Identify the solid produced by rotating the figure around the given axis.

Answer:

Example 1

A backyard farmer wants to enclose a rectangular space for a new garden. She has purchased 80 feet of wire fencing to enclose 3 sides, and will put the 4th side against the backyard fence. Find a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length

L.

In a scenario like this involving geometry, it is often helpful to draw a picture. It might also be helpful to introduce a temporary variable,

W, to represent the side of fencing parallel to the 4th side or backyard fence.

Since we know we only have 80 feet of fence available, we know that

L + W + L = 80, or more simply, 2L + W = 80. This allows us to represent the width, W, in terms of L: W = 80 – 2L

Now we are ready to write an equation for the area the fence encloses. We know the area of a rectangle is length multiplied by width, so

A = LW = L(80 – 2L)

A(L) = 80L – 2L2

This formula represents the area of the fence in terms of the variable length

L.

Example 2

Returning to our backyard farmer from the beginning of the section, what dimensions should she make her garden to maximize the enclosed area?

Earlier we determined the area she could enclose with 80 feet of fencing on three sides was given by the equation

A(L) = 80L – 2L2. Notice that quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

In finding the vertex, we take care since the equation is not written in standard polynomial form with decreasing powers. But we know that

a is the coefficient on the squared term, so a = -2, b = 80, and c = 0.

Finding the vertex:

h

=

−

80

2

(

−

2

)

=

20

,

k

=

A

(

20

)

=

80

(

20

)

−

2

(

20

)

2

=

800

The maximum value of the function is an area of 800 square feet, which occurs when

L = 20 feet. When the shorter sides are 20 feet, that leaves 40 feet of fencing for the longer side. To maximize the area, she should enclose the garden so the two shorter sides have length 20 feet, and the longer side parallel to the existing fence has length 40 feet.

Example 3

A ball is thrown upwards from the top of a 40 foot high building at a speed of 80 feet per second. The ball’s height above ground can be modeled by the equation

H(t) = –16t2 + 80t + 40.

What is the maximum height of the ball?

When does the ball hit the ground?

To find the maximum height of the ball, we would need to know the vertex of the quadratic.

h

=

−

80

2

(

−

16

)

=

80

32

=

5

2

,

k

=

H

(

5

2

)

=

−

16

(

5

2

)

2

+

80

(

5

2

)

+

40

=

140

The ball reaches a maximum height of 140 feet after 2.5 seconds.

To find when the ball hits the ground, we need to determine when the height is zero—when

H(t) = 0. While we could do this using the transformation form of the quadratic, we can also use the quadratic formula:

t

=

−

80

±

√

80

2

−

4

(

−

16

)

(

40

)

2

(

−

16

)

=

−

80

s

q

r

t

8960

−

32

Since the square root does not simplify nicely, we can use a calculator to approximate the values of the solutions:

t

=

−

80

−

s

q

r

t

8960

−

32

a

p

p

r

o

x

5.458

The second answer is outside the reasonable domain of our model, so we conclude the ball will hit the ground after about 5.458 seconds.Step-by-step explanation:

Answer:

m∠b = 92 ; m∠c = 92

Step-by-step explanation:

∠b and ∠c both form supplementary angles with the 88° angle. I'll just choose b in this instance.

b + 88 = 180

b = 92

Now we know that ∠b is 92°.

Moreover, ∠c and ∠b are known as vertical angles meaning they are equivalent to each other. Therefore, ∠c is also 92°

Answer:

144

Step-by-step explanation:

8 x 9= 72

72 x 2= 144

Answer:

E

Step-by-step explanation:

Answer:

B. The mean would be higher than the median and mode

Step-by-step explanation:

Answer:

QR=PS in a parallelogram

Therefore, 17.7 is the right answer.

Answer:27%

Step-by-step explanation: 4/15

Answer:

The answer is C on Edge 2021

Step-by-step explanation:

In step 2 he confused the multiplication and addition signs

Answer:

C

Step-by-step explanation:

got it right

Answer: B

Step-by-step explanation: B is in slope-intercept form

Answer:

1. C

2. C

Step-by-step explanation:

1. 5x+12=57

Subtract 12 from both sides

5x=45

Divide both sides by 5

x=9

2.  7-4x=12-3x

Combine like terms =

-4x+3x=-12-7

x=-12-7

x=19

Answer:

5

Step-by-step explanation:

Hence, the average speed to the cyclist is 16mph.

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

We know,

distance covered = 4 miles

time taken = 15 minutes = [tex]\frac{1}{4}[/tex]hours

speed = [tex]\frac{4}{\frac{1}{4} }[/tex] = 16

Hence, speed is 16.

to learn more about speed: https://brainly.in/question/27709746

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Answer:

5.364

Step-by-step explanation:

5.3635 is the given number, and because the number next to the thousandths is a five, the number in the thousandths place can be rounded to 4.

Answer:

8 and 0

Step-by-step explanation:

Answer:

yes they are

Step-by-step explanation:

4:20 can be simplified till 1:5

Answer:

Yes

Step-by-step explanation:

If you simplify 4:20 by dividing both sides by 4, you'll end up with 1:5, meaning they are equivalent.

Answer:

12+6.5x

Step-by-step explanation:

Hope this helps!! if you in step by step ill comment it in the comments!!

Answer:

The first brother is 16, the second brother is 8 and the third brother is 4.

Step-by-step explanation:

Since the sum of all the brothers  is 28, that means the cap of how old the oldest can be is 28. I just stated with numbers less then 28 that were dividable by two which means all the numbers had to be. So 16 for the first, 8 for the second and 4 for the youngest is the right answer I hop.

Answer:

Given that he length of a 2-inch-long thorn was measured by Sandrine to be 1.9 inches long. The measurement that is more precise among the choices given is:

2 inches.

This is because it is the closest approximation of the length compared to the rest of the approximations.

Step-by-step explanation: can i have brainliest pls

Answer:

I'm note sure but I think it's the first one

Answer:

the answer is 6 units

Step-by-step explanation:

find point A and point B and then just count the units over from

A to B and you will get AB is 6 units

Answer c

Step-by-step explanation: bc its 6 units

Answer:

dial it up

2:16

simplify

1:8

now multiply 8 by the number of gigs

2:16

3:24

and so on.....

ring ring

1:9

again multiply the cost by the number of gigs

2:18

3:27

and so on....

Answer:

The discount is $8

Step-by-step explanation:

Step one

Given data

Jane paid $40 for an item after she received a 20% discount.

Required

The initial cost of the item

Now in other to check whether Jane's friend is correct, let us solve for the initiai cost as follows

Let the initial cost be x

so

20% of 40

20/100*40

=0.2*40= $8

Therefore the discount is $8

hence the original price is

discount+ discounted sale(amount paid)

=8+40

=$48

Answer:

72 hope it helps............

Answer:

72

is you answer because 8×9=72

Answer:

The answer is

[tex]y = \frac{1}{4} x - 2[/tex]

Step-by-step explanation:

Remmeber:

[tex]Slope = \frac{rise}{run} [/tex]

Answer:

change in y 3-9/ change in x 4-1  =-6/3  = -2  there u go

Step-by-step explanation:

Answer:

B. [tex]-(3x+1) (x+5)[/tex]

Step-by-step explanation

factored the equation to solve. Hope this helps!

Answer: C. -82

Step-by-step explanation:

-82 is the depth which is the farthest from sea level.

The deep ocean is generally defined as the depth at which light begins to dwindle, typically around 200 meters (656 feet).

Given that, Four deep-sea divers reported the depths they went below sea level on their last dive.

The farthest point in sea among the given options, is -82, this is because, the distance down the sea is marked as a negative, and 82 is the greatest in the options, therefore, -82 is the greatest distance.

Hence, -82 is the depth which is the farthest from sea level.

Learn more about depth of the sea, click;

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Answer:

Inequality Form:

x<7

Interval Notation:

(−∞,7)

Step-by-step explanation:

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