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finlep [7]
3 years ago
6

Find the angle theta in radians. ( PLEASE SHOW STEPS )

Mathematics
2 answers:
Kisachek [45]3 years ago
8 0
If you notice, the radius of the circle is 5, and the arc made by θ is 15 units long.

\bf \textit{arc's length}\\\\
s=r\theta ~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
r=5\\
s=15
\end{cases}\implies 15=5\theta \implies \cfrac{15}{5}=\theta 
\implies \stackrel{radians}{3}=\theta
yKpoI14uk [10]3 years ago
3 0
Hello!

As you can see, we have a radius of 6. If we divide, this means that this is 2.5 radians. To convert radians to degrees we use the formula below.

\frac{180}{ \pi }x

First of all we divide 180 by pi.

180/\pi≈57.3

Now we multiply by 2.5

57.3(2.5)=143.25°

Note that the angle we see is obtuse, or greater than 90°.

Therefore, ∠<span>θ</span>≈143.25°

Now we need to convert this back into radians. This can be represented by the equation below.

\frac{ \pi }{180}x

First we divide pi by 180 then multiply by our angle.

\pi/180(143.25)≈2.5

Therefore, our angle theta is about 2.5 radians.

I hope this helps!
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5 0
3 years ago
I need help simplifying both of these. thank you!
4vir4ik [10]
<h3>Answer:</h3>
  1. -100x +100; 3
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<h3>Step-by-step explanation:</h3>

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  a(b + c) = ab + ac

It can also be used to simplify the product of binomials (or other polynomials).

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1. (x -10)^2 -x(x +80) = (x^2 -20x +100) +(-x^2 -80x)

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For the purposes of calculation, it can be easier to factor out 100:

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Then for x = 0.97

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___

2. (2x +9)^2 -x(4x +31) = (4x^2 +36x +81) -4x^2 -31x = 5x +81

For x = 16.2, this is ...

  5(16.2) +81 = 81 +81 = 162

_____

The purpose of the attachment is to show the evaluation is correct.

5 0
3 years ago
two pumps of different sizes, working together, can empty a fuel tank in 3 hours. the larger pump can empty the tank in 4 hours
bonufazy [111]
Suppose the larger pump alone can empty the tank in L hours, and the smaller pump can finish the job in S hours, then each hour the large pump empties 1/L portion of the tank, and the small pump empties 1/S per hour
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Larger pump can empty the tank in 4 hours less than the smaller one, so L=S-4
replace L: 3/(S-4)+3/S=1
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3S/[S(S-4)] +3(S-4)/[S(S-4)]=1
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8 0
3 years ago
Read 2 more answers
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nata0808 [166]
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4 0
3 years ago
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Answer:

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Step-by-step explanation:

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8 0
3 years ago
Read 2 more answers
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