an open tank has tge shape of circular cone. the tank is 8feet across the top and 6 feet high. watwr is pumped through the buttom of the tank. how much work is done to fill the tank from a depth of 4 feet to a depth of 6 feet? water weighs 62.4 pounds per cubic foot

Answers

Answer 1

Answer:

[tex]W=22652.98ft-lb[/tex]

Step-by-step explanation:

We are given that

Height of tank=6feet

Diameter of tank=8 feet

Radius of cone,r=d/2=8/2=4 feet

Let  a layer of thickness dy at distance yr from the bottom at origin

y=6 feet

Using similar triangle property

[tex]\frac{r}{y}=\frac{4}{6}=\frac{2}{3}[/tex]

[tex]r=\frac{2}{3}y[/tex]

Weight of water=62.4 pounds per cubic foot

Now,

Weight of layer=[tex]62.4\times \pi r^2 h=62.4(\frac{4}{9}\pi y^2 dy[/tex]

Now, work done to fill the tank from a depth of 4 feet  to a depth of  6 feet is given by

[tex]W=\int_{a}^{b}62.4\times \frac{4}{9}\pi y^2(y) dy=\int_{4}^{6}62.4\times \frac{4}{9}\pi y^3 dy[/tex]

[tex]W=\frac{62.4\times 4\pi}{9}[\frac{y^4}{4}]^{6}_{4}[/tex]

[tex]W=\frac{249.6\pi}{36}(6^4-4^4)[/tex]

[tex]W=22652.98ft-lb[/tex]


Related Questions

What is the range of 12,20,18,25,6

Answers

Answer:

19

Step-by-step explanation:

The range is the difference between the biggest number and the smallest number

Let's put these numbers in order:

25,20,18,12,6

The biggest number is 25, the smallest number is 6

25-6=?

19

ignore the black words on the bottom but i’ll be giving brainliest!

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Answer:

2. the figure has rotatinal symetry

Step-by-step explanation:

Answer:

1. x = 4; y = 7

2. rotational symmetry.

3. No. 360°÷ 50° is not a whole number, so the points will not be evenly spaced all the way around the center.

Step-by-step explanation:

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A local farm has a 0.5 acre field that was planted with 26,100 corn plants. One acre is equivalent to 43,500 square feet. Assuming the same planting density, how many corn plants could they plant on a field with an acre of 80,000 square feet

Answers

Answer:

96000 corn

Step-by-step explanation:

80,000/43500 = 1.84

1.84/0.5 = 3.678

3.678 x 26100 = 96000

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Answers

Answer:

K must be greater than 5

G must be less than  4

Step-by-step explanation:

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Answers

Answer:

44.5 degrees.

Step-by-step explanation:

Since these triangles are congruent, their angles are the same.

Therefore, we can set an equation with the 2 labeled angles (which are angles C and F):

2.5x+8=3.5x-7

8=x-7

x=15

We can plug 15 back into one of the equations:

2.5(15)+8 = 45.5

This means angle F is 45.5.

To find out the measure of angle E, recall the fact that the angles in a triangle add up to 180. Since this is a right triangle, and F = 45.5, we can set up an equation and solve for x:

90 + 45.5 + x = 180

135.5 + x = 180

x = 44.5

Therefore, the angle E is 44.5 degrees.

Answer:

44.5

Step-by-step explanation:

These triangles are the same so we know that

2.5x + 8 = 3.5x - 7

Subtract 2.5 x from both sides

8 = x - 7

Add 7 to both sides

15 = x

Substitute x

37.5 +8

45.5

There is a right angle so we must add 45.5 + 90 to get 135.5

Subtract 135.5 from 180 to get

44.5

Use the slope formula to determine the slope of the line.
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Answers

Answer:

2/3

Step-by-step explanation:

y2-y1/x2-x1

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Answer:

9/5

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer: a, b, d

Step-by-step explanation: don’t count me on it

Answer:

B, D

Step-by-step explanation:

just find the common denominator and see if it works

Look at the figure. If ∆LMC ≅ ∆BJK, then _____ ≅ ∆KB
A. BJ
B. CM
C. ML
D. CL

Answers

The answer to your question is D.CL

If ∆LMC ≅ ∆BJK, then ∆CL ≅ ∆KB. so the correct option is D.

What is the congruent triangle?

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We have been given that ∆LMC ≅ ∆BJK.

The image of the triangles are attached below;

The triangle are congruent to each other so,

∆LMC ≅ ∆BJK

∆LM ≅ ∆BJ

∆LC ≅ ∆BK

∆MC ≅ ∆JK

Thus, ∆LC ≅ ∆BK so the correct option is D.

Learn more about congruent triangles;

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enrico is laying 1-ft tiles ok a square bathroom floor. if he needs 81 tiles to cover the floor, how many tiles run along each wall?

Answers

Answer:

9

Step-by-step explanation:

you would need to find the square root of the total amount of tiles. luckily 81 is a square number meaning the answer is each side is 9 tiles long.

What is the value of -8(17-12)/-2(8-(-2))

Answers

This answer is 2. Please give brainliest.

Answer:

it's 2 got it right on edg

Step-by-step explanation:

Students in grades 7 and 8 were asked which food they liked the best. The results are shown in the table. What percentage of all students prefer hotdog

Answers

Answer:

Where's the table?

Step-by-step explanation:

Answer:

55%

Step-by-step explanation:

The length of a quarter is 0.955 inch. Round the length of a quarter to the nearest tenth of an inch

Answers

Answer:

the answer to the question is 0.96.

Answer:

1 inch

Step-by-step explanation:

the 9 is in the tenths place.  5 or more you need to round up.

Solve for x 2(-4x+2)=28

Answers

Answer:

x=-3

Step-by-step explanation:

Divide both sides by 2, so -4x+2=14

Subtract 2 from both sides, -4x=12

Divide both sides by -4, so x=-3

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Write a word problem that can be represented by the expression 5/6 divided by 1/3.

Answers

Answer:

I have 5/6 of a candy bad and I want to give each of my 3 friends some. How much would each friend get?

Step-by-step explanation:

The word problem that can be represented by the expression 5/6 divided by 1/3 is "There are a total of 5/6 chocolates. Divide these chocolates such that each person will get 1/3 part of that".

Given :

The expression 5/6 is divided by 1/3.

The following steps can be used in order to determine the word problem that can be represented by the expression 5/6 divided by 1/3:

Step 1 - The knowledge of arithmetic operations can be used in order to determine the word problem that can be represented by the expression 5/6 divided by 1/3.

Step 2 - There are a total of 5/6 chocolates. Divide these chocolates such that each person will get 1/3 part of that.

Step 3 - Solve the above problem by dividing 5/6 by 1/3.

[tex]= \dfrac{5\times 3}{6\times 1}[/tex]

= 2.5

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https://brainly.com/question/25834626

2,9,23,51,107
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Answers

Answer:

answer is 142

Step-by-step explanation:

A student missed 51 problems on a history test and received a grade of 4%. If all the problems were of equal value, how many problems were on the test? Follow the problem-solving process and round your answer to the nearest integer.

Answers

there were 53.125 (or 53 1/8) questions on the test.

cross multiply and divide:

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hope this helps! let me know if you have any questions :)

C is the circumcenter of PQR
PC=3x+7, RC=5x-15 and QC=51-x.
what does RC equal?

Answers

Answer:

[tex] RC = 40 [/tex]

Step-by-step explanation:

Given:

PC = 3x + 7,

RC = 5x - 15,

QC = 51 - x.

Required:

measure of RC

SOLUTION:

Given that C is the circumcenter of ∆PQR, therefore, vertices P, Q, and R are equidistant from C.

So therefore,

[tex] PC = RC = QC [/tex]

Let's find the value of x using:

[tex] PC = RC [/tex]

[tex] 3x + 7 = 5x - 15 [/tex] (substitution)

Collect like terms

[tex] 3x - 5x = -7 - 15 [/tex]

[tex] -2x = -22 [/tex]

Divide both sides by -2

[tex] x = \frac{-22}{-2} [/tex]

[tex] x = 11 [/tex]

Find the measure of RC

[tex] RC = 5x - 15 [/tex]

substitute x = 11 into the equation

[tex] RC = 5(11) - 15 [/tex]

[tex] RC = 55 - 15 [/tex]

[tex] RC = 40 [/tex]

Answer:

40

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Which of the following statement is false? 8 < 8 2>8 2<8 2<8 2<8

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Answer:

D

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Answers

Answer:

The answer is D

Step-by-step explanation:

(4x6)^3

(24)^3=13,824

when you multiply 4^3 with 6^3 you get the same answer of 13,824

Answer:

Answer=D

Step-by-step explanation:

(for powers outside a bracket it splits in the numbers inside the bracket)

(4×6)^3

=([tex]4^{3}[/tex]×[tex]6^{3}[/tex]) as in D

To proof

-if we multiply them first we will get 24 and that to the power of three will equal to 13824.

-if we did as in the answer so,

[tex]4^{3}[/tex]×[tex]6^{3}[/tex]

=64×216

=13824

they are equal to each other 13824=13824 so answer D is correct.

Find the domain for f(x) = 2x + 9

Answers

Answer:9

Step-by-step explanation:Set x to 0 and the answer is 9

2.
A line goes through the points (0, 10) and (-1, 1).
2a
What is the slope of the line?

Answers

Answer:

9

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 1 -10)/(-1 -0)

   = -9/-1

   = 9

Answer:

9

Step-by-step explanation:

1 - 10 / -1 +0 = -9 / -1 = 9

1 If f(x) = x - x9, what is the value of f(2)?
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Answers

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Answers

Answer:

-18

Step-by-step explanation:

The order in which you multiply inverse matrices is not relevant.
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Answers

True the answer is true
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