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3 years ago

Given an arc length of 6 pie and a radius of 2 find the measure of the central angle formed by the arc

Mathematics

1 answer:

Semmy [17]3 years ago

6 0

Θ=3 $\pi$ radians

Step-by-step explanation:

Step 1:

Let the arc length (S) be 6 $\pi$ units

Radius of Arc(r) = 2 units

By the basic formula to find the central angle we have

$S=r*$ Θ

where, S= Arc length

r= Radius of arc

Θ = Central angle

Step 2:

From the formula to find Θ,

Θ = (S/r)

Θ = ( 6 $\pi$ ) / ( 2 )

Θ = 3 $\pi$ radians

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The graph shows the charges of an instructor. The instructor charges an initial fee and then an hourly rate of $8.00 an hour for

Tasya [4]

Answer:

The instructor’s initial charge is $20

see the attached figure

Step-by-step explanation:

Let

x ----> the time in hours

y ----> the total cost in dollars

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or the unit rate of the linear equation

b is the y-intercept or initial value (in this problem is the instructor’s initial charge)

we have

The slope is equal to the hourly rate

$m=\$8.00\ per\ hour$

substitute

$y=8.00x+b$

To find out the y-intercept join the given points in the graph and find out the value of y when the value of x is equal to zero

see the attached figure

The y-intercept is the point (0,20)

therefore

The instructor’s initial charge is $20

<u><em>Verify</em></u>

take any point on the graph

(5,60)

For x=5, y=60

substitute in the linear equation and solve for b

$60=8.00(5)+b$

$60=40+b$

$b=\$20$ ----> is ok

therefore

The instructor’s initial charge is $20

4 0

3 years ago

Read 2 more answers

Joel says to Kevin, "Give me $100, and I shall become twice as rich as you."

Bess [88]

DON'T OPEN IT, IT IS EVERYWHERE, IT IS AGAINST BRAINLYS TOS, AND IT IS A VIRUS also
The answer is $310

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2 years ago

Selena played 32 games of chess. If she won x games, which expression represents her losses?

melamori03 [73]

The answer is ........ (C)

4 0

3 years ago

Read 2 more answers

The top and bottom margins of a poster are each 15 cm and the side margins are each 10 cm. If the area of printed material on th

12345 [234]

Answer:

the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.

Step-by-step explanation:

From the given question.

Let p be the length of the of the printed material

Let q be the width of the of the printed material

Therefore pq = 2400 cm ²

q = $\dfrac{2400 \ cm^2}{p}$

To find the dimensions of the poster; we have:

the length of the poster to be p+30 and the width to be $\dfrac{2400 \ cm^2}{p} + 20$

The area of the printed material can now be: $A = (p+30)(\dfrac{2400 }{p} + 20)$

= $2400 +20 p +\dfrac{72000}{p}+600$

Let differentiate with respect to p; we have

$\dfrac{dA}{dp}= 20 - \dfrac{72000}{p^3}$

Also;

$\dfrac{d^2A}{dp^2}= \dfrac{144000}{p^3}$

For the smallest area $\dfrac{dA}{dp }=0$

$20 - \dfrac{72000}{p^2}=0$

$p^2 = \dfrac{72000}{20}$

p² = 3600

p =√3600

p = 60

Since p = 60 ; replace p = 60 in the expression q = $\dfrac{2400 \ cm^2}{p}$ to solve for q;

q = $\dfrac{2400 \ cm^2}{p}$

q = $\dfrac{2400 \ cm^2}{60}$

q = 40

Thus; the printed material has the length of 60 cm and the width of 40cm

the length of the poster = p+30 = 60 +30 = 90 cm

the width of the poster = $\dfrac{2400 \ cm^2}{p} + 20$ = $\dfrac{2400 \ cm^2}{60} + 20$ = 40 + 20 = 60

Hence; the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.

4 0

3 years ago

Consider the line -6x-2y=-4.

Rzqust [24]

Answer:

Parallel Slope: -3 Perpendicular Slope: 1/3

Step-by-step explanation:

First, solve for y to get the simplified equation for the line.

Once you solve, the equation should be y=-3x+2

Seeing this, we know that the slope of this line is -3. A line parallel will have the same slope as the original equation, and a line perpendicular will have a slope that is the opposite reciprocal.

Hope that helps!

3 0

3 years ago