A rectangle has dimensions of 7 in. by 5 in. Consider the solid of revolution formed when the rectangle is rotated about its 7 in. side. What is the solid formed by the revolution?
cone cylinder What is the radius (in inches) of the base of the solid of revolution?
in What is the height (in inches) of the solid of revolution?
in Find the exact volume (in cubic inches) of the solid of revolution.

Answers

Answer 1

Answer:

(a) Cylinder, R = 5 in, H = 7 in

(b) Volume = 549.5 cubic inches

Step-by-step explanation:

length, L= 7 in

width, W = 5 in

(a) The solid is cylinder.

Radius, R = 5 in

(b) Height = 7 in

Volume of the cylinder

[tex]V = \pi r^2 h\\\\V = 3.14 \times 5 \times 5\times 7\\\\V = 549.5 in^3[/tex]


Related Questions

help asap pleaseeee asap

Answers

-63/7 = -9
The 3rd answer is correct

A wedge of cheese is shaped like a triangular prism. The wedge of cheese is 7 inches tall. The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches. If you ate this whole block of cheese, about how many cubic inches would you have eaten (ignoring the holes)?


420 in
193 in
385 in
210 in

Answers

Answer:

193 in

Step-by-step explanation:

Volume of a triangular prism:

The volume of a triangular prism is the base area multiplied by the wedge, that is:

[tex]V = A_bw[/tex]

The base area is one half times the triangle base times it's height, so:

[tex]V = 0.5*b*h*w[/tex]

The wedge of cheese is 7 inches tall.

This means that [tex]w = 7[/tex]

The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches.

This means that [tex]b = 11, h = 5[/tex]

Volume:

[tex]V = 0.5*b*h*w = 0.5*11*5*7 = 192.5[/tex]

Rounding, approximately 193 in.

find inverse of f(x)=- 1/2 x+11

Answers

Answer:

-2x + 22

Step-by-step explanation:

We have the function f(x) = -1/2x + 11 and are asked to find the inverse of it.

To find the inverse, we will follow the according steps :

Replacing x with ySolving for y

Let's do as followed:

Replacing x with y :

Since f(x) can be also written as y, we can do y = -1/2x + 11, thus making the switch alot easier.

y = -1/2x + 11

x = -1/2y + 11

Solve for y :

We have to get y alone to find the inverse, to do so, get rid of the outlier by subtracting 11 from both sides :

x - 11 = -1/2y

Now divide both sides by -1/2 to get y alone and retrieve our inverse :

-2(x - 11)

Distribute to get the inverse :

-2x + 22

Complete the equation: x2 + 8x + __ = (__)^2

Answers

Answer:

B

Step-by-step explanation:

16,x+4

by completing square formula

University Trailer Sales Company sold 356 utility trailers during a recent year. If the gross annual sales for the company was ​$328128​, what was the average selling price for each​ trailer?

The average selling price of each trailer was nearly ​$
​(Round to the nearest whole​ number.)

Answers

Answer:

The Answer is 2000$..........

Find the probability that a randomly
selected point within the circle falls
in the white area.
r = 4 cm
2.5 cm
3 cm
3 cm
[?]%
Round to the nearest tenth of a percent.

Answers

Answer:

61.2%

Step-by-step explanation:

Area of the circle π(4²) = 50.265... cm²

Area of the triangle = ½(6)(6.5) = 19.5 cm²

probability of landing is white is

1 - (19.5 / 50.265) = 0.612059...

The probability that a randomly selected point within the circle falls in the white area is 61.22%.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

As we know the circle is a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The total outcomes = The area of a circle

The area of the circle = πr²

The area of the circle = π(4)²

Because r = 4 cm

The area of the circle = 50.285 square cm

The area of the triangle = (1/2)(3+3)(4+2.5)

The area of the triangle = 19.5 square cm

The area of the white region = 50.285 - 19.5 = 30.785 square cm

Probability = 30.785/50.285

Probability = 0.6122 or

Probability = 61.22%

Thus, the probability that a randomly selected point within the circle falls in the white area is 61.22%.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ5

If triangle ABC has the following measurements, what is the measure of angle B? a=5 b=7 c=10

Answers

Answer: about 40.54°

Step by step explanation:

7^2 =  5^2 + 10^2  - 2(5)(10)cos(B)

cos(B)  = (7^2 - 5^2 - 10^2) / (-2(5)(10) )

B = cos-1 [ (7^2 - 5^2 - 10^2) / (-2(5)(10) ]  =  cos-1 (.76) = about 40.54°

The length of a rectangle is four more than three times the width. If the perimeter of this rectangle is at least 70 square centimeters. Write an inequality that can be solved to find the width of the rectangle

Answers

Answer:

Step-by-step explanation:

Let L represent the length of the triangle.

Let W represent the width of the triangle.

The length of a rectangle is four more than three times the width. This means that

L = 3W + 4

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

If the perimeter of this rectangle is at least 70 square centimeters, an inequality that can be solved to find the width of the rectangle is

2(L + W) ≥ 70

L + W ≥ 70/2

L + W ≥ 35

Answer:

6w +8 ≥70

Step-by-step explanation:

Let w be the width

The length is then 3w+4 ("the length is 4 more than 3 times the width")

Since a rectangle has opposite sides equal, the perimeter would be 2(l+w) or 2(w+3w+4) which would be 6w +8.  If the perimeter is at least 70, that is, 70 or more, the inequality would be

  6w + 8 ≥ 70.  

The units, however, would not be SQUARE centimeters, just centimeters.  If the question were asking for area, the units would be square units, but since perimeter is a linear measurement,  the units would have to be linear.

When a sample has an even number of observations, the median is the

Group of answer choices

observation in the center of the data array

average of the two observations in the center of the data array

value of the most frequent observation

Answers

Answer:

average of the two observations in the center of the data array

Step-by-step explanation:

When there is an odd number, we use the middle

Example

1,5,9

The median is 5

When there is an even number

1,3,5,7

The middle is between the 3 and 5 so we average the middle number

(3+5)/2 = 4

Answer:

the answer is => observation in the center of the data array

Step-by-step explanation:

[tex]\sf{}[/tex]


I need help answering this ASAP

Answers

can you zoom in on my pic more or no does it say 1/z

Answer:

Option A. Reciprocal

Answered by GAUTHMATH

Function A is a linear function. An equation for Function A is 3x + 4y = 28.
Which of the following functions has the same slope as Function A?
4
3
3
y = -x
4
4
y = -x
3
-
3
4.
4 3
y = --X +
3 4
3 4
y = --X +
4 3

Answers

First, convert that into a y=mx+b form.

Move the x to the other side so y is the only thing on the left. Since you moved it to the other side of the equal sign, be sure to make that number negative (the opposite sign)

Now… you have 4y=-3x+28
Let’s get y by itself. Since you’re multiplying 4 and y, you divide everything by 4 to get your y.

That leaves you with y=-3/4x+7.

We are looking at slope, which is your m in the y=mx+b form.

That is -3/4. The answer is the last square.

Which is equivalent to 10’6

Answers

Answer:          

35/5 (if you mean 10.6)    

1000000 (if you mean 10 to the sixth power)      

0.000001 (if you mean 10/6)

Answer:

There are 126 inches in 10'6

Step-by-step explanation:

take our feet and multiply the value by 12

Clara travels from her home to Stoke.
The distance from her home to Stoke is 100 miles.
She travels at an average speed of 50 miles per hour.
She stops for 20 minutes on the journey. Clara arrives in Stoke at 10:10 am.
At what time did she leave home?​

Answers

Answer:

7:50 am

Step-by-step explanation:

Clara took 2 hours to reach, and she took a 20 min break, so she left at 7:50 and arrived at 10:10.

Answer:

7:50

Step-by-step explanation:

50 miles per hour/50 miles per 60 min.

50 miles + 50 miles = 100 miles.

if 50 miles takes 1 hour, 100 miles would equal to 2 hours.

considering clara took a 20 min break, thats 2 hours and 20 minutes.. subtract that from the time she arrived and you would get 7:50

if f(x)=3x²-7 and f(x+n)=3x²+24x+41, what is the value of n?

Answers

Answer:

n=4

Step-by-step explanation:

f(x+n)=3(x+n)^2-7=3x^2+24x+41

3x^2+3n^2+6xn-7=3x^2+24x+41

Comparing and we will get, n=4

what is 6 3/5 - 4 3/10

Answers

The Answer would be 2.3.

Answer:

2 3/10

Step-by-step explanation:

3/5x2=6/10

6/10-3/10=3/10

Help please. I need the answer

Answers

No, this is not a function. We can see if this is a function by doing the vertical line test. 5, 0 is assigned to 5, 3 and 5, 8 which means it fails the vertical line test.
Yes this is a function as every x-value has a y-value

Please help on my hw

Answers

Answer:

x^2 - 7x - 30 = 0

Step-by-step explanation:

since solutions are 10 and -3

a factorised quad eqn can be formed:

(x-10)(x+3)=0

expand the eqn

x^2-7x-30 = 0 is the answer

Please help!!!!! Nowwww

Answers

Answer:

It has 1 term and a degree of 4.

Step-by-step explanation:

3j⁴k-2jk³+jk³-2j⁴k+jk³

= 3j⁴k-2j⁴k-2jk³+jk³+jk³

= j⁴k

So, in this expression, there is 1 term, and it has a degree of 4.

I) Find the volume in terms of pie

ii) curved surface area in terms of pie

iii) capacity in litres (correct to nearest litre)

Answers

Answer:

i) pi×4500 cm³

ii) pi×600 cm²

iii) 14 liters

Step-by-step explanation:

in general : the diameter is 30 cm, the radius is half of that (15 cm)

i)

the volume of a cylinder is base area times height.

Vc = pi×r²×h = pi×15²×20 = pi×225×20 = pi×4500 cm³

ii)

similar to volume, the side "mantle" area of the cylinder is the circumference of the base area times height.

surface area of the cylinder mantle is

Scm = 2×pi×r×h = 2×pi×15×20 = pi×30×20 = pi×600 cm²

iii)

for this we need now to do the multiplication with pi and then convert the cm³ to liters.

1 liter = a cube of 10 cm side length = 10×10×10 = 1000 cm³

pi×4500 = 14137.17 cm³ = 14.13717 liters or rounded 14 liters

What is the maximum value of the objective function, P, with the given constraints?

P = 25x+45y

(4x+y≤16)
(x+y≤10)
(x≥0)
(y≥0)

Options

A: 100
B: 410
C: 450
D: 720

Answers

Answer:

D

Step-by-step explanation:

Please help on 25 it’s confusing me I need the correct answer

Answers

Answer:

X * 0.8 = $64

x = $80

Step-by-step explanation:

Answer:

$80 (D)

Step-by-step explanation:

If Richard is getting a discount and his final price is $64 that means the answer must be above 64. That eliminates A, B, and C.

Use the formula: 20% of x = $64 and substitute the other two options. 20 percent of 84 is 16.8. 84-16.8=67.2 (not the correct answer). 20 percent of 80 is 16. 80-16=64(The Correct Answer).The answer must be $80 (D)    

Nancy left a bin outside in her garden to collect rain water. She notices the 1/2 gallon fills 2/3 of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.

Answers

Here we want to solve a question involving fractions, we will find that:

3/4 gallon fils the complete bin.

Ok, so we know that 1/2 gallon of water, fills 2/3 of the bin.

We want to find the total amount of water that would fill the entire bin.

So we could write an equation like:

amount of water =  amount of the bin that it fills.

Then, using the above information, we have:

1/2 gal  = 2/3 of a bin

Now we want to get at 1 on the right side, this would mean "1 bin"

Then we multiply both sides by (3/2)

(3/2)*(1/2) gal = (3/2)*(2/3) of a bin

3/4 gal = 1 bin

From this, we can conclude that (3/4) gallons of water would fill the complete bin.

If you want to learn more about algebra, you can read:

https://brainly.com/question/4837080

x = 0,75 gallons      or       x  = 3/4   gallons      The volume of the bin

The volume of the bin is: In terms of a fraction

1  =  3/3      or any unitary fraction   5/5    7/7    9/9

We will take 3/3 since we have the information that 2/3 of the volume of the bin was filled with 2/3 of a gallon

If  2/3 of the volume of the bin was filled with 1/2 gallon then we make a rule of three according to:

If     0,5  gal.         fill    2/3 of the volume of the bin   then

          x   gal         fill     3/3  ( the volume of the bin)

solving

0,5 (gal) * 3/3    =   (2/3)*x       ( The equation)

0,5*3 = 2*x

x  =  (0,5*3)/2

x = 0,75 gallons      or       x  = 3/4   gallons

lim(x-0) (sinx-1/x-1)

Answers

lim ( sinx-1)/(x-1)

x=>0

apply x=0

(sin(0)-1)/(0-1)

(0-1)/(-1)

=1

Find the area of the shaded regions.

Answers

Answer: About 21.98 cm²

Step-by-step explanation:

First, find the area of the large shaded circle:

[tex]r^{2} \pi =3^{2} \pi =9\pi[/tex]

Find the area of the two small unshaded circles:

[tex]1) r^{2} \pi =1^{2} \pi =1\pi \\2) r^{2} \pi =1^{2} \pi=1\pi[/tex]

Subtract the area of the small circle from the large circle:

[tex]9\pi -1\pi -1\pi =9\pi -2\pi =7\pi[/tex]

Therefore, the area of the shaded region is:

[tex]7\pi =7*3.14=21.98[/tex]

A boat has a rip-hole in the bottom while 20 miles away from the shore. The water comes in at a rate of 1.5 tons every minute, and the boat would sink after 70 tons of water came in. How fast must the boat go in order to reach the shore before sinking?

Answers

Answer:

t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks

S = V * t

V = S / t = 20 mi * 5280 ft/mi / 2800  sec  = 37.7 ft/sec

Since 88 ft/sec = 60 mph

the speed is 60 * 37.7 / 88 = 25.7 mph

Solve the polynomial by finding all roots.
X^3-6x^2-2x+12=0

Answers

I hope this is the correct answer

The 90% confidence interval for the mean one-way commuting time in New York City is
5.22 < < 5.98 minutes. Construct a 95% confidence interval based on the same data.
Which interval provides more information?

Answers

Answer:

95% provides more information

Step-by-step explanation:

The confidence interval is obtained by using the relation :

Xbar ± Zcritical * σ/√n

(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)

(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)

Adding (1) and (2)

2xbar = 5.22 + 5.98

2xbar = 11.2

xbar = 11.2 / 2 = 5.6

Margin of Error :

Xbar - lower C.I = Zcritical * σ/√n

Zcritical at 90% = 1.645

5.6 - 5.22 = 1.645 * (σ/√n)

0.38 = 1.645 * (σ/√n)

(σ/√n) = 0.38 / 1.645 = 0.231

Therefore, using the se parameters to construct at 95%

Zcritical at 95% = 1.96

Margin of Error = Zcritical * σ/√n

Margin of Error = 1.96 * 0.231 = 0.45276

C.I = xbar ± margin of error

C. I = 5.6 ± 0.45276

C.I = (5.6 - 0.45276) ; (5.6 + 0.45276)

C. I = (5.147 ; 6.053)

Hence, 95% confidence interval provides more information as it is wider.

Matematykakdbebox
Jaggbn

Answers

Answer:

theres no question....

Step-by-step explanation:

???

I need help guys thanks so much

Answers

I think its A) (f+g)(z)=|2x+4|-2

Step-by-step explanation:

♥️♥️♥️♥️♥️♥️♥️♥️♥️ help me

Answers

9514 1404 393

Answer:

AC = 2.0 mm = 41.3 kg

Step-by-step explanation:

The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.

__

a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).

The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)

These are equal, so we have ...

  16(AC -1.5) = 7(3 -AC)

  16AC -24 = 21 -7AC . . . . . eliminate parentheses

  23AC = 45 . . . . . . . . . . . add 7AC+24

  AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC

  AC ≈ 2.0 meters . . . . rounded to 1 dp

__

b) The torques in this scenario are ...

  M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m

  M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M

  M = 41.3 kg . . . . rounded to 1 dp

_____

Additional comment

Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.

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