A water tank is in the shape of a cone.Its diameter is 50 meter and slant edge is also 50 meter.How much water it can store In it ? it releases water to a gated apartment building at the rate of 400 liters per second. In how many minutes tank will be empty?

Answers

Answer 1

To get the most accurate answer possible, we're going to have to go into some unsightly calculation, but bear with me here:

Assessing the situation:

Let's get a feel for the shape of the problem here: what step should we be aiming to get to by the end? We want to find out how long it will take, in minutes, for the tank to drain completely, given a drainage rate of 400 L/s. Let's name a few key variables we'll need to keep track of here:

[tex]V[/tex] - the storage volume of our tank (in liters)
[tex]t[/tex] - the amount of time it will take for the tank to drain (in minutes)

We're about ready to set up an expression using those variables, but first, we should address a subtlety: the question provides us with the drainage rate in liters per second. We want the answer expressed in liters per minute, so we'll have to make that conversion beforehand. Since one second is 1/60 of a minute, a drainage rate of 400 L/s becomes 400 · 60 = 24,000 L/min.

From here, we can set up our expression. We want to find out when the tank is completely drained - when the water volume is equal to 0. If we assume that it starts full with a water volume of [tex]V[/tex] L, and we know that 24,000 L is drained - or subtracted - from that volume every minute, we can model our problem with the equation

[tex]V-24000t=0[/tex]

To isolate [tex]t[/tex], we can take the following steps:

[tex]V-24000t=0\\ V=24000t\\ \frac{V}{24000}=t [/tex]

So, all we need to do now to find [tex]t[/tex] is find [tex]V[/tex]. As it turns out, this is a pretty tall order. Let's begin:

Solving for [tex]V[/tex]:

About units: all of our measurements for the cone-shaped tank have been provided for us in meters, which means that our calculations will produce a value for the volume in cubic meters. This is a problem, since our drainage rate is given to us in liters per second. To account for this, we should find the conversion rate between cubic meters and liters so we can use it to convert at the end.

It turns out that 1 cubic meter is equal to 1000 liters, which means that we'll need to multiply our result by 1000 to switch them to the correct units.

Down to business: We begin with the formula for the area of a cone,

[tex]V= \frac{1}{3}\pi r^2h [/tex]

which is to say, 1/3 multiplied by the area of the circular base and the height of the cone. We don't know [tex]h[/tex] yet, but we are given the diameter of the base: 50 m. To find the radius [tex]r[/tex], we divide that diameter in half to obtain r = 50/2 = 25 m. All that's left now is to find the height.

To find that, we'll use another piece of information we've been given: a slant edge of 50 m. Together with the height and the radius of the cone, we have a right triangle, with the slant edge as the hypotenuse and the height and radius as legs. Since we've been given the slant edge (50 m) and the radius (25 m), we can use the Pythagorean Theorem to solve for the height [tex]h[/tex]:

[tex]h^2+25^2=50^2\\ h^2+625=2500\\ h^2=1875\\ h=\sqrt{1875}=\sqrt{625\cdot3}=25\sqrt{3}[/tex]

With [tex]h=25\sqrt{3}[/tex] and [tex]r=25[/tex], we're ready to solve for [tex]V[/tex]:

[tex]V= \frac{1}{3} \pi(25)^2\cdot25\sqrt{3}\\ V= \frac{1}{3} \pi\cdot625\cdot25\sqrt{3}\\ V= \frac{1}{3} \pi\cdot15625\sqrt{3}\\\\ V= \frac{15625\sqrt{3}\pi}{3} [/tex]

This gives us our volume in cubic meters. To convert it to liters, we multiply this monstrosity by 1000 to obtain:

[tex]\frac{15625\sqrt{3}\pi}{3}\cdot1000= \frac{15625000\sqrt{3}\pi}{3}[/tex]

We're almost there.

Bringing it home:

Remember that formula for [tex]t[/tex] we derived at the beginning? Let's revisit that. The number of minutes [tex]t[/tex] that it will take for this tank to drain completely is:

[tex]t= \frac{V}{24000} [/tex]

We have our [tex]V[/tex] now, so let's do this:

[tex]t= \frac{\frac{15625000\sqrt{3}\pi}{3}}{24000} \\ t= \frac{15625000\sqrt{3}\pi}{3}\cdot \frac{1}{24000} \\ t=\frac{15625000\sqrt{3}\pi}{3\cdot24000}\\ t=\frac{15625\sqrt{3}\pi}{3\cdot24}\\ t=\frac{15625\sqrt{3}\pi}{72}\\ t\approx1180.86[/tex]

So, it will take approximately 1180.86 minutes to completely drain the tank, which can hold approximately [tex]V= \frac{15625000\sqrt{3}\pi}{3}\approx 28340615.06[/tex] L of fluid.

Related Questions

HELP URGENT NEED TO PASS :(((((

Answers

It goes through (4,0) and (0,-4) so by slope formula, (4-0)/(0--4)=4/4=1

Slope is rise divided by run, or rise over run.
Look at a point on the graph, for example, (0, -4).
How much do you need to go up and then right to get to the next point?
If you go up 1 and right 1, you get to point (1, -3) which is also on the graph.
Going up 1 is a rise of 1.
Going right 1 is a run of 1.
Slope = rise/run = 1/1 = 1

Mark the statements that are true.

A. An angle that measures is a reflex angle.
B. An angle that measures 65 is an acute angle.
C. An acute angle measures less than .
D. An angle that measures 300 is an obtuse angle.

Answers

The correct options are B. An angle that measures 65 is an acute angle. and C. An acute angle measures less than 90 degrees.

To determine the truth of each statement, let's analyze each option:

A. An angle that measures 180 degrees is a reflex angle.

This statement is false. An angle that measures exactly 180 degrees is a straight angle, not a reflex angle. A reflex angle is greater than 180 degrees but less than 360 degrees.

B. An angle that measures 65 degrees is an acute angle.

This statement is true. An acute angle is an angle that measures less than 90 degrees. Since 65 degrees is less than 90 degrees, it is indeed an acute angle.

C. An acute angle measures less than 90 degrees.

This statement is true. By definition, an acute angle is any angle whose measure is less than 90 degrees.

D. An angle that measures 300 degrees is an obtuse angle.

This statement is false. An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. Since 300 degrees is greater than 180 degrees, it is not an obtuse angle but rather a reflex angle.

Ruchi measured the area of her kitchen as

Answers

Ruchi measured the area of her kitchen as,

Answer:

She is incorrect because 2.81 × 10^4 is around 30,000 so the units must be smaller than feet. She most likely measured in inches.

The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).

Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram.

Answers

Slope of JK=((-1)-2)/(4-(-3)=-3/7 Slope of KL=((-5)-(-1)/(2-4=2 Slope of LM=((-2)-(-5))/(-5-2)=-3/7 Slope of MJ=(2-(-2))/((-3)-(-5))= 2 JK is parallel to LM and KL is parallel to MJ. Therefore JKLM is a parallelogram.

Solve 12g=12(2/3g-1)+11

Answers

Solve for g:12 g = 12 ((2 g)/3 - 1) + 11
Put each term in (2 g)/3 - 1 over the common denominator 3: (2 g)/3 - 1 = (2 g)/3 - (3)/3:12 g = 12 (2 g)/3 - (3)/3 + 11
(2 g)/3 - (3)/3 = (2 g - 3)/3:12 g = 12 (2 g - 3)/3 + 11
12/3 = (3×4)/3 = 4:12 g = 4 (2 g - 3) + 11
4 (2 g - 3) = 8 g - 12:12 g = 8 g - 12 + 11
Grouping like terms, 8 g - 12 + 11 = 8 g + (11 - 12):12 g = 8 g + (11 - 12)
11 - 12 = -1:12 g = 8 g + -1
Subtract 8 g from both sides:12 g - 8 g = (8 g - 8 g) - 1
12 g - 8 g = 4 g:4 g = (8 g - 8 g) - 1
8 g - 8 g = 0:4 g = -1
Divide both sides of 4 g = -1 by 4:(4 g)/4 = (-1)/4
4/4 = 1:Answer: g = (-1)/4

For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x squared plus three divided by the quantity x squared minus nine

Answers

The vertical asymptotes are: "x = 3" and "x = -3" .
__________________________________________
The horizontal asymptote is: "y = 2" .
___________________________________________
Explanation:
___________________________________________

f(x) = [tex] \frac{x^{2}+ 3}{ x^{2} - 9}[/tex] ;

We know that "(x² − 9) ≠ 0 ; since we cannot divide by "0" ; so the "denominator" in the fraction cannot be "0" ;

since: 9 − 9 = 0 ; "x² " cannot equal 9.

So, what values for "x" exist when "x = 9" ?

x² = 9 ;

Take the square root of EACH SIDE of the equation ; to isolate "x" on one side of the equation ; and to solve for "x" ;

√(x²) = √9 ;

x = ± 3
__________________________________________
So; the vertical asymptotes are: "x = 3" and "x = -3" .
__________________________________________
The horizontal asymptote is: "y = 2" .
__________________________________________
(since: We have: f(x) = [tex] \frac{x^{2}+ 3}{ x^{2} - 9}[/tex] ;

The "x² / x² " as the highest degree polymonials; both with "implied" coefficients of "1" ; and both raised to the same exponential power of "2".

A total of 820 tickets were sold for the school play. they were either adult tickets or student tickets. there were 70 more student tickets sold than adult tickets. how many adult tickets were sold?

Answers

375 numbers of adult tickets were sold

By setting up a system of equations, we find that 375 adult tickets were sold for the school play.

To solve this problem, we need to set up a system of equations using the information provided:

There are only two types of tickets: adult tickets and student tickets.A total of 820 tickets were sold.There were 70 more student tickets sold than adult tickets.

Let's define the following variables:

A for the number of adult tickets.S for the number of student tickets.

According to the problem:

A + S = 820 (since the total number of tickets is 820)S = A + 70 (since there are 70 more student tickets than adult tickets)

Now we substitute the second equation into the first:

A + (A + 70) = 8202A + 70 = 8202A = 750A = 375

So, 375 adult tickets were sold.

Julie needs 3 lengths of string that are each 6 inches long. Marlene needs 7 lengths of string that are each 8 inches long.

How much string do the girls need altogether?

in.

Answers

seventy four because 6*3 is 18 and 7*8 is 56, add them to get 74

y + 3 = –y + 9 solve

Answers

You need to isolate the variable.

y + 3 = -y + 9
Add y to both sides.
2y + 3 = 9
Subtract 3 from both sides.
2y = 6
Then divide 2 to solve for y.
y = 6
I hope this helps love! :)

Tape diagram to subtract 33-19

Answers

well 33 - 19 = 14 and what do u mean tape diagram?

To subtract 19 from 33 using a tape diagram, draw a rectangle labeled 33, mark off a section labeled 19, and the unshaded difference represents the result, which is 14.

To create a tape diagram to show the subtraction of 33-19, we start by drawing a long rectangle to represent the number 33. We then mark off the length that represents the number 19 on the same tape, indicating the part we want to subtract. Lastly, the remaining part of the tape diagram represents the difference between the two numbers.

Draw a rectangle and label it 33.Mark a section of the rectangle and label it 19.Shade in or distinguish the remaining part of the rectangle; this is the result of 33 minus 19.See the unshaded part, which represents the difference, and count if necessary to find that it equals 14.

The final result is the length of the unshaded part of the tape diagram, which shows the difference when you subtract 19 from 33.

Terrance bought 3 markers. his sister bought 5 markers. terrance and his sister spent a total of $16 on the markers. what was the price of each marker?

Answers

each marker will cost $2

Hurry When solving a system of equations, Jared found y = x 10 for one equation and substituted x 10 for y in the other equation. Nicole found x = y – 10 for the same equation and substituted y – 10 for x in the other equation. Who is correct? Explain.

Answers

I can say that Jared and Nicole are correct because they manipulated the equation right. They can either write the equation as y as a function of x then substitute it to the y in the other equation and solve for x. They can also write the equation as x as a function of y and substitute it to x in the other equation and solve for y. For both solution, they will still obtain the same answers.

Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

Given information:

Jared found that [tex]y = \dfrac{x} {10}[/tex] for one equation and substituted [tex]\dfrac{x}{10}[/tex] for y in the other equation.

Nicole found [tex]x = y -10[/tex] for the one equation and substituted [tex]y -10[/tex] for x in the other equation.

So, there are two equations. Based on the question, the equation should be,

[tex]x=10y[/tex] and [tex]y-x=10[/tex].

Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.

This method is the substitution method which is used to find the solution of the system of equations.

Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

For more details, refer to the link:

https://brainly.com/question/14619835

A histogram can help you make predictions about a set of data. True False

Answers

This is true because a histogram lets you discover and show the underlying frequency distribution

A one celled organism measures 32 millimeters in a length in a photograph. If the photo has been enlarged by a factor of 100, what is the actual length of the organism? Show your work

Answers

Final answer:

The actual length of the organism is 0.32 millimeters, which is obtained by dividing the photograph length (32 mm) by the magnification factor (100).

Explanation:

To determine the actual length of the one-celled organism when the photograph has been enlarged by a factor of 100, we use the formula:

Actual length = Photograph length ÷ Magnification factor

Substituting the given values:

Actual length = 32 mm ÷ 100

Actual length = 0.32 mm

This calculation shows that the actual length of the organism is 0.32 millimeters, which is equivalent to 320 micrometers (320 µm). It's interesting to note that this is well within the size range for many microorganisms, which may require magnification to be seen clearly, such as with a microscope.

He length of a rectangle is six times its width. if the perimeter of the rectangle is 70 in , find its area.

Answers

The width is 150 inches squared

Help please
Solve for r.

s=2πrh

Answers

s/2πh=r

hope this helps u

Here it is
I hope that will help you

Hot dogs cost $2.00 each, candy bars cost $1.00 each, and soft pretzels cost $2.50 each. How much would it cost to buy two hot dogs and one candy bar?

a. too much
b. too little

Answers

the answer for this question is too much

Final answer:

To calculate the total cost, multiply the price of each item by the number purchased then add those totals together. In this case, purchasing two hot dogs and one candy bar costs $5.00.

Explanation:

To find the total cost of purchasing two hot dogs and one candy bar, you would simply multiply the cost of each item by the number of that item you are buying, and then add all these costs together. So, if a hot dog is $2.00 and you want to buy two, this costs $2.00 * 2 = $4.00. A candy bar is $1.00 each, and if you want to buy one, this costs $1.00 * 1 = $1.00. So, the total cost would be the cost of the hot dogs plus the cost of the candy bar, which is $4.00 + $1.00 = $5.00. Therefore, the total cost of two hot dogs and one candy bar is $5.00.

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A stop sign is a regular octagon formed by cutting triangles off the corners of a square. if we have a square with sides of length square root 2, what is the side length of the resulting octagon

Answers

the answer is 3.5147 inches

Final answer:

The side length of the resulting octagon is 2√2.

Explanation:

A stop sign is a regular octagon formed by cutting triangles off the corners of a square. To find the side length of the resulting octagon, we can use the Pythagorean theorem. Since the square has sides of length √2, its diagonal can be found by multiplying its side length by √2. This gives us a diagonal length of 2√2. The diagonal of each triangle cut off the corners of the square will be the side length of the resulting octagon. So, the side length of the octagon is 2√2.

If chungs go kart can travel 48 miles on 1 gallon of gas,how far can his go kart travel with 1.15 gallons of gas?

Answers

your answer is 55.2
you take 1.15 times 48
i hoped i helped

He can travel 55.2 miles with 1.15 gallons of gas on his go-kart.

Set up a proportion. 1 over 48 is equal to 1.15 over x. Use cross products multiply 48 by 1.15 to get 55.2 and divide that by 1 to get 55.2.

x=55.2 miles.

Hope this helps!
Can u plz mark me as brainliest? I really need it!

please help. !!!!!!!!

Answers

Basically you find the data points and fill in the values. For Point J it is (2,4). They want you to do this: (2-4,4-6)...it then becomes (-2,-2).
So
J: (-2,-2)
K: (-1, -4)
I: (-2, -5)
Those are your new points. I hope this helps love! :)

For a craft project, two equilateral triangles are taped together to create a quadrilateral

Answers

The quadrilateral that is made is a rhombus. The triangle lines cause the quadrilateral to look like an uneven square or diamond which is also known as a rhombus.

Find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.

Answers

Hello Melissamv9321, find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse In this right triangle, you are given the measurements for the hypotenuse, c, and one leg, b. The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg a, substitute the known values into the Pythagorean Theorem. Solve for a2.

is it possible to draw three lines in two planes such that all three lines are skew?

Answers

Answer with explanation:

→Two lines in three dimensional plane are said to be Skew if they are neither parallel nor Intersecting.

→Skew lines can be drawn in three dimensional plane only.

→Drawn two skew lines in a Plane , and then drawn another line in a plane and found that , they are skew.

⇒Yes, it is possible to draw three lines in two planes such that all three lines are skew.

Skew lines are non-coplanar lines that are not parallel, and they do not intersect.

In a 2D plane, it is not possible to draw three skew linesIn a 3D plane, it is possible to draw three skew lines

The question does not state the type of plane. So, I will answer this question in 2 ways.

(a) 2D plane

Lines in 2D planes can only be drawn in a flat direction.

This means that, when three lines are drawn in the two planes, one of the following would happen.

The three lines would intersectTwo lines would intersect

See attachment for illustration

So, 3 lines in a 2D plane cannot be skewed lines

(b) 3D plane

Lines in 3D planes can only be drawn in several directions.

The above statement imply that:

Several lines can be drawn where none of the lines would be parallel and none of the lines would intersect.

This means that, when three lines are drawn in the two planes, one of the following would happen.

The three lines would intersectTwo lines would intersectNone of the lines would intersect

The third highlight means that:

It is possible to have skew lines in a 3D plane

Answers

6 can go into 59, nine times. Therefore 9 times 6 equals 54

All you have to do is divide 59/6, you get 9.83 hopefully this helps

If six plus two what does it equal

Answers

Six = 6

Two = 2

6 + 2 = 8

What is the measure of an angle if the measure of its supplement is 39 degrees more than twice the measure of its complement?

Answers

angle is x. sup - adds up to 180. comp adds up to 90

180-x = 2(90-x)+39
180-x = 180-2x+39
180-x = 219-2x
180+x = 219
x = 39

Measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.

What is angle?

" Angle is defined as when two rays meet at one endpoint known as vertex."

According to the question,

'x' represents the measure of an angle

Measure of its supplement angle = 180 - x

Measure of its complement angle= 90 - x

As per given condition of angle we get,

[tex]180 - x = 2(90 - x) +39\\\\\implies 180-x= 180 -2x +39\\\\\implies 2x-x = 39\\\\\implies x=39degrees[/tex]

Hence, measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.

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Nathan and Steven stacked boxes on a shelf. Nathan lifted 13 boxes and Steven lifted 15 boxes. The boxes that Nathan lifted each weighed 12 lb more than the boxes Steven lifted.

Let s represent the weight of the boxes that Steven lifted.

Which expression represents the total number of pounds Nathan lifted?

s + 12

12(s+13)

15(s+12)

13(s+12)

Answers

13(s+12) is your answer
13 boxes that each weigh 12 more pounds than steven's boxes.

Answer:

13(s+12) is your answer

Step-by-step explanation:

Which of these ratios is NOT in simplest form? 12/5 8/5 7/10 9/15

Answers

9/15, it can be simplified to 3/5

9/15
9 / 3 = 3
15 / 3 = 5

The sum of two numbers is 35 . the smaller number is 19 less than the larger number. what are the numbers?

Answers

let the smaller number be x and the larger be (x+19)
x+x+19=35
2x=16
x=8
x+19=27

the numbers are 8 and 27.

Which function below has the smallest slope?

f(x)

f(x) = 2x − 3

g(x)

graph going through (0, negative 5) and (4, 3)
h(x)

x h(x)
−1 3
1 7
3 11
f(x)
g(x)
h(x)
The functions all have the same slope

Answers

Answer: The functions all have the same slope

Step-by-step explanation:

just took the assessment and I got it right.

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