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2 years ago

on a distant planet, a central angle intercepts an arc of miles. what is the radius of the planet at its equator?

1 answer:

6 0

If on a distant planet, a 10° central angle intercepts an arc of (136π) miles, then the radius of the planet at its equator is 2448 Miles.

As per the question-statement, on a distant planet, a 10° central angle intercepts an arc of (136π) miles. [Refer to the photo attached]

We are required to find the radius of the planet at its equator based on the above data.

To solve this question, we need to know the relation between arc length, radius and angle, and we will form a linear equation in one variable, based on the conditions mentioned in the question statement, and solving the equation, we will obtain our desired answer

[Arc length = (Radius * Angle)],

We are already provided with data about the arc length (136π miles) and central angle (10°), and let us assume radius of the planet be "r".

We will convert the central angle from degrees to radians, i.e.,

10° = $\frac{180}{18}=\frac{\pi }{18} rads$ .

Now, using the data provided in the question statement about arc length and central angle, and our assumed radius in the relation between arc length, radius and angle, we get

$136\pi =(r*\frac{\pi }{18} )\\or, r = \frac{136\pi }{\frac{\pi }{18} } \\or, r = 136\pi * \frac{18}{\pi} \\or, r = (136*18) = 2448$ miles.

Therefore, radius of the planet at its equator is 2448 Miles.

Linear Equation: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and thus, comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.
Arc: An arc is a part of the circumference of a circle or of any over curve.

To learn more about Arc lengths, click on the link below.

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Answer:

Step-by-step explanation:

A barn is in form of rectangular prism

Given the dimension

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Width W = 38 ft

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Width W = 19 ft

Given that,

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So, we need to total surface area to be shaded

First for the rectangular prism, only the four exteriors wall that can be painted, the bottom and the top where the triangular rest on cannot be painted,

So, Area of rectangular prism

A = 2(LW + LH + WH)

But in this case, no length and width covers so, LW = 0

A = 2(LH + WH)

A1 = 2(84 × 20 + 38 × 20)

A1 = 2(1680 + 760)

A1 = 2 × 2440

A1 = 4880 ft²

Now, area to be covered in the triangular prism

Only two regular face is needed to be covered

Then,

Area of a triangle is ½b×h

Then, the two sides to be cover will have

A2 = 2 × (½ × 19 × 12)

A2 = 228ft²

So, total area to be painted is

A = A1 + A2.

A = 4880 + 228

A = 5108 ft²

So,

1 gallon = 232ft²

x gallon = 5108ft²

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x gallon = 5108ft² × 1gallon / 232ft²

x gallon = 22.017

So, approximate 22 gallon will be enough, but for design reason, it is advisable to get 23 gallons,

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4 years ago

Charlie is a car salesman. He earns $800 plus a 9% commission on all of his sales for the week . If charlie received a paycheck

Iteru [2.4K]

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3 years ago

She completes the problem as seen in the steps below.

prisoha [69]

Answer:

• All her steps are right, and the answer is right as well

Step-by-step explanation:

$2(x + 1) + 1 = 5 \\ 2(x + 1) = 5 - 1 \\ 2(x + 1) = 4 \\ \\ \frac{2(x + 1)}{2} = \frac{4}{2} \\ \\ x + 1 = 2 \\ x = 2 - 1 \\ x = 1$

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3 years ago

Read 2 more answers

Linear equations... HELP!

fgiga [73]

The answer is m = 250 - 25w.
This is because this answer is in y=mx+b format (slope-intercept form) and has the correct values.
In slope-intercept form, m is the slope and b is y-intercept.
In m = 250 - 25w, the y-intercept is 250 and the slope is -25.
This matches the graph.
Y-intercept is where a line crosses the y-axis, which is 250 in this case.
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4 0

4 years ago

On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percenta

sashaice [31]

Answer:

Percentage of scores that fall between 70 and 80 = 24.34%

Step-by-step explanation:

We are given a test with a population mean of 75 and standard deviation equal to 16.

Let X = Percentage of scores

Since, X ~ N( $\mu,\sigma^{2}$ )

The z probability is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1) where, $\mu$ = 75 and $\sigma$ = 16

So, P(70 < X < 80) = P(X < 80) - P(X <= 70)

P(X < 80) = P( $\frac{X-\mu}{\sigma}$ < $\frac{80-75}{16}$ ) = P(Z < 0.31) = 0.62172

P(X <= 70) = P( $\frac{X-\mu}{\sigma}$ < $\frac{70-75}{16}$ ) = P(Z < -0.31) = 1 - P(Z <= 0.31)

= 1 - 0.62172 = 0.37828

Therefore, P(70 < X < 80) = 0.62172 - 0.37828 = 0.24344 or 24.34%

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4 years ago

on a distant​ planet, a central angle intercepts an arc of miles. what is the radius of the planet at its​ equator?

on a distant planet, a central angle intercepts an arc of miles. what is the radius of the planet at its equator?