All categories

3 years ago

If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?

2 answers:

7 0

81 degrees
1 degree = 2 pi / 360
81 degrees = 162 pi / 360
=9 pi / 20

L (arc) = radius x angle
= 10 x 9 pi / 20
90 pi /20
9/2 pi : D

The answer is D

OlgaM077 [116]3 years ago

5 0

Answer:

The length of arc is $L=\dfrac{9}{2}\pi$ feet

D is correct

Step-by-step explanation:

Given: If the radius of a circle is 10 feet and arc subtended by an angle measuring 81°

Formula:

$\theta=\dfrac{\text{Length of arc}}{\text{Radius}}$

where,

Length of arc = L?

Radius of circle, R= 10 feet

Central angle, Ф=81°

First we will change 81 degree to radian

$Radian = \dfrac{\pi}{180}\times degree$

In radian $=\dfrac{\pi}{180}\times 81$

Substitute the value into formula

$\dfrac{\pi}{180}\times 81=\dfrac{L}{10}$

$L=\dfrac{810}{180}\pi$

$L=\dfrac{9}{2}\pi$ feet

Hence, The length of arc is $L=\dfrac{9}{2}\pi$ feet

You might be interested in

The equation πr²Gives the area,A of a circle with a radius,r,. Solve the function for π

zalisa [80]

$\bf \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies \qquad \cfrac{A}{r^2}=\pi$

7 0

3 years ago

A function is a type of ___________.

miv72 [106K]

Answer:

A function is a type of vertical line test.

5 0

2 years ago

Read 2 more answers

Use the equation below to find A, if b=6 and h=7. A=bh A = Х ?

CaHeK987 [17]

Answer:

A=42

Step-by-step explanation:

A=(6)(7)=42

7 0

2 years ago

Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ

-Dominant- [34]

Answer:

$\tan(\beta)$

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.

${\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}$ and ${\sec(\theta)}={\dfrac{1}{\cos(\theta)}$

Recall the following reciprocal identity:

$\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}$

So, the original expression can be written in terms of only sines and cosines:

$\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)$

$\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }$

$\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}$

$\sin(\beta) *\dfrac{1 }{\cos(\beta) }$

$\dfrac{\sin(\beta)}{\cos(\beta) }$

Working toward one of the answers provided, this is the tangent function.

The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to $\tan(\beta)$ .

8 0

2 years ago

11. For each table Ariella waits on at a restaurant, she is paid $4.00 plus 18% of the

lisabon 2012 [21]

Answer:

m=0.18b+4

She'll earn $10.30

Step-by-step explanation:

m=0.18b+4

m=0.18(35)+4

m=6.3+4

m=10.3

5 0

3 years ago