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Furkat [3]
3 years ago
13

Find the length of the​ arc, s, intercepted by the given central​ angle, thetaθ​, in a circle of​ radius, r. θ=30 ​rad; r=18 m.

Mathematics
1 answer:
Charra [1.4K]3 years ago
7 0

Answer:

540 m

Step-by-step explanation:

We are given that

Central angle,\theta=30rad

Radius of circle=18 m

We have to find the length of the arc s.

We know that

Length of arc,s=r\theta

Using the formula then, we get

Length of arc,s=18\times 30=540 m

Hence, the length of arc=540 m

You might be interested in
The length of a rectangle is four times its width. If the area of the rectangle is 324m^2, find its perimeter.
Anuta_ua [19.1K]

Answer:

perimeter=90

Step-by-step explanation:

We know that the length is four times the width, so:

l=4w

We also know the area, which is 324 m². The formula for area:

A=l*w

Insert the known values:

324=(4w)*w

Solve for w. Simplify by removing parentheses:

324=4w*w\\324=4w^2

Divide 4 from both sides to isolate the variable:

\frac{324}{4}=\frac{4w^2}{4}  \\\\81=w^2

Find the square root of both sides:

\sqrt{81} =\sqrt{w^2} \\\\w=9

The width is 9 m.

We know the width. Now find the length by using the area formula and inserting known values:

324=l*9

Solve for l. Divide both sides by 9:

\frac{324}{9}=\frac{l*9}{9}\\\\  l=36

The length of the rectangle is 36. (You can check: 4 times 9 is 36)

Now find the perimeter:

P=2l+2w

Insert values:

P=2(36)+2(9)\\\\P=72+18\\\\P=90

The perimeter is 90 m.

5 0
3 years ago
What is the justification for each step in solving the inequality?
alekssr [168]
HELLO  ANNA!!

Given inequality
=> −2(x+1)≥3x+8
=>
- 2x - 2 \geqslant 3x + 8 \\ \\ add \: 2 \: in \: both \: sides \\ \\ - 2x \geqslant 3x + 10 \\ \\ subtract \: with \: - 3x \: in \: both \: sides \: \\ \\ - 5x \geqslant 10 \\

now multiply with - on both sides.

As we know now sign will change
=> 5x >_ -10

Now divide by 5 on both sides
=> x >_ -2
HOPE IT HELPED YOU.
4 0
3 years ago
Read 2 more answers
I have the formula <br><br> A fraction • π r^2
MatroZZZ [7]

Answer:

22.2 ft²

Step-by-step explanation:

The area (A) of a sector is calculated as

A = area of circle × fraction of circle

  = πr² × \frac{50}{360}

  = π × 7.13² × \frac{5}{36}

  = \frac{7.13^2(5)\pi }{36} ≈ 22.2 ft² ( nearest tenth )

4 0
3 years ago
at the start of 2014 mikes car was worth 12000 thee value of the car decreased by 30% every year work out the value of his car a
Bas_tet [7]

Answer:

4116

Step-by-step explanation:

2014

12000÷10=1200 (10%)

1200x3=3600

12000-3600=8400

2015

8400÷10=840

840x3=2520

8400-2520=5880

2016

5880÷10=588

588x3=1764

5880-1764=4116

7 0
3 years ago
One angle of an isosceles triangle measures 100°. Which other angles could be in that isosceles triangle?
REY [17]

Answer:40 degrees

Step-by-step explanation:

4 0
3 years ago
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