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Juliette [100K]
3 years ago
9

What is the arc length of the arc sub tended in a circle with radius 6 and an angle of 7 pi/ 8

Mathematics
1 answer:
KengaRu [80]3 years ago
7 0

Answer:

Formula for the Arc length is given by:

\text{Arc length} = 2 \pi r \cdot \frac{\theta}{360^{\circ}}

As per the statement:

radius of circle(r) = 6 units

Angle (\theta) = \frac{7 \pi}{8} radian

Use conversion:

1 rad = \frac{180}{\pi}

\frac{7 \pi}{8} = \frac{180}{\pi} \cdot \frac{7 \pi}{8} = \frac{1260}{8} = 157.5^{\circ}

then;

substitute these given values we have;

Use value of \pi = 3.14

\text{Arc length} = 2\cdot 3.14 \cdot (6) \cdot \frac{157.5^{\circ}}{360^{\circ}}

or

\text{Arc length} = 2\cdot 3.14 \cdot (6) \cdot 0.4375

Simplify:

\text{Arc length}=16.485

Therefore, the arc length of the arc substended in a circle with radius 6 units an angle of 7 pi/8 is 16.485 units

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Determine the explicit formula in the sequence 11, 14, 19, 26, 35
slamgirl [31]

Answer:

Pattern is you add odd numbers, as in 1, 3, 5, 7, 9, etc.

Step-by-step explanation:

11 + 3 = 14

14 + 5 = 19

19 + 7 = 26

26 + 9 = 35

hope this helps

3 0
2 years ago
The graphs of f(x)=-2x and g(x)=(1/2)^x are shown. what are the solutions to thr equation -2x=(1/2)^x? select each correct answe
sineoko [7]

Answer:

<h2>-2</h2>

Step-by-step explanation:

hello :

f(x)=-2x and g(x)=(1/2)^x

f(-2)=-2(-2) =4

g(-2)=(1/2)^-2 = 1/2^-2 = 2²=4

4 0
3 years ago
You are looking at the New York ball drop on New Year’s Eve at a distance of 100 m away from the base of the structure. If the b
Fofino [41]

The question is an illustration of related rates.

The rate of change between you and the ball is 0.01 rad per second

I added an attachment to illustrate the given parameters.

The representations on the attachment are:

\mathbf{x = 100\ m}

\mathbf{\frac{dy}{dt} = 2\ ms^{-1}} ---- the rate

\mathbf{\theta = \frac{\pi}{4}}

First, we calculate the vertical distance (y) using tangent ratio

\mathbf{\tan(\theta) = \frac{y}{x}}

Substitute 100 for x

\mathbf{y = 100\tan(\theta) }

\mathbf{\tan(\theta) = \frac{y}{100}}

Differentiate both sides with respect to time (t)

\mathbf{ \sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dy}{dt}}

Substitute values for the rates and \mathbf{\theta }

\mathbf{ \sec^2(\pi/4) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

This gives

\mathbf{ (\sqrt 2)^2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

\mathbf{ 2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

Divide both sides by 2

\mathbf{ \frac{d\theta}{dt} = \frac{1}{100} }

\mathbf{ \frac{d\theta}{dt} = 0.01 }

Hence, the rate of change between you and the ball is 0.01 rad per second

Read more about related rates at:

brainly.com/question/16981791

8 0
2 years ago
Consider Michelle and Gladys, two neighbors who each earn the same salary. Gladys pays less in federal income taxes than Michell
goldenfox [79]

Sad to say it is likely D.  If you are in the United States, I wouldn't know what deductions are available, but here are some possibilities.

1. Gladys is a single Mom. She gets to deduct her child.

2. Gladys owns her own home and gets to deduct her municipal tax. Michelle is renting and may be able to deduct something but not as much.

3. Gladys gets to deduct medical expenses. Michelle does not.

4. Gladys has a travelling allowance that is deductible. Michelle does not.

5. Gladys goes to church and tithes. Michelle does not.

6. Gladys has a registered savings plan. Michelle does not.

The problem is that the two women might very well be in a different tax bracket when all the deductions are considered. That depends on how the US system works. I don't think you are supposed to choose A. All other things being equal, they should be in the same tax bracket.

I don't see how B would come about. Usually state is dependent on Federal (it is in Canada anyway).

C is definitely wrong unless the savings plan is registered. Any savings plan that produces dividends or interest that is not registered is taxable.


8 0
3 years ago
Read 2 more answers
Round 290951.867863 to the nearest hundred.
andreev551 [17]

Answer: 290951.87

Step-by-step explanation:

Hope this helps :D

5 0
2 years ago
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