A cone has a base of [tex]5.4[/tex] and a height of [tex]8[/tex]. The diameter is [tex]6[/tex]. What is the volume? If you were to dilate the cone with a scale factor of [tex]2[/tex], what would the new radius be?

Answers

Answer 1

Answer:

(I) V = 24π ≈ 75.3982 units³

(II) V = 192π ≈ 603.186 units³

General Formulas and Concepts:

Math - Symbols

π - pi, the number 3.1415926535897932384626433832795

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Geometry

DilationsDiameter: d = 2rVolume of a Cone: [tex]V= \frac{1}{3} \pi r^2h[/tex]

Step-by-step explanation:

Step 1: Define

Height h = 8

Diameter d = 6

Base b = 5.4 (not needed in calculations)

Step 2: Find radius r

Substitute:                    6 = 2rIsolate r:                        3 = rRewrite:                         r = 3

Step 3: Find V of Normal Dimensions

Substitute:                    [tex]V= \frac{1}{3} \pi (3)^2(8)[/tex]Exponents:                   [tex]V= \frac{1}{3} \pi (9)(8)[/tex]Multiply:                        [tex]V= 24 \pi[/tex]Evaluate:                      [tex]V \approx 75.3982[/tex]

Step 4: Find Dilations

Scale Factor: 2

Define radius:                    r = 3Dilate:                                 r' = 3(2)Multiply:                              r' = 6Define height:                    h = 8Dilate:                                 h' = 8(2)Multiply:                              h' = 16

Step 5: Find V of Dilated Dimensions

Substitute:                     [tex]V= \frac{1}{3} \pi (6)^2(16)[/tex]Exponents:                    [tex]V= \frac{1}{3} \pi (36)(16)[/tex]Multiply:                         [tex]V= 192 \pi[/tex]Evaluate:                       [tex]V \approx 603.186[/tex]

Related Questions

2n + 3 = -3.2 what is the answer to n

Answers

Answer:n=-3.1

Step-by-step explanation:

2n + 3 = -3.2

Subtract 3 on both sides

2n+3-3=-3.2-3

2n=-6.2

Divide 2 on both sides

2n/2=-6.2/2

n=-3.1

Answer:

n= -3.1

Step-by-step explanation:

hope this helps have a nice day :)

Enter the equation of the line in slope-intercept form. Enter the answer in fraction form.

The line perpendicular to y =
6
5
x + 2 that passes through (6, −2).

The equation of the line that passes through (6, −2) is y = .

Answers

What grade of math is this ?

This is 8 grade math plZ help me I’m stuck

Answers

9514 1404 393

Answer:

  y = -3/4x -1

Step-by-step explanation:

The given equation is in the slope-intercept form, which lets you see that its slope is 4/3.

The slope of the perpendicular line will be the negative reciprocal of this:

  -3/4

Then the slope-intercept form equation will be ...

  y = -3/4x +b . . . . . . for some b

We can find the value of b that makes the line go through (4, -4) by using those values in this equation.

  -4 = -3/4(4) +b

  -4 +3 = b . . . . . . . . add 3

  -1 = b

Then the equation you're looking for is ...

  y = -3/4x -1

Ben ran for president of his class. If there are 410 students and he received 70% of the vote, how many students voted for Ben?​

Answers

Answer:

287

Step-by-step explanation:

70/100*410

(cross out the zeroes then multiply 7 by 41 and you'll get 287)

Find the discriminant and state the number and type of solutions.
-3.02 - 6x + 5 = 8

Answers

1.98 -6x = 8
x = 1.00(3)

f(x) = x + 6
x=-2, 0, and 5

Answers

Answer:

f(x)=x+6

-2+6

4

when x=0

0+6

6

when x=5

5+6

11

Step-by-step explanation:

Jill has a photograph that is 4 inches wide by 6 inches high. If she enlarges it so that the width is 12
inches, what will be the height?

Answers

Answer:

The inches in height will be 18 inches.

Step-by-step explanation:

Okay so we know that the original width is 4 inches and she enlarged that to 12 inches

So what we first have to do is find out how much did the photograph "grow" per se. To find this we have to divide 12 by 4. 12 divided by 4 = 3.

So, the width of the photograph grew "times 3" inches

Now whatever you do to the width you have to do to the height. In this case, what is "3 times" 6 (which is the height). 3 times 6 = 18 inches

So in simpler words 12 divided 4 = 3 x 6 = 18 inches

The inches in height will be 18 inches.

Jill has a square with a width of 12 inches, and a height of 18 inches.

Have a wonderful day!

For each question, solve for the length of the unknown side, as
denoted by the variable. You may round your answers to the nearest
tenth, if necessary. Make sure you show all steps needed to solve the
problem.

Answers

Answer:

[tex]a=9[/tex]

Step-by-step explanation:

In this problem, you can use the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex]) to find what a is. The steps are shown below:

Steps (variables a, b, and c are in italics):

-You can rearrange the formula from the Pythagorean Theorem, which is[tex]a^{2} +b^{2} =c^{2}[/tex] to only get a because we want to know what a is.

Rearranged: [tex]a=\sqrt{c^{2}-b^{2} }[/tex] or [tex]a=-\sqrt{c^{2}-b^{2} }[/tex]  It has to ways/options for a because when finding the square root of a number, it can be either positive or negative. But in this problem, it’s going to be positive because we’re finding the length of something.

-Since we know what c and b are, you can plug them into the new formula:

[tex]a=\sqrt{15^{2}-12^{2} }[/tex]

-Simplify it:

[tex]a=\sqrt{225-144}[/tex]

-Subtract inside the radical:

[tex]a=\sqrt{81}[/tex]  Then simplify it to get [tex]a=9[/tex].

You can check your answer by putting a back into the original Pythagorean Theorem formula ([tex]a^{2} +b^{2} =c^{2}[/tex]):

Steps

-Plug a, b, and c into the formula [tex]a^{2} +b^{2} =c^{2}[/tex]:

[tex](9)^{2} +(12)^{2} =(15)^{2}[/tex]

-Simplify to get:

[tex]81+144=225[/tex]

-Add:

[tex]225=225[/tex]  This is very true. So our answer is correct.

ANSWER: [tex]a=9[/tex]

Sorry for the long explanation, but I hope you understand and that this helps with your question! :)

Answer:

a = 9

Step-by-step explanation:

lets make is short and simple

Pythagorean theorem: a² + b² = c²

a² + 12² = 15²

a² = 15² - 12²

a = √81

a = 9

PLEASE HELP ASAP DUE In 5 MINUTES

Answers

C hahjfmroahcnfnosjajd

barney has 14 dimes and quarters worth $2.15. write the system of equations

Answers

Answer: 14 dimes and 3 quarters

Step-by-step explanation:

14x10=140+25=165+25=190+25=215 aka $2.15 meaning that there is 14 dimes and 3 quarters

Please discuss the relationship between the value of "a" in a quadratic function [y = a(x - h)2 + k or y = ax2 + bx + c] and the distance the focus is from the vertex. Please give examples to support your conclusion.


Please Help!

Answers

Answer:

The given equations are;

y = a·(x - h)² + k or y = a·x² + b·x + c

We have;

(x - h)² = 4·p·(y - k),

Where;

(h, k) are the x, and y coordinates of the vertex

p = The distance from the focus to vertex distance;

Comparing, we have;

y - k = a·(x - h)²

(y - k)/a = (x - h)²

(x - h)² = 4·p·(y - k)

4·p·(y - k) = (x - h)²

∴ 4·p = 1/a

p = 1/(4·a)

Therefore, the focus to vertex distance inversely proportional to the value of a

The distance of every point on the parabola is equidistant from the directrix and the focus

Therefore, the equation of the directrix is y = k - p

For example, we have;

y = 2·x² + 3·x + 1

h = -b/2a = -3/4

k = (4ac - b²)/4a = (4×2×1 - 3²)/(4×2) = -1/8

The coordinate of the focus is (h, k + p) = (-3/4, -1/8 + 1/8) = (-3/4, 0)

The directrix, y = k - p = -1/8 - 1/8 = -1/4

For a point x = 2, we have, y = 2·2² + 3·2 + 1 = 15

The coordinate of the point is (2, 15)

The distance of the point from the directrix = 15 - (-1/4) = 15 + 1/4 = 15.25

The distance of the point from the focus is √((2 - (-3/4))² + (15 - 0)²) = 15.25

Therefore, all points on the parabola have equal distances from the focus and the directrix

Step-by-step explanation:

Which expression is equal to 6(−3m)4​

Answers

Answer: -18m x 4 (I think)

Step-by-step explanation:

If this isn’t correct, what you have to do is simplify, hopefully this helps

Stephanie is giving a presentation to a new client. It took her 1713 minutes to finish a 13-slide presentation. She took the same amount of time on each slide. How long did she spend on each slide?

Answers

Answer:

Time taken per slides = 131.77 minutes.

Step-by-step explanation:

Given the following data;

Total time, t = 1713 mins

Number of slides, n = 13

To find the amount of time spent on each slides;

Time taken per slides = t/n

Substituting into the equation, we have;

Time taken per slides = 1713/13

Time taken per slides = 131.77 minutes.

Therefore, the amount of time Stephanie spent on each slide is 131.77 minutes.

It took Stephanie about 1 minute to finish each slide of the 13-slide presentation.

Equation

Equation is used to show the relationship between two or more numbers and variables.

Le x represent the amount of time spent on each slide.

Given that she spent  13 minutes to finish a 13-slide presentation. Therefore:

13x = 13

Divide through by 13:

13x/13 = 13/13x = 1

It took Stephanie about 1 minute to finish each slide of the 13-slide presentation.

Find out more on equation at: https://brainly.com/question/13763238

how many times larger then 2x10² is 2x10⁸​

Answers

Answer:

1,000,000 times larger

Step-by-step explanation:

2 x [tex]10^{8}[/tex] = 200,000,000

2 x [tex]10^{2}[/tex] = 200

200,000,000 divided by 200 is 1,000,000

It can also be solved by subtracting the exponents from 10. Then dividing the two number being put the scientific notation.

[tex]10^{8} - 10^{2}[/tex] = [tex]10^{6[/tex]

2 ÷ 2 = 1

Now solve:

1 x [tex]10^{6[/tex] = 1,000,000

Evaluate f(x) = - 3x - 4 for x = 1 .

Answers

[tex]f(x)=-3x-4[/tex]

Substitute x = 1 in the equation.

[tex]f(1)=-3(1)-4\\f(1)=-3-4\\f(1)=-7[/tex]

Therefore, the answer is f(1) = -7

One-third cup of black beans provides 20% of the potassium you need daily. You must get the remaining 1,360 milligrams from other sources.

How many milligrams of potassium should you consume daily?

____ milligrams

Answers

1,360 is 80%
Plus ? 20%
Is 100%
So 80 is 4 times 20
So you can divide 1360 by 4 to find 20%
So 340mg is 20% of your daily value

So then add 340 plus 1360 to get total daily value

1700mg

what's the pagathorium theorem

Answers

Answer:

c=a2+b2

Step-by-step explanation:

Find the value of x.

The side opposite the right angle is the side labelled x. ...

x=√100=10.

Maybe you remember that in an equation like this, x could also be –10, since –10 squared is also 100. ...

Find the value of y.

y=√80=√16×5=4√5.

x=√17.45≈4.18 miles.

Answer:

thats the formula

a^2 + b^2 = c^2

Step-by-step explanation:

a =  side of the right angle/adjacent side

b = side of the right triangle/opposite side

c= hypotenuse

Please help I’m stupid

Answers

Answer:

it would be 70

Step-by-step explanation:

you are not stupid

Answer:

the answer is -50

Step-by-step explanation:

which one doesn’t belong?

Answers

come to your house to pick it lowest to go with D

Answer:

All of them have different answers so gonna say D because its only one number  

Step-by-step explanation:

Hope this helps

sorry If its wrong

If∠

Answers

Answer:

where is tge other half question?

Aubree invested $500 into a mutual fund that paid 3% interest each year compounded annually. Find the value of the mutual fund in 12 years.

Answers

Answer:

FV= $712.88

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $500

Number of periods (n)= 12 years

Interest rate (i)= 3% compounded annually

To calculate the future value, we need to use the following formula:

FV= PV*(1+i)^n

FV= 500*(1.03^12)

FV= $712.88

Answer:

25%

Step-by-step explanation:

Because she divided it

A car travels 60 miles due north then makes a turn due west. It travels 72 miles west. How far is the car from ils starting point?​

Answers

Answer:

132 miles

Step-by-step explanation:

Answer: the answer is 93.7 miles

find the slope of the line​

Answers

Answer:

Up 5, 2 to the right (5/2)

Step-by-step explanation:

I just counted the units of the Cartesian Plane

An amusement park has two types of season passes. Plan 1 charges a one-time fee of $175.00 for admission plus $8.00 every trip for parking
Plan 2 charges a one-time fee of $125.00 for parking plus $13.00 every trip for admission. For what number of trips is the cost of these plans
the same?

Answers

Answer:

The answer is stan twice

Step-by-step explanation:

simple

Answer:

x=10

Step-by-step explanation:

pls help I'm gonna give brainliest but just help pls I need to do this but I don't get it.
A car travels 1/6 of the distance between two cities in 3/5 of an hour. At this rate, what fraction of the distance between the two cities can the car travel in 1 hour?

Answers

Answer:

They travel 5/18 in one hour

Step-by-step explanation:

Answer:

In an hour the car can cover 5/18 of the distance

What is the slope of -2,-5 and 18,-5

Answers

Answer:

Quadrant III and Quadrant I

Step-by-step explanation:

Answer:

Zero; 0

Step-by-step explanation:

(-5+5)/(18+2) = 0

HELP I WILL MARK U BRAINEST what is (29/59)*(42/24)
btw / means divide

Answers

Answer:

0.86016949152

Step-by-step explanation:

This is the answer because 29 divided by 59 is 0.49152542372 and 42 divided by 24 is 1.75 and 0.49152542372 multiplied by 1.75 is 0.86016949152

A boy saved over $5. His father gave him $2. The boy now had $y altogether. Write an inequality in y

Answers

Answer:

$7 total

Step-by-step explanation:

$5 + $2 = $7

Divide using polynomial long division. (Show your work)
Hint: don’t forget the 0x
(x^3-2x^2+4) ÷ (x+3)

Answers

Answer:

x^3−2x2+4x+3=x2−5x+15+−41x+3

Step-by-step explanation:

1.Divide the leading term of the dividend by the leading term of the divisor: x3x=x2.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: x2(x+3)=x3+3x2.

Subtract the dividend from the obtained result: (x3−2x2+4)−(x3+3x2)=−5x2+4.

2.Divide the leading term of the obtained remainder by the leading term of the divisor: −5x2x=−5x.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: −5x(x+3)=−5x2−15x.

Subtract the remainder from the obtained result: (−5x2+4)−(−5x2−15x)=15x

3.Divide the leading term of the obtained remainder by the leading term of the divisor: 15xx=15.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: 15(x+3)=15x+45.

Subtract the remainder from the obtained result: (15x+4)−(15x+45)=−41.

-8 + 2/3x + 4 = 2x -5-x
PLEASE FIND WHAT X IS!!! Also, please show steps so I can understand!‍♀️
I will give brainiest to correct answer WITH STEPS!!!

Answers

Answer:

3

Step-by-step explanation:

Let's isolate x on one side.

2x - x - 2/3x = -8+5+4

1/3x=1

x=3

Answer:

X = 3

Step-by-step explanation:

-8 + 2/3x + 4 = 2x - 5 - x

2/3x - 2x - x = -5 + 8 - 4

-1/3x = -1

x = -1 * -3

x = 3

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