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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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kirill115 [55]

Answer:

f(x) = x^{4} + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + \sqrt{2} is a zero then - 1 - \sqrt{2} is also a zero

\sqrt{3} is a zero then - \sqrt{3} is also a zero

Thus the corresponding factors are

(x - (- 1 + \sqrt{2}) ), (x - (- 1 - \sqrt{2}) ), (x - \sqrt{3}), (x - (- \sqrt{3})), that is

(x + 1 - \sqrt{2}), (x + 1 + \sqrt{2}), (x - \sqrt{3}), (x + \sqrt{3})

The polynomial is then the product of the roots

f(x) = (x + 1 - \sqrt{2})(x + 1 + \sqrt{2})(x - \sqrt{3})(x + \sqrt{3})

     = ((x + 1)² - (\sqrt{2})²)((x² - (\sqrt{3})²)

     = (x² + 2x + 1 - 2)(x² - 3)

     = (x² + 2x - 1)(x² - 3) ← distribute

     = x^{4} - 3x² + 2x³ - 6x - x² + 3

     = x^{4} + 2x³ - 4x² - 6x + 3

6 0
3 years ago
PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS
muminat

Answer:

6280 mm squared

Step-by-step explanation:

To find the area Of a cylender we multiply pi times r squared times the height, and we can put pi as 3.14

the radius is 10 mm, and the height is 20 mm.

pug it in.

3.14 times 10 squared times 20.

3.14 time 100 time 20

314 times 20

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8 0
2 years ago
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dusya [7]

Answer:

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Step-by-step explanation:

The slope of the line between two points can be found using the slope formula:

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  m = (2 -0)/(-1 -(-3)) = 2/2

  m = 1 . . . . . the slope of the line is 1

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The value of the y-intercept can be found by solving the slope-intercept equation for b.

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The equation of the line with slope 1 and y-intercept 3 can be written as ...

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a bathtub is filled with 110 gallons of water. The tub drains at a rate of 5 gallons every 2 minutes. How long will it take befo
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Answer:

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4 0
3 years ago
Solve for r and t: 6r - 3t = 6 6r + 8t = -16
Slav-nsk [51]
6r - 3t = 6     /*8
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48r - 24t = 48
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---------------------- + 
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t = ( -16 + 6r)/8 = - 16/8 = - 2




3 0
3 years ago
Read 2 more answers
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