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deff fn [24]
3 years ago
6

put the steps, for changing the formula for the arc length of a circle in degrees to the formula for the arc length of a circle

in radians in the correct order.​

Mathematics
1 answer:
Ede4ka [16]3 years ago
5 0

9514 1404 393

Answer:

  top down: 1, 5, 6, 4, 8, 2, 3, 7

Step-by-step explanation:

It appears the expected order may be ...

__

Write the formula for the arc length of a circle with central angle, θ, in degrees.

  \textit{Arc  Length}=\dfrac{\theta}{360^{\circ}}\cdot 2\pi r

Replace 360° with 2π radians.

  \dfrac{\theta}{360^{\circ}}=\dfrac{\theta}{2\pi}

Replace the angle ratio in degrees with the angle ratio in radians.

  \textit{Arc  Length}=\dfrac{\theta}{2\pi}\cdot 2\pi r

Simplify by cancelling

  \textit{Arc Length}=\theta r

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Find m∠4 if m∠1 = 100°
11111nata11111 [884]

Answer:

obtuse angle

Step-by-step explanation:

7 0
3 years ago
find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[1,2,-2]. B
SashulF [63]

Answer:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3

|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{ab}{|a| |b|}

And the angle is given by:

\theta = cos^{-1} (\frac{ab}{|a| |b|})

If we replace we got:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

3 0
3 years ago
The nth term of a sequence is n^2 + 20.
Olegator [25]

Answer:

\large\boxed{a)\ 21,\ 24,\ 29}\\\boxed{b)\ \text{five terms}}

Step-by-step explanation:

a_n=n^2+20\\\\a)\\\\\text{Substitute}\ n=1,\ n=2\ \text{and}\ n=3\ \text{to the }\ a_n:\\\\a_1=1^2+20=1+20=21\\\\a_2=2^2+20=4+20=24\\\\a_3=3^2+20=9+20=29

b)\\\\\text{You have to solve the inequality:}\\\\n^2+20

3 0
3 years ago
(ASAP)Someone help me out please
ludmilkaskok [199]

Answer:

Y= 1/3x + 4

Step-by-step explanation:

4 is the y intercept and it goes across one and down 3 for the get the slope of  1/3.

8 0
3 years ago
A boat travels 36 miles in 1.5 hours ans then in 14 miles in 0.75 hour. what is the average speed?
allochka39001 [22]

The average speed can be obtained by the formula:

V_{\text{average}}=\dfrac{\text{total distance}}{\text{total time}}.

If a boat travels 36 miles in 1.5 hours ans then in 14 miles in 0.75 hour, then find:

  • total distance is 36+14=50 miles;
  • total time: 1.5+0.75=2.25 hours.

Therefore,

V_{\text{average}}=\dfrac{50}{2.25}=\dfrac{5000}{225}=\dfrac{200}{9}=22.(2) miles per hour.

Answer: V_{\text{average}}=\dfrac{200}{9}=22.(2) miles per hour.

6 0
3 years ago
Read 2 more answers
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