The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 249 cubic units.
What is the height of the cylinder?
O2 units
4 units
O 6 units
O 8 units

Answers

Answer 1

Answer:

h = 6 units

Step-by-step explanation:

Volume of a cylinder = πr²h

where r is the radius

h is the height

The height of a right cylinder is 3 times the radius of the base is written as

h = 3r

Volume = 249cubic units

So we have

249 = π r²(3r)

249 = π3r³

Divide both sides by 3π

r³ = 249/3π

r = 2

h = 3(2)

h = 6 units

Hope this helps you


Related Questions

HELP PLEASE ASAP 20 points

Answers

Answer:

Its d [tex]x^{2} -6x+7=0[/tex]

Step-by-step explanation:

A= [tex]2+\sqrt{3\\}[/tex]

B= [tex]3\sqrt{2}[/tex]

C= [tex]-3+\sqrt{2}[/tex]

Answer:

D. x^2 - 6x + 7 = 0.

Step-by-step explanation:

The roots are 3 plus or minus sqrt(2). That means the equation is...

(x - [3 + sqrt(2)]) * (x - [3 - sqrt(2)])

= [x - 3 - sqrt(2)] * [x - 3 + sqrt(2)]

= x^2 - 3x - xsqrt(2) - 3x + 9 + 3sqrt(2) + xsqrt(2) - 3sqrt(2) - (sqrt(2))^2

= x^2 - 3x - 3x + 9 - 2 - xsqrt(2) + xsqrt(2) + 3sqrt(2) - 3sqrt(2)

= x^2 - 6x + 7.

Hope this helps!

Find the volume of the cylinder.

Answers

Answer:Exact volume = 32piApproximate volume =  100.48

The approximate volume only applies when pi = 3.14

Use either answer, but not both of course.

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

Work Shown:

V = volume of cylinder

V = pi*r^2*h

V = pi*2^2*8

V = pi*32

V = 32pi .... exact volume in terms of pi

V = 32*3.14

V = 100.48 .... approximate volume when we use pi = 3.14

A ball is thrown straight down from the top of a 435-foot building with an initial velocity of -27 feet per second. Use the position function below for free-falling objects. s(t) = -16t^2 + v_0t + s_0 What is its velocity after 2 seconds? v(2) = -91 ft/s What is its velocity after falling 364 feet? v = 1.61 ft/s Find an equation of the parabola y = ax^2 + bx + c that passes through (0, 1) and is tangent to the line y = 5x - 5 at (1, 0). Y = 5x + 10

Answers

Answer:

a) The velocity of the ball after 2 seconds is -91 feet per second, b) The velocity of the ball after falling 364 feet is 155 feet per second, c) The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is [tex]y = 6\cdot x^{2}-7\cdot x +1[/tex].

Step-by-step explanation:

a) The velocity function is obtained after deriving the position function in time:

[tex]v (t) = -32\cdot t -27[/tex]

The velocity of the ball after 2 seconds is:

[tex]v(2\,s) = -32\cdot (2\,s) -27[/tex]

[tex]v(2\,s) = -91\,\frac{ft}{s}[/tex]

The velocity of the ball after 2 seconds is -91 feet per second.

b) The time of the ball after falling 364 feet is found after solving the position function as follows:

[tex]435\,ft - 364\,ft = -16\cdot t^{2}-27\cdot t + 435\,ft[/tex]

[tex]-16\cdot t^{2} - 27\cdot t + 364 = 0[/tex]

The solution of this second-grade polynomial is represented by two roots:

[tex]t_{1} = 4\,s[/tex] and [tex]t_{2} = -5.688\,s[/tex].

Only the first root is physically reasonable since time is a positive variable. Now, the velocity of the ball after falling 364 feet is:

[tex]v(4\,s) = -32\cdot (4\,s) - 27[/tex]

[tex]v(4\,s) = -155\,\frac{ft}{s}[/tex]

The velocity of the ball after falling 364 feet is 155 feet per second.

c) Let consider the equation for a second order polynomial that passes through (0, 1) and its first derivative that passes through (1, 0) and represents the give equation of the tangent line. That is to say:

Second-order polynomial evaluated at (0, 1)

[tex]c = 1[/tex]

Slope of the tangent line evaluated at (1, 0)

[tex]5 = 2\cdot a \cdot (1) + b[/tex]

[tex]2\cdot a + b = 5[/tex]

[tex]b = 5 - 2\cdot a[/tex]

Now, let evaluate the second order polynomial at (1, 0):

[tex]0 = a\cdot (1)^{2}+b\cdot (1) + c[/tex]

[tex]a + b + c = 0[/tex]

If [tex]c = 1[/tex] and [tex]b = 5 - 2\cdot a[/tex], then:

[tex]a + (5-2\cdot a) +1 = 0[/tex]

[tex]-a +6 = 0[/tex]

[tex]a = 6[/tex]

And the value of b is: ([tex]a = 6[/tex])

[tex]b = 5 - 2\cdot (6)[/tex]

[tex]b = -7[/tex]

The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is [tex]y = 6\cdot x^{2}-7\cdot x +1[/tex].

If the sum of the first n terms of an AP is 1/2 (3n^2+7n),then find its nth term.Hence write its 20th term.​

Answers

Answer:

62

Step-by-step explanation:

Sn=1/2(3n^2+7n)

S1=1/2(3+7)=5

S2=1/2(3*4+7*2)=26/2=13

We know

S1=a1=5

S2=a1+a2=13

S2-s1=a1+a2-a1

13-5=a2

a2=8

We know d=a2-a1

d=8-5=3

nth term of AP =an=5+(n-1)3

an= 2+3n

Therefore 20th term =

a20= 2+3(20)=62

Hence 20th term of AP is 62

I hope this helps

Find the perimeter and total area of the polygon shape shown below. All measurements are given in inches. Helps please !!!!

Answers

Answer:

perimeter = 56 in

area = 192 sq. in.

Step-by-step explanation:

area of a triangle = 0.5 * b * h

b = 12

h = 8

At = (0.5 * 12 * 8)  = 48

Area of a square

As = 12 * 12 = 144

total area = At + As

total area = 48 + 144

total area = 192 sq. in.

perimeter = add all sides

12 + 12 + 12 + 10 + 10 = 56 in

hope it helps

By rounding to one significant figure, estimate the answers to the question circled​

Answers

The answer would have to be 2.2580

aryn needs enough mulch to cover a rectangle flower bed measuring 2 1/4 yd by 3 1/2yd each bag cover 3 square yds and cost $4 how many bags does she need and how much money she need

Answers

Answer:

cars are dum

Step-by-step explanation:

Can you draw the reflection Across the y-axis of the attached image.

Answers

Answer:

see graph

Step-by-step explanation:

A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.

Solve application problems using radical equations. Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 378 square feet. How long can a side of his patio be?

Answers

Answer:

3(sqrt42) ft

Step-by-step explanation:

If l is side length of square patio, then area of patio would be l^2.

l^2 = 378

l = sqrt378 = 3(sqrt42)

i will give 50 points and brainliest amd whatever u want pls its urgent PLS ​

Answers

Answer:

The answer to your question is 24 cm³

Step-by-step explanation:

Data

Initial volume = 2/5

Additional volume = 42 cm³

Final volume = 4/7

the total volume of the glass = ?

Process

1.- Write a proportion to help you solve the problem

                  42 cm³  -------------------- 4/7 of the total

                   x            -------------------  7/7

2.- Solve the proportion

                  x = (7/7 x 42) / 4/7

3.- Simplification

                  x = 42 / 4/7

                  x = 168/7

                 x = 24 cm³                  

Answer:

y = mx + c

since m = 0

c = 9

Step-by-step explanation:

y = mx + c

since m = 0

c = 9

SLOPE THESE DAYS

1). f(x) = 3x + 15 then what's f^-1(x)?​

Answers

Answer:

Step-by-step explanation:

f(x)=3x+15

let  f(x)=y

y=3x+15

flip x and y

x=3y+15

3y=x-15

y=1/3 x-5

or f^{-1}x=1/3 x-5

what is the solution to the system of equations?

y = 4x-10
y=2

A) (3,2)
B) (2,3)
C) (-2,2)
D) (2,-2)

Answers

Answer:

A) (3, 2)

Step-by-step explanation:

y = 4x - 10

y = 2

Substitute y with 2 in the first equation and solve for x.

y = 4x - 10

2 = 4x - 10

12 = 4x

3 = x

Solution: x = 3, y = 2

Answer: A) (3, 2)

Winston and Alice are taking a trip. Winston left at 8 am and traveled an average of 50 miles per hour. Alice left at 10 am and traveled an average of 70 miles per hour. At what time are they at the same place at the same time? Write a system of equation to represent this situation. Then use the substitution method with that system to determine at the time they will be in the same location. How many miles away from home will they be at that time?

Answers

Answer:

3 PM

350 miles

Step-by-step explanation:

Let's say t is the number of hours since 8 AM.

The distance traveled by Winston is:

w = 50t

The distance traveled by Alice is:

a = 70(t−2)

When w = a:

50t = 70(t−2)

50t = 70t − 140

140 = 20t

t = 7

Winston and Alice will be at the same place 7 hours after 8 AM, or 3 PM.

The distance they travel is 350 miles.

Country X (a developed country) currently has a per capita ecological footprint of 3.2 hectares, while country Y (a developing country) has a per capita ecological footprint of 0.6 hectare. If everybody in the world has an ecological footprint the size of the average footprint between these two countries and there are ~7 billion people on Earth, how many total hectares would be needed

Answers

Answer:

Total hectares needed = 13.3 billion hectares of ecological footprint.

Step-by-step explanation:

Country X's per capita ecological footprint = 3.2 hectares

Country Y's per capita ecological footprint = 0.6 hectares

Earth's population = 7 billion

Average footprint between the two nations = 1.9 (3.2 + 0.6) hectares

If everybody in the world (i.e. the earth's population) has an ecological footprint the size of the average footprint between these two countries, i.e. = 1.9 per capita of earth's population,

Therefore, the total hectares of ecological footprint needed will be equal to 7 billion x 1.9

= 13.3 billion hectares of ecological footprint.

The line passing through points
(4,0) and (-2, 1) has a slope of?

A. -6
B. -1/6
C. 1/2
D. 2
E. 1/6

Answers

Answer:

b. -1/6

Step-by-step explanation:

slope = (difference in y)/(difference in x)

slope = (1 - 0)/(-2 - 4) = 1/(-6) = -1/6

Answer:

m = -1/6 = B

Step-by-step explanation:

[tex]m = \frac{y_2-y_1}{x_2-x_1} \\ x_1=4\\ y_1=0\\ x_2=-2\\y_2=1.\\m = \frac{1-0}{-2-4} \\m = \frac{1}{-6}[/tex]

In June, Jasmine earned $1200 in commission. In July, her commission decreased by 7% Write an expression that can be used to find her commission in July.

Answers

Answer:

$1116

Step-by-step explanation:

An infinite population has a standard deviation of 10. A random sample of 100 items from this population is selected. The sample mean is determined to be 60. At 80% confidence, the margin of error is

Answers

Answer:

1.28

Step-by-step explanation:

Margin of error is also called confidence interval, and it shows how much the results from sample reflects the characteristics of the larger population.

The following steps are used to calculate margin of error.

- obtain population standard deviation (σ) and sample size (n)

- divide standard deviation by square root of sample size

- multiply result by z score consistent with the given confidence. In this case confidence is 80% and z score for it is 1.28

Margin of error= z * (σ ÷ √n)

Margin of error = 1.28 * (10 ÷ √100)

Margin of error= 1.28 * (10 ÷ 10) = 1.28

ASAP 300* POINTS PLUS BRAINLIEST!!! ONLY IF THE ANSWER IS CORRECT!!! What is the value of this expression when a = 3 and b = negative 2? (StartFraction 3 a Superscript negative 2 Baseline b Superscript 6 Baseline Over 2 a Superscript negative 1 Baseline b Superscript 5 Baseline EndFraction) squared? THERE ARE NO OPTIONS FOR THIS QUESTION MUST SHOW STEPS!!!



*/20, or 300/20.

Answers

Answer:

The value of this expression when a = 3 and b = -2 is -1.

Step-by-step explanation:

The expression is:

[tex]X=\frac{3a^{-2}b^{6}}{2a^{-1}b^{5}}[/tex]

Compute the value of X for a = 3 and b = -2 as follows:

[tex]X=\frac{3a^{-2}b^{6}}{2a^{-1}b^{5}}[/tex]

    [tex]=\frac{3\cdot (3)^{-2}\cdot (-2)^{6}}{2\cdot (3)^{-1}\cdot (-2)^{5}}\\\\=\frac{(3^{-1})\times (-2)^{6}}{2\cdot (3^{-1})\cdot (-2)^{5}}\\\\=\frac{(-2)^{1}}{2}\\\\=-1[/tex]

Thus, the value of this expression when a = 3 and b = -2 is -1.

Question 8(Multiple Choice Worth 1 points) (07.01 MC) Find the measure of arc DF. Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x plus 10 degrees, the measure of angle EGC is 70 degrees, and the measure of arc DF is 11x plus 2 degrees. 50° 90° 100° 140°

Answers

Answer:   90°

Step-by-step explanation:

As known ∡EGC=(arcEC+arcDF)/2

arcEC+arcDF=70°*2

5x+10+11x+2=140

16x+12=140

16x=128

x=128:16

x=8

So arcDF=11*x+2=11*8+2=90°

The measure of arc DF is 90°.

What is circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

Given,  Circle A with chords EF and CD that intersect at point G,

arc EC = 5x + 10°

arc DF = 11x + 2°

∠EGC = 70°

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite

so

∠EGC=(1/2)[arc EC+arc DF]

substitute the values

70 = 1/2(5x + 10 + 11x + 2)

70 = 1/2(16x + 12)

140 = 16x + 12

16x = 128

x = 128/16 = 8

so ac DF = 11x + 2

arc DF = 11(8) + 2

arc DF= 88 + 2 = 90°

Hence the value of arc DF is 90°.

Learn more about circle;

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A storage basin is 1240 ft by 637 ft. It’s 15.63 ft deep. How many gallons of water is in the basin

Answers

Answer:

12345824.4

Step-by-step explanation:

I'm not really sure. I just did 1240x637x15.63=12345824.4

answer:

53,445.1 gallons of water

Step-by-step explanation:

im not exactly sure but i looked up how to calculate gallons in a container and the website i went to told me to measure the interior length, width, and height which was already done, then it told me to multiply the length by width by height to get the volume of the container then it told me to divide the volume by 231 to get the number of gallons in the container, so 1,240* 637= 789,880* 15.63= 12,345,824.4÷231= 53,445.127272727272727272727272727 which rounded to the nearest tenth is 53,445.1, i honestly hope that this is right and that it helps

Please answer this correctly without making mistakes
Please simplify the correct answer

Answers

Hi there!! (✿◕‿◕)

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Hillsboro: 700 houses sold

Lowell: 100 houses sold

700 + 100 = 800

Hillsboro and Lowell: 800 houses sold

Other: 600

800 + 600 = 1,400

Clay County: 1,400 houses sold

800/1,400 = 4/7

Hope this helped!!  ٩(◕‿◕。)۶

Answer:

4/7

Step-by-step explanation:

Well first we need to find the total amount of houses sold in Clay County.

700 + 100 + 600

= 1,400

Now we need to find the total of houses sold in Lowell and Hillsboro.

700 + 100

= 800

Now we can make the fraction,

800/1400

and simplify

400/700

200/350

20/35

4/7

Thus,

the fraction of houses sold in Hillsboro and Lowell in Clay County is 4/7.

Hope this helps :)

Determine whether each red path in the vector field is positive, negative, or zero

Answers

If the path is perpendicular to the field it is zero.

If the path is along the field it is positive or negative depending on it's direction.

See the attached picture.

Please answer please please thank you thank

Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent x values? Select both in the
list.

Answers

In any coordinate pair, the first number is the x-value and the second number is the y-value.

To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is -5/3.

It is find the slope of the line.

what is slope?

The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:

m = Rise/Run

If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex]  So, the equation would be:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

In any coordinate pair, the first number is the x-value and the second number is the y-value.

The difference of the y values and divide by the difference in the x values:

m=(14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is  -5/3.

Learn more about slope here:

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These are the weekly wages paid to staff in a hotel. £245 £140 £525 £163 £195 £174 £140 What is the range of these wages? £ What is the mean wage?

Answers

Answer:

Range of wages is £140 to £525.

Mean wage = £226

Step-by-step explanation:

Given:

Weekly wages paid to the staff are :

£245, £140, £525, £163, £195, £174 and £140.

To find:

Range of these wages = ?

Mean wage = ?

Solution:

First of all, let us learn about the range of wages and mean wage.

Range of wages has a minimum pay and a maximum pay.

Here, if we have a look £140 is the minimum pay and

£525 is the maximum pay.

So, range of wages is £140 to £525.

Mean wage means the average of all the wages given to the staff.

Mean is defined as the formula:

[tex]\text{Average/Mean =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]

Here, Sum of all observations mean sum of the wages of all the staff members.

Number of observations mean the number of staff members i.e. 7 here.

Applying the formula:

[tex]\text{Average/Mean =} \dfrac{\text{245+140+525+163+195+174+140}}{\text{7}} \\\Rightarrow \text{Average/Mean =} \dfrac{\text{1582}}{\text{7}}\\\Rightarrow \text{Average/Mean =} 226[/tex]

So, the answer is:

Range of wages is £140 to £525.

Mean wage = £226

A pharmacist wants to mix a 30% saline solution with a 10% saline solution to get 200 mL of a 12% saline solution. How much of each solution should she use

Answers

Answer:

30% constituents=20 mL

10% constituents=180 mL

Step-by-step explanation:

x= 30% volume

y=10% volume

For our first equation, we know the total volume is 200 mL and is the sum

x+y=200

y=200-x (1)

For our second equation, we do a mass balance for 200 mL of final solution.

12% w/v = 0.12 g/mL

This means that in 1 mL of solution, we have 0.12 g of NaCl.

For any solution, concentration multiplied by volume will give the mass of NaCl:

Mass in x mL= C*V (g/mL) (mL)

So in 200 mL, we have

0.12*200 (g/mL) (mL)

=24g of NaCl

Cx*Vx + Cy*Vy=24

0.3x+0.1y=24 (2)

Substitute y=200-x into (2)

0.3x+0.1(200-x)=24

0.3x+20-0.1x=24

0.2x=24-20

0.2x=4

Divide both sides by 0.2

0.2x/0.2=4/0.2

x=20

Substitute x=20 into (1)

y=200-x

y=200-20

y=180

30% constituents=20 mL

10% constituents=180 mL

2.35=11x Equals What

Answers

Answer:

x=0.2136

Step-by-step explanation:

Answer:

x=0.214 rounded to the thousandths

Step-by-step explanation:

2.35=11x

divide each side by 11 to isolate the x

x=0.214 rounded to the thousandths

if 176 dollars can be exchanged for the 140pounds and 1 pound is exchanged for RS 130 how many dollars can be exchanged for RS 2925​

Answers

Answer:

Number of dollar = 28.28 (Approx)

Step-by-step explanation:

Given:

176 dollar = 140 pound

1 pound = Rs.130

Find:

Number of dollars in Rs 2925

Computation:

1 pound = Rs.130

Number of pound = 2925 / 130

Number of pound = 22.5 pound

1 pound = 176 / 140

Number of dollar = [176 / 140]22.5

Number of dollar = 28.28 (Approx)

Solve for the x in the diagram below. 50°, 2x°, and 150°

Answers

The value of x from the diagram is 50 degrees. Vertical angles are angles that meets at a point of intersection.

Vertical angles

Vertical angles are angles that meets at a point of intersection. From the given diagram 150 and 50+2x are vertical angles showing that they are equal to each other. Hence;

50 + 2x = 150

2x = 150 - 50

2x = 100

Divide both sides by 2

2x/2 = 100/2

x = 50

Hence the value of x from the diagram is 50 degrees

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Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive direction, and then move downward along the z-axis a distance of 7 units. What are the coordinates of your position

Answers

Answer:

(4,0,-7)

Step-by-step explanation:

The initial position was (0,0,0) since it was the origin

Now, we have a movement of positive x at a distance of 4 units, with a distance of z a total of 7 units(negative since downward)

The current position is thus;

(4,0,-7)

Thus correlates to (x,y,z) and our y has remained zero as there is no movement along the y-axis

An open box is to be made from a 5 ft by 9 ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.

Answers

Answer:  21 ft³

Step-by-step explanation:

Let x represent the height of the box.

Then the 5 ft width of cardboard is (5 - 2x) when creating the box

and the 9 ft length of cardboard is (9 - 2x) when creating the box.

Volume = length x width x height

            = (9 - 2x)(5 - 2x)(x)

            = 45x - 28x² + 4x³

Using Calculus to solve for x, set the derivative equal to zero and use the quadratic formula to solve for x:

V' = 45 - 56x + 12x²

0 = 12x² - 56x + 45

x = 3.6, x = 1.0

Use those values to find the width, length, and volume:

height(x)   ×  width (5 - 2x)   ×  length (9 - 2x) = Volume

  3.63       ×       -2.26*                                            

     1          ×          3               ×         7              =    21

*width cannot be negative so the height cannot be 3.63

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