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3 years ago

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, $\theta=30$ rad

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

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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

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.

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.