0

Part 3) we have

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we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

f(x)+60=-x^{2}+16x

Factor the leading coefficient

f(x)+60=-(x^{2}-16x)

Complete the squares

f(x)+60-64=-(x^{2}-16x+64)

f(x)-4=-(x^{2}-16x+64)

Rewrite as perfect squares

f(x)-4=-(x-8)^{2}

f(x)=-(x-8)^{2}+4

The vertex is the point (8,4)

The vertex represent the maximum profit

Part 4) Solve for x

we have

-2(x-2)^{2}+5=0

-2(x-2)^{2}=-5

(x-2)^{2}=2.5

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we know that

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In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

-x^{2}+50x-264=0

-x^{2}+50x=264

Factor -1 of the leading coefficient

-(x^{2}-50x)=264

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(x^{2}-50x+625)=361

Rewrite as perfect squares

(x-25)^{2}=361

square root both sides

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x=25(+)19=44

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Factor the leading coefficient

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Rewrite as perfect square

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Convert to vertex form

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Factor -1 the leading coefficient

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Rewrite as perfect square

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Convert to vertex form

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Complete the square

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Rewrite as perfect squares

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Rewrite as perfect squares

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Rewrite as perfect squares    

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