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4 years ago

If a sector in a circle of radius 10 has an area of 5pi, what is the measure of the central angle that forms the sector?

Mathematics

2 answers:

Degger [83]4 years ago

4 0

Answer:

pi/10

Step-by-step explanation:

Nadya [2.5K]4 years ago

3 0

Answer:

$\frac{\pi }{10}$

Step-by-step explanation:

The area (A) of the sector is calculated using the formula

A = area of circle × fraction of circle

let x be the measure of the central angle, then

A = πr² × $\frac{x}{2\pi }$ ← substitute values

5π = π × 10² × $\frac{x}{2\pi }$

5π = 100π × $\frac{x}{2\pi }$ (cancel 50π and 2π )

5π = 50x ( divide both sides by 50 )

x = $\frac{5\pi }{50}$ = $\frac{\pi }{10}$ ← central angle

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Mars2501 [29]

Answer:

See explanation

Step-by-step explanation:

1. Given the expression

$\dfrac{\sqrt[7]{x^5} }{\sqrt[4]{x^2} }$

Note that

$\sqrt[7]{x^5}=x^{\frac{5}{7}} \\ \\\sqrt[4]{x^2}=x^{\frac{2}{4}}=x^{\frac{1}{2}}$

When dividing $\sqrt[7]{x^5}$ by $\sqrt[4]{x^2},$ we have to subtract powers (we cannot subtract 4 from 7, because then we get another expression), so

$\dfrac{5}{7}-\dfrac{2}{4}=\dfrac{5}{7}-\dfrac{1}{2}=\dfrac{5\cdot 2-1\cdot 7}{14}=\dfrac{3}{14}$

and the result is $x^{\frac{3}{14}}=\sqrt[14]{x^3}$

2. Given equation $3\sqrt[4]{(x-2)^3} -4=20$

Add 4:

$3\sqrt[4]{(x-2)^3} -4+4=20+4\\ \\3\sqrt[4]{(x-2)^3}=24$

Divide by 3:

$\sqrt[4]{(x-2)^3} =8$

Rewrite the equation as:

$(x-2)^{\frac{3}{4}}=8\\ \\(x-2)^{\frac{3}{4}}=2^3$

Hence,

$\left((x-2)^{\frac{3}{4}}\right)^{\frac{4}{3}}=(2^3)^{\frac{4}{3}}\\ \\x-2=2^{3\cdot \frac{4}{3}}\\ \\x-2=2^4\\ \\x-2=16\\ \\x-2+2=16+2\\ \\x=18$

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3 years ago

What is the midpoint of AB?

BabaBlast [244]

Answer:

A picture of the problem might help

7 0

3 years ago

Solve 30% which = 60

Brrunno [24]

30% of x = 60
60/.30 = x
18 = 30% of 60

8 0

3 years ago

Read 2 more answers

Enter the phrase as an algebraic expression.

liraira [26]

Answer:

The algebraic expression is p/9

Step-by-step explanation:

8 0

2 years ago

Match each algebraic expression with the method to use for factoring.

LekaFEV [45]

Answer:

Prime: 3
GCF: 1
Factoring Trinomials: 4
Difference of Squares: 2
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Step-by-step explanation:

1. Each term has an even coefficient, so a factor of 2 can be removed:

2(3x^2 +7x -15)

The remaining quadratic factor is prime.

2. Each of these two terms is a square, so this is the difference of two squares.

3. This cubic has one irrational negative real root. It is prime.

4. This trinomial factors in the usual way: (x +15)(x -2). It is factored by "factoring trinomials."

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3 years ago