MATHEMATICS MIDDLE SCHOOL

Find the radius of a circle on which a central angle measuring 2π/3 radians intercepts an arc on the circle with a length of 35π kilometers.

Answers

Answer 1

Answer:

The radius of the circle is of 52.5 kilometers.

This question is solved using the length of arc formula, which states that:

$L = r\theta$

In which:

L is the length of the arc.
r is the radius.
$\theta$ is the measure of the central angle, in radians.

-------------------------

In this question:

Central angle of 2π/3 radians, so $\theta = (2\pi)/(3)$
Length of $35\pi$ .

Thus, to find the radius, we solve for r.

$L = r\theta$

$35\pi = r(2\pi)/(3)$

$2\pi r = 105\pi$

Simplifying both sides by $\pi$

$r = (105)/(2) = 52.5$

The radius of the circle is of 52.5 kilometers.

A similar question is given at brainly.com/question/15162755

Answer 2

Answer:

Answer:

Radius= 105/2 km

Step-by-step explanation:

The formula for arc length (in radians) is Arc Length = Radius*Angle(in radians)

The arc length is 35π km and the angle is 2π/3

Plug in the values and solve for r

35π = (2π/3)*r

35π*3/2π= r

r = 105/2 km or 52.5 km

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restaurant etiquette dictates that you should leave a 15% tip for the server if the service is acceptable. If that is the case, how much should you tip if your total is $24.00

Answers

3.60
bc using a part to whole chart you cross multiply 24*15 get 360 then divide it by 100 and get 3.60

Answer:

Your tip should be $3.60

Step-by-step explanation:

24.00*.85=20.4

24.00-20.4=3.60

Solve the system of equations using substitution.
y= 3/4x-7
4x- 6y=50

Answers

$\begin{cases} y= (3 )/(4)x-7 \n 4x- 6y=50 \end{cases}\n \n\begin{cases} y= (3 )/(4)x-7 \n 4x- 6((3 )/(4)x-7)=50 \end{cases}\n \n\begin{cases} y= (3 )/(4)x-7 \n 4x- (9 )/(2)x+42=50 \end{cases}\n \n \begin{cases} y= (3 )/(4)x-7 \n 4x- 4(1 )/(2)x =50 -42\end{cases}$

$\begin{cases} y= (3 )/(4)x-7 \n - (1 )/(2)x =8 \ \ /*(-2)\end{cases}\n \n \begin{cases} y= (3 )/(4)*(-16)-7 \n x =-16\end{cases}\n \n \begin{cases} y= -12-7 \n x =-16\end{cases} \n \n\begin{cases} y= -19 \n x =-16\end{cases}$

Y=3/4x-7
4x-6y=50

4x-6y=50
4x-6(3/4x-7)=50
4x-18/4x+42=50
-1/2x=8
x=-16

y=3/4(-16)-7
y=-12-7
y=-19

The Art club is having a fundraiser, and 198 people are attending. if 12 people can sit at EACH table, what is the least number of the tables needed?

Answers

Answer:

Step-by-step explanation:

because 12 people can sit at each table, so youd divide 198 by 12 to see how many tables youd need, and you get 16.5. you cant have 16.5 tables, so always round up when it comes to objects, humans, things, etc. so you get 17

Enter the solution to the equation in the box.

5(x - 8 ) =7 (x - 4)

Answers

5x-40=7x-28
-12=2x
X=-6 is your answer

Final answer:

The solution to the equation 5(x - 8 ) =7 (x - 4) is x = 6.

Explanation:

To solve the equation 5(x - 8 ) =7 (x - 4), you first need to distribute the numbers outside the parentheses to the terms inside. It leads to : 5*x - 40 = 7*x - 28. To find the value of x, first combine like terms and then isolate x on one side of the equation. By doing so, the equation yields 40 - 28 = 7*x - 5*x, simplifies to 12 = 2x, and thus x = 6.