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3 years ago

7

In a circle, a central angle whose measure is pi/2 radians intercepts an arc whose length is 3pi/2 centimeters. How many centime

ters are in the radius of the circle?

1 answer:

Alja [10]3 years ago

6 0

Attached the solution and work.

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Surface area of a cylinder 1m radius and 5m side

damaskus [11]

Answer:

37.7 m

Step-by-step explanation:

Use this formula:

A=2πrh+2π $r^{2}$

3 0

4 years ago

Read 2 more answers

In 1955 an antique car that originally cost 3,943 is valued at 64,125 if in excellent condition, winch is 2 1/4 times as much as

nika2105 [10]

Answer:

The value of the car in very nice condition is $28,500.

Step-by-step explanation:

Consider the provided information.

In 1955 an antique car that originally cost 3,943 is valued at 64,125 if in excellent condition, winch is 2 1/4 times as much as a car in very nice condition.

The mixed fraction can be written as:

$2 \frac{1}{4}=\frac{9}{4}$

Let x is the value of car in very nice condition.

$64,125 =\frac{9}{4}x$

$x=\frac{64,125\times 4}{9}$

$x=28,500$

Hence, the value of the car in very nice condition is $28,500.

7 0

3 years ago

Fun center rents popcorn machines for &20 per hour. In addition to the hourly charge, there is a rental fee of $35. Is this

Gelneren [198K]

Answer:

No. It is not proportional.

4 0

3 years ago

The graph of this function is shifted downwards and the axis of symmetry remains x=1. Which function below the equation of the n

Natali5045456 [20]

Answer:

$y=-x^{2}+2x$

$y=-x^{2}+2x-4$

$y=-x^{2}+2x-3$

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex

The axis of symmetry is equal to the x-coordinate of the vertex

so

$x=h$

If a> 0 then the parabola open upward (vertex is a minimum)

If a< 0 then the parabola open downward (vertex is a maximum)

In this problem we have

$y=-x^{2} +2x+3$

The vertex is the point $(1,4)$ ------> observing the graph

The axis of symmetry is $x=1$

If the graph of this function is shifted downwards and the axis of symmetry remains x=1

then

The x-coordinate of the vertex of the new graph must be equal to 1

The y-coordinate of the vertex of the new graph must be less than 4

The parabola of the new graph open downward

therefore

<u>Verify each case</u>

case a) $y=-x^{2}+2x$

Convert to vertex form

$y=-(x^{2}-2x)$

$y-1=-(x^{2}-2x+1)$

$y-1=-(x-1)^{2}$

$y=-(x-1)^{2}+1$

The vertex is (1,1)

therefore

The function could be the equation of the new graph

case b) $y=-x^{2}-2x+3$

Convert to vertex form

$y-3=-(x^{2}+2x)$

$y-3-1=-(x^{2}+2x+1)$

$y-4=-(x+1)^{2}$

$y=-(x+1)^{2}+4$

The vertex is (-1,4)

therefore

The function cannot be the equation of the new graph

case c) $y=-x^{2}+2x-4$

Convert to vertex form

$y+4=-(x^{2}-2x)$

$y+4-1=-(x^{2}-2x+1)$

$y+3=-(x-1)^{2}$

$y=-(x-1)^{2}-3$

The vertex is (1,-3)

therefore

The function could be the equation of the new graph

case d) $y=-x^{2}+2x+4$

Convert to vertex form

$y-4=-(x^{2}-2x)$

$y-4-1=-(x^{2}-2x+1)$

$y-5=-(x-1)^{2}$

$y=-(x-1)^{2}+5$

The vertex is (1,5)

therefore

The function cannot be the equation of the new graph

case e) $y=-x^{2}+2x-3$

Convert to vertex form

$y+3=-(x^{2}-2x)$

$y+3-1=-(x^{2}-2x+1)$

$y+2=-(x-1)^{2}$

$y=-(x-1)^{2}-2$

The vertex is (1,-2)

therefore

The function could be the equation of the new graph

8 0

3 years ago

The value of a rare comic book is expected to follow a geometric sequence from year to year. It is presently worth $800 and is e

makvit [3.9K]

You add 1/4 each year:
800 to 1000 in one year
1000 to 1250 in 2
1250 to around 1812.5

6 0

3 years ago