Identify the domain of the function shown in the graph.

Problem 1

Ignore the smaller circle for now. We'll be focusing on the portion on the right.

It's a partial circle with central angle theta = 150 degrees and radius r = 24 inches. The 24 inches also happens to be the slant height of the cone when we form the 3D figure.

Let's compute the arc length based on those inputs.

L = arc length

L = (theta/360)*2*pi*r

L = (150/360)*2*pi*24

L = 20pi

This is the distance along the green curve of this portion.

Now imagine we rolled up that partial circle on the right. We'd form the curved slanted roof of the cone. The green curve wraps around to help match up with the circular base. The 20pi calculated earlier is the circumference of this circular base. Use this to find r.

C = 2pi*r

20pi = 2pi*r

r = (20pi)/(2pi)

r = 10

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

So far we found that this cone has:

Now compute the height (h) perpendicular to the base

[tex]h^2+r^2 = s^2\\\\h = \sqrt{s^2-r^2}\\\\h = \sqrt{24^2-10^2}\\\\h = \sqrt{476}[/tex]

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

We can now compute the volume

[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*10^2\sqrt{476}\\\\V \approx 2284.7153\\\\[/tex]

The units of which are cubic inches.

The surface area is of this cone is:

[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*10*24 + \pi*10^2\\\\SA \approx 1068.1415\\\\[/tex]

The units are in square inches.

For each case, I used the calculator's stored value of pi to get the most accuracy possible. Round the decimal values however you need to, or however your teacher instructs.

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Answers:

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Problem 2

Use the pythagorean theorem to find the slant height

[tex]h^2+r^2 = s^2\\\\s = \sqrt{h^2+r^2}\\\\s = \sqrt{15^2+8^2}\\\\s = \sqrt{289}\\\\s = 17\\\\[/tex]

This slant height will act as the radius of the partial circle that results when forming the net of the unrolled cone.

The process used in the previous problem was to use the slant height and central angle to find the circumference of the base.

We'll follow that process in reverse to use the circumference and slant height to find the central angle.

But first, we need to find the circumference of the base.

C = 2*pi*r

C = 2*pi*8

C = 16pi

This is the arc length similar to the green arc shown in the previous problem (the figure on the right side of that diagram)

This means we'll plug in L = 16pi and r = 17 (not to be confused with the previous radius of 8 inches) to determine theta

L = (theta/360)*2*pi*r

16pi = (theta/360)*2*pi*17

16pi = theta*(34pi/360)

theta = 16pi*(360/(34pi))

theta = 169.4118 degrees approximately

This is the central angle of the unrolled net. The diagram is basically the same as the previous drawing, where we have a circle on the left to represent the base of the cone. The other portion forms the roof of the cone.

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

Let's compute the volume (V) and surface area (SA)

[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*8^2*15\\\\V \approx 1005.3096\\\\[/tex]

and,

[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*8*17 + \pi*8^2\\\\SA \approx 628.3185[/tex]

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

Answers:

Answer:

  16.8 hours

Step-by-step explanation:

An exponential population increase can be modeled by the function ...

  p(t) = a·b^(t/p)

where 'a' is the initial value (at t=0), b is the multiplier in time period p.

__

The colony increased by a factor of b = 80/50 = 1.6 in p = 3 hours. Since we want to find the additional time to reach a population of 1119, the initial population we're working with is 80, not 50.

  p(t) = 80·1.6^(t/3)

  1119 = 80·1.6^(t/3)

__

Solving this for t, we find ...

  1119/80 = 1.6^(t/3) . . . . . . . . . . . . divide by 80

  log(1119/80) = (t/3)log(1.6) . . . . . take logarithms

  t = 3·log(1119/80)/log(1.6) . . . . . divide by the coefficient of t

  t ≈ 16.8 . . . . hours

It will take about 16.8 more hours for the population to increase from 80 to 1119.

Check the picture below.

so hmmm if Lydia is correct, then there's one angle in the triangle that is 90°, hmmm well, looking at the picture, we can pretty much forget about angle Z or Y, they're both acute, hmm how about angle X? is it 90°?

well, if angle X is indeed a right-angle, the lines XZ and XY are perpendicular, but are they?  if that's so then the slopes of XZ and XY are  negative reciprocal of each other, let's check

[tex]X(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Z(\stackrel{x_2}{2}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{-6 +4}{2 +0}\implies -1[/tex]

now, the negative reciprocal of that will be

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1}\implies 1}}[/tex]

well, let's see if XY has a slope is 1 then

[tex]X(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Y(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{-3 +4}{2 +0}\implies \cfrac{1}{2}[/tex]

OMG!!! Lydia needs to go get a nice Latte with cinnamon and to recheck her triangle.

Answer:

Yes

Step-by-step explanation:

At the age of 22 Alex will have twice the age of His brother who is 11 years old

Answer:

9

Step-by-step explanation:

Answer:

4 large folders     ( and 8 small folders....with $ 1 left over)

Step-by-step explanation:

x = small    y = large folders

x+y >= 12      x >= 12-y

3x + 5y <= 45

3 (12-y) + 5y <=45

36 -3y + 5y <= 45

    y <= 4.5               you cannot buy .5 of a large folder, so 4 large folders

Considering the area of the hole, it is found that there is a 4.9% probability of hitting a ball into the circular hole.

The area of a circle of radius r is given by:

[tex]A = \pi r^2[/tex]

In this problem, the hole has a diameter of 1 ft, hence it is radius is of r = 1 ft/2 = 0.5 ft, and it's area is given by:

[tex]A = \pi \times (0.5)^2 = 0.7854 \text{ft}^2[/tex]

Hence the probability is given by:

p = 0.7854/16 = 0.049 = 4.9%

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Answer:

3/16 of the whole pie

Step-by-step explanation:

Lexi had 3/4 of an apple pie. She gave 1/4 of it to Julie. That means what Julie receives is the product of the whole and the portion.

==========================================================

Solving :

Therefore, the equation is :

⇒ 3/4 × 1/4

⇒ 3/16 of the whole pie

Answer:

Step-by-step explanation:

1) Angle 1 and angle 2 are complementary angles. If angle 1 measures (3x + 2), what is the measure of angle 2? 3x+2 + y = 90

2) Angle A and angle b are supplementary angles. Angle A measures (2m – 10) degrees and angle b measures (m + 25) degrees. Find the measure of angle A and angle b.

3) Three angles are supplementary angles. If one angle measures 25 degrees, the second angle measures m + 15. The third angle measures 2m degrees. What is the value of m?

The temperature at midnight is 55.4  degrees Fahrenheit

The information that completes the question is "At what temperature is the building at midnight?"

The function is given as:

f(t) = -8.3cos(π/5)t + 63.7

At midnight, t = 0.

So, we have:

f(0) = -8.3cos(π/5) * 0 + 63.7

Evaluate the product

f(0) = -8.3cos(0) + 63.7

Evaluate the expression

f(0) = 55.4

Hence, the temperature at midnight is 55.4  degrees Fahrenheit

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Answer:

[tex]8 \times(2+15)[/tex]

Step-by-step explanation:

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to write "8 times the sum of 2 and 15" as an algebraic expression.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So, we add 2 and 15:

[tex]\mathtt{2+15}[/tex]

Now we multiply 8 times this expression:

[tex]\mathtt{8\times(2+15)}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

The revenue function when the assumed values and parameters are used is F(x) = (60 + 8x)(250 - 30x)

Let the number of people be x, and the revenue function be F(x).

Using the assumed values, the revenue function is:

F(x) = (60 + 8x)(250 - 30x)

We have:

F(x) = (60 + 8x)(250 - 30x)

Expand

F(x) = 15000 - 1800x + 2000x - 240x²

Differentiate the function

F'(x) = -1800 + 2000 - 480x

Evaluate

F'(x) = 200 - 480x

Set to 0

200 - 480x = 0

This gives

480x = 200

Divide both sides by 480

x = 0.42

Substitute x = 0.42 in F(x)

F(x) = (60 + 8 * 0.42)(300 - 30* 0.42)

Evaluate

F(x) = 18210

Hence, the maximum revenue is $18210, at a rate of $0.42 per person.

We start by setting F(x) to 5000.

So, we have:

15000 - 1800x + 2000x - 240x² = 5000

Evaluate the like terms

10000 + 200x - 240x² = 0

Using a graphing tool, we have:

x = 6.89

Hence, they would reach their goal at a rate of $6.89 per ticket.

We have:

People = x

Cost per person = 20

So, the cost function is:

C(x) = 20x

Profit is calculated using:

P(x) = F(x) - C(x)

So, we have:

P(x) = 15000 - 1800x + 2000x - 240x² - 20x

Evaluate

P(x) = 15000 + 180x - 240x²

This is the point where P(x) = 0.

So, we have:

15000 + 180x - 240x²  = 0

Using a graphing tool, we have:

x = 8.29

Hence, the break even price is $8.29

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Answer:

There two images below,

one is the final product and one of how it was reflected

[tex]~~~~~~15=6y+5-8y\\\\\implies 15-5=-2y\\\\\implies 10 = -2y\\\\\implies -\dfrac{10}2 = y\\\\\implies -5 = y\\\\\implies y = -5[/tex]

Answer:

y=−5

Step-by-step explanation:

15=6y+5−8y

⟹15−5=−2y

⟹10=−2y

⟹−210=y

⟹−5=y

⟹y=−5

answer this fully! i need to know what x equals

X equal minus 0.5

A beam measuring 2 meters can support 172 kilograms

The variation is a direct variation.

So, we have:

w = kl

Where k is the constant of variation.

When l = 5, w = 430.

This means that:

430 = 5k

Divide both sides by 5

k = 86

So, we have:

w = 86l

When l = 2, we have:

w = 86 * 2

Evaluate

w = 172

Hence, a beam measuring 2 meters can support 172 kilograms

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A function assigns the value of each element of one set to the other specific element of another set. The correct option is D.

A function assigns the value of each element of one set to the other specific element of another set.

The time at which the ball will hit the ground is,

h(t) = −16t² + 10t + 6

0 = -16t² + 10t + 6

8t² - 8t + 3t - 3= 0

8t(t-1)+3(t-1) = 0

(8t+3)(t-1)=0

t = -0.375, 1

Hence, the ball hit the ground at 1 second, while the function in intercept form can be written as h(t) = (−8t − 3)(2t − 2).

Thus, the correct option is D.

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Answer:

The answer above is correct, a teacher confirmed it, and the quiz marked it as correct.

Step-by-step explanation:

Answer:

-x²-2

Step-by-step explanation:

x² = the curve faces upwards

but

-x² the curve faces downwards.

also

the downward curve touches -2 on the y axis.

therefore gx = -x²-2

Answer:

16

Step-by-step explanation:

the range is the amount of numbers between the highest and lowest number in a set.  if the lowest number is 3, and the range is thirteen, and the number must be a positice, the highest number in the range is 16.

Answer:

a) (f + g)(x) = 8x + 2

b) (f - g)(x) = 4x - 6

Step-by-step explanation:

Given:

a) Find (f + g)(x):

a. (f + g)(x) = f(x) + g(x)

⇒ (f + g)(x) = (6x - 2) + (2x + 4)

⇒ (f + g)(x) = 6x + 2x - 2 + 4

⇒ (f + g)(x) = 8x + 2

b) Find (f - g)(x):

b. (f - g)(x) = f(x) - g(x)

⇒ (f - g)(x) = (6x - 2) - (2x + 4)

⇒ (f - g)(x) = 6x - 2x - 2 - 4

⇒ (f - g)(x) = 4x - 6

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Answer:

8 cubic cm

Step-by-step explanation:

6 * ( L square ) = 24

L= 2

then

v= l cube

= 2*2*2

=8

Answer:

3:36PM

Step-by-step explanation:

Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.

Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at [tex]\frac{1}{4}[/tex] capacity, we can use the equation:

[tex]\frac{1}{4} * 12 = \boxed{3}[/tex]

This shows [tex]\frac{1}{4}[/tex] of his tank's capacity ([tex]12[/tex]) is equal to [tex]3[/tex] gallons. This means he will stop for gas when [tex]3[/tex] gallons are remaining.

Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.

[tex]\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}[/tex]

This is a simple proportion, and now we know he uses [tex]2.5[/tex] gallons of gas per hour.

Now we can how many hours of gas Leon has left.

He has [tex]7[/tex] gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.

[tex]\frac{7-3}{2.5} = 1.6[/tex]

The [tex]7-3[/tex] is because Leon doesn't stop when his tank is empty, he stops [tex]3[/tex] gallons earlier. We are dividing by [tex]2.5[/tex] because that is how much gas he uses per hour, meaning the result of this division ([tex]1.6[/tex]) is how many hours he has left.

Now we can solve for what time Leon will stop to get gas.

12PM + [tex]2[/tex] hours of driving + the remaining [tex]1.6[/tex] hours = 3:36PM

([tex]1.6[/tex] hours is equal to 1 hour and 36 minutes)

Therefore, Leon will stop for gas at 3:36PM

Answer:

both

Step-by-step explanation:

that's the answer to the question

The length of the arc is 3.5 cm

The attached image completes the question

The given parameters are:

The length of the arc is calculated as:

[tex]L = \frac{x}{360} * \pi d[/tex]

So, we have:

[tex]L = \frac{25}{360} * 3.14 * 16[/tex]

Evaluate the product

L =  3.5cm

Hence, the length of the arc is 3.5 cm

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Answer:3.5

Step-by-step explanation:

Answer:  [tex]-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9[/tex]

=======================================================

Explanation

Let:

[tex]x = \sqrt{2}\\\\y = \sqrt{6}-\sqrt{3}\\\\[/tex]

We can then say:

[tex](\sqrt{2}-\sqrt{3}+\sqrt{6})(\sqrt{6}-\sqrt{3})\\\\(\sqrt{2}+\sqrt{6}-\sqrt{3})(\sqrt{6}-\sqrt{3})\\\\(x+y)(y)\\\\xy+y^2\\\\2\sqrt{3}-\sqrt{6}+9-6\sqrt{2}\\\\-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9\\\\[/tex]

Check out the screenshot below for the scratch work on how I computed the [tex]xy[/tex] and [tex]y^2[/tex] terms.

Answer: 11. [tex]11b-6[/tex]

12. [tex]14d^2-4d[/tex]

13. [tex]2x^2[/tex]

14. [tex]-4x+10[/tex]

15. [tex]19+x[/tex]

16. [tex]4c[/tex] (all together, the problems aren't entered correctly)

17. Nothing further can be done with these equations. Please check the expression entered.

18. [tex]2p-q[/tex] (All together, the problems aren't entered correctly)

Step-by-step explanation:

[tex]\quad \:a+\left(b+c\right)=a+b+c[/tex]

[tex]7b+\left(4b-6\right)=7b+4b-6[/tex]

[tex]=7b+4b-6[/tex]

[tex]7b+4b=11b[/tex]

[tex]=11b-6[/tex]

[tex]2d*(7d-2)=14d^2-4d[/tex]

[tex](8 * (d^2)) + ((2*3d^2) - 4d)[/tex]

[tex]2^3d^2 + (6d^2 - 4d)[/tex]

[tex]14d^2 - 4d = 2d * (7d - 2)[/tex]

[tex]((5*(x^2))+4)+((0-3x^2)-4)[/tex]

[tex](5x^2 + 4) + (-3x^2 - 4)[/tex]

[tex]=2x^2[/tex]

[tex]-4x+10-5x+5x[/tex]

[tex]-4x-5x+5x+10[/tex]

[tex]-4x-5x+5x=-4x[/tex]

[tex]=-4x+10[/tex]

[tex]8+5+6+x[/tex]

[tex]\:8+5+6=19[/tex]

[tex]=19+x[/tex]

Answer: 2a + c is the answer for #17 and #18 is 2p.

17.

3a + 8b - 5c

6a - 9b + 4c

-7a + b + 2c =

2a + c

18.

+6p - 3q + z

- 3p + 2q - z

- p +    q =

2p

Step-by-step explanation:

Answer:

y=3x+5

Step-by-step explanation:

See attached image

Answer:

D.) y = 3x + 5

Step-by-step explanation:

The general structure for an equation in slope-intercept form is:

y = mx + b

In this form, "m" is the slope and "b" is the y-intercept.

To convert the given equation into slope-intercept form, you need to do some expanding and rearranging.

y - 2 = 3(x + 1)                       <----- Given equation

y - 2 = 3x + 3                        <----- Multiply 3 by every term in the parentheses

y = 3x + 5                            <----- Add 2 to both sides

Answer:

The answer is 0.75

Hope this helps!

Answer:

2

Step-by-step explanation:

Answer:

3 to the fourth power, which equals 81.

Step-by-step explanation:

Answer:

A

Step-by-step explanation: