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s344n2d4d5 [400]
3 years ago
6

What is the area of the sector ?​

Mathematics
1 answer:
worty [1.4K]3 years ago
8 0

They forget to say "not to scale".  I'm guessing this is trig because I don't see another way to do it.

Let's consider x=chord PQ first.  By the Law of Cosines

x^2 = 3^2 + 5^2 - 2(3)(5) \cos 81^\circ = 34 - 30\cos 81^\circ

We have an isosceles triangle formed by two radii of 9 cm and x=PQ.  By the Law of Cosines again,

x^2 = 9^2 + 9^2 - 2(9)(9) \cos B

x^2 = 162 - 162 \cos B

\cos B = \dfrac{162 - x^2}{162} = 1 - \dfrac{x^2}{162}

\cos B = 1 - \dfrac{34 - 30\cos 81^\circ}{162}

B = \arccos \left(1 - \dfrac{34 - 30\cos 81^\circ }{162} \right)

The area of the circle is the fraction given by the angle,

A = \dfrac{B}{360^\circ} \pi r ^2

A \approx \dfrac{ \arccos \left(1 - \dfrac{34 - 30\cos 81^\circ}{162} \right) }{360} (3.142)9^2

A\approx 24.7474332960707

Answer: 24.7 sq cm

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3 years ago
A farmer plans to fence a rectangular corral. The diagonal distance from one corner of the corral to the opposite corner is five
garik1379 [7]

Answer:

Length of diagonal is 7.3 yards.

Step-by-step explanation:

Given: The diagonal distance from one corner of the corral to the opposite corner is five yards longer than the width of the corral. The length of the corral is three times the width.

To find: The length of the diagonal of the corral.

Solution: Let the width of the rectangular garden be <em>x</em> yards.

So, the length of the diagonal is x+5

width of the rectangular corral is 3x

We know that the square of the diagonal is sum of the squares of the length and width.

So,

(3x)^{2} +x^{2} =(x+5)^{2}

9x^{2} +x^{2} =x^{2}+10x+25

9x^{2}-10x-25=0

9x^{2}-10x-25=0

x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a}

x=\frac{10\pm\sqrt{(-10)^{2} -4(9)(-25)} }{2(9)}

x=\frac{10\pm\sqrt{100}}{18}

Since, side can't be negative.

x=\frac{5}{9}+\frac{5}{9}\sqrt{10}

Now, length of the diagonal is

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4 0
3 years ago
What is another way to write (2x - 3)?​
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Answer:

See below

Step-by-step explanation:

Many ways...

x+x-3

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5x-3x-3

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8 0
3 years ago
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Answer:

(-3, +4)Q

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2 years ago
A ball moves in a straight line has an acceleration of a(t) = 2t + 5. Find the position function of the ball if its initial velo
Vlad1618 [11]

Answer:

s(t) = frac{t^3}{3} + \frac{5t^2}{2} - 3t + 12

Step-by-step explanation:

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The position function is the integral of the velocity function.

Acceleration:

As given by the problem, the acceleration function is a(t) = 2t + 5

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v(t) = t^2 + 5t - 3

Position:

s(t) = \int v(t) dt = \int (t^2 + 5t - 3) = \frac{t^3}{3} + \frac{5t^2}{2} - 3t + K

In which K, the constant of integration, is the initial position. Since it is 12:

s(t) = frac{t^3}{3} + \frac{5t^2}{2} - 3t + 12

4 0
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