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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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2 years ago

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Use front-end estimation to estimate the sum. 56.7 + 23.44

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3 years ago

Mary's car will go 261 miles on 14.5 gallons of gasoline in highway driving.

suter [353]

Answer:

a) 91 1/6 gallons

b) 2502 miles

Step-by-step explanation:

You are given a number of miles and a number of gallons for the car. The ratio of these numbers is ...

(261 mi)/(14.5 gal) = 18 mi/gal

We presume this value is constant for this car. Then the questions can be answered by forming and solving a proportion:

a) 1641 miles/(gallons) = 18 mi/(1 gal)

Multiplying by gallons and dividing by 18 mi/gal, we get

1641/18 gal = (gallons) = 91 1/6 gal

It will take 91 1/6 gallons of gasoline for Mary to drive to her friend's house.

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b) Same deal, but the miles are unknown.

(miles)/(139 gal) = (18 mi)/(1 gal)

Multiplying by 139 gal gives ...

(18 mi)·139 = (miles) = 2502 mi

139 gallons of gasoline will let Mary drive 2502 miles.

3 0

2 years ago

A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as s

Pepsi [2]

Answer:

$3\sqrt{3} + 72$

Step-by-step explanation:

I attached an image to aid the understanding of the question.

Looking at the image, we see that the 8 shaded parts are congruent, as affirmed in the question as well. And we are told that T = 3, this implies that the area of the square with T as it's side is 9ft². Since all the 8 squares are congruenrt, it means each square has its area to be 9. Therefore, the total area of the 8 shaded squares will be:

$9 \times 8 = 72ft^{2}$

It remains the area of the shaded square with side S.

From the question, we have the following ratio:

$\frac{9}{S} = \frac{S}{T}[\tex]But[tex]\frac{9}{S} = \frac{S}{3}[\tex]Multiplying through by 3S we have27 = S² and this gives:[tex]S = \sqrt{27} = 3\sqrt{3}$

I did not add ± because length is always positive, so the case of negative is eliminated.

Now the areas of S is $3\sqrt{3}$

Therefore, the total area of the shaded squares is

$3\sqrt{3} + 72$

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3 years ago

Please help me with these two, and please explain how to do it. Thank you.

pychu [463]

Answer:

So for number 1 we can use the trigonometry to find out the radius/diameter of the circle then we can use the formula to get the area then we divide by 2 because its half of a circle. So we can get that the cos(68) = 7/x x being the diameter. We then can multiply it by x on both sides. That gives xcos(68) = 7. So then we can do the inverse and get x = cos^-1(68)*7. That gives us approx 18.686 as the diameter, we can divide by 2 and get 9.343. So then we can use the formula which is A = pi*r^2. So that gives us 87.291*pi 274.233. Then if we divide by 2 we get 137.12 that is the answer to first question.

I was able to simplify it into the factored form for number 2.(x-1)^2+(y-2)^2=sqrt(17))^2. Therefore using the circle equation formula we can determine that the center is 1,2. The radius is sqrt(17). We square it and we get 17. So that means that the area is pi*17. Then we get 51.407 as the area.

<h2><u>Answer to 1: 137.12 round to tenth and you get 137.1</u></h2><h2><u></u></h2><h2><u>Answer to 2: </u></h2><h2><u>Center: 1,2 </u></h2><h2><u>Area: 51.407.</u></h2>

3 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.