A cistern in the form of an inverted circular cone is being filled with water at the rate of 65 liters per minute. if the cistern is 5 meters deep, and the radius of its opening is 2 meters, find the rate at which the water level is rising in the cistern 30 minutes after the filling process began.

Answers

Answer 1

Let's start by finding the volume of the cistern at any given time t. Since the cistern is in the form of an inverted circular cone, its volume can be expressed as:

V = (1/3)πr^2h

where r is the radius of the circular opening, h is the height of the cone (which is also the depth of the cistern), and π is the constant pi.

We are given that the cistern is 5 meters deep, and the radius of its opening is 2 meters. Therefore, we can plug these values into the equation above to get:

V = (1/3)π(2^2)(5)

V = 20/3 π

Now, we need to find the rate at which the water level is rising in the cistern after 30 minutes. Let's call this rate dh/dt (the change in height with respect to time).

We know that the water is being added to the cistern at a rate of 65 liters per minute. Since 1 liter is equal to 0.001 cubic meters, the volume of water being added per minute is:

(65 liters/minute) × (0.001 m^3/liter) = 0.065 m^3/minute

Therefore, the rate at which the height of the water in the cistern is changing is:

dh/dt = (0.065 m^3/minute) / (20/3 π m^3) = 3.87/π meters/minute

After 30 minutes, the height of the water in the cistern will have risen by:

h = (65 liters/minute) × (0.001 m^3/liter) × (30 minutes) / (20/3 π m^3) = 0.2925 meters

Therefore, the rate at which the water level is rising in the cistern 30 minutes after the filling process began is:

dh/dt = 3.87/π meters/minute

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Related Questions

Hey my friend needs help with finding the challenges for sum reason does it not pop out for sum people as well

Hey my friend needs help with finding the challenges for sum reason does it not pop out for sum people

Answers

Answer:

yah for some reason i cant find it

Answer:

sssssssssssssss

Step-by-step explanation:

Which number would fit in?

Which number would fit in?

Answers

Answer:

Answer is 3/6th

Step-by-step explanation:

Because 2/4 is a half so what is 3 as a half of a fraction which is

3/6

Answer:

6

Step-by-step explanation:

2/4 would simplify to 1/2. If you were to cross multiply 2x3=x, x=6.

Hope this helped! Please mark me brainliest.

the length of segment HJ if H lies at (-1,7) and J lies at (8,-5)​

Answers

Answer:

HJ = 15

Step-by-step explanation:

To get the length of segment HJ if H lies at (-1,7) and J lies at (8,-5)​, we will use the formula for calculating the distance between two points as shown;

D = √(x₂-x₁)²+(y₂-y₁)²

From the coordinates x₁ = -1, y₁ = 7, x₂ = 8, y₂ = -5

HJ = √(8-(-1))²+(-5-7)²

HJ = √(8+1)²+(-12)²

HJ = √81+144

HJ = √225

HJ = 15

Hence the length of segment HJ is 15 units

6 in.
10 in.
12 in.
8 in.
16 in.
What is the area of the figure?
OA. 52 square inches
B. 152 square inches
O c. 192 square inches
D. 272 square inches

6 in.10 in.12 in.8 in.16 in.What is the area of the figure?OA. 52 square inchesB. 152 square inchesO

Answers

Answer:

152 square inches

Step-by-step Explanation:

To answer this, please look at the picture below. We can find the area by separating and combine the value of areas after calculating three values for each areas. (Notice that when we separate them, we get three rectangles which we can use the formula of width × length)

We should get 80+48+24 which add up to 152.

In case if you are confused which parts you don't understand in these photos, you can ask in the comment.

6 in.10 in.12 in.8 in.16 in.What is the area of the figure?OA. 52 square inchesB. 152 square inchesO

Which expression is equivalent to this expression?
4a + (–6b) – 3a + 2b

Answers

Answer:

a−4b

Step-by-step explanation:

=4a+−6b+−3a+2b

Combine Like Terms:

=4a+−6b+−3a+2b

=(4a+−3a)+(−6b+2b)

=a+−4b

I like your cut g ;)

plz help
Functions f, g, and h are defined as follows: f(x) = x +1, g(x) = x^2 +1, and h(x) = x^3 +1.
(a) Find the inverse of function g(x).
(b) Find f(h(-2))
(c) Find g(f(3)

Answers

Answer:

a. let the gx be x

g(x) = x^2+1

or, x^2+1=y

or, x^2= y-1

:. x=2 root y-1

inter changing the relation of xand y

:. x=2 root y-1

:. g-1(x)= 2root x-1

b.

2z-1/3- 3z+1/5=1
z=?
Have a good Earth day!

Answers

Answer:

Z=23

Step-by-step explanation:

Multiply both sides of the equation by 15, the least common multiple of 3,5.

Use the distributive property to multiply 5 by 2z−1.

Use the distributive property to multiply −3 by 3z+1.

Combine 10z and −9z to get z.

Subtract 3 from −5 to get −8.

Add 8 to both sides.

Add 15 and 8 to get 23.

Explain briefly the six main criteria that can be used to define normality and abnormality, by illustrating them with one psychological "abnormality" (other than homosexuality).
What may be the values and limitations of using the medical model and classification systems (which are originated from diagnosing and treating physical illnesses) to the understanding and treating of psychological disorders?
The six criteria are:
1. Abnormality as statistical infrequency (Involves comparison with other people)
2. Abnormality as personal distress (Involves consequences of the behavior for self)
3. Abnormality as others’ distress (Involves the consequences of the behavior for others)
4. Abnormality as unexpected behavior (Involves another kind of comparison with others’ behavior)
5. Abnormality as highly consistent/inconsistent behavior (Involving making comparisons between both the actor and others, and between the actor and him/herself in different situations)
6. Abnormality as maladaptiveness or disability (Concerns about the (disabling) consequences for the actor)

Answers

The six main criteria to define normality and abnormality include statistical infrequency, personal distress, others' distress, unexpected behavior, highly consistent/inconsistent behavior, and maladaptiveness/disability.

1. Abnormality as statistical infrequency: This criterion defines abnormality based on behaviors or characteristics that deviate significantly from the statistical norm.

2. Abnormality as personal distress: This criterion focuses on the individual's subjective experience of distress or discomfort. It considers behaviors or experiences that cause significant emotional or psychological distress to the person as abnormal.

For instance, someone experiencing intense anxiety or depression may be considered abnormal based on personal distress.

3. Abnormality as others' distress: This criterion takes into account the impact of behavior on others. It considers behaviors that cause distress, harm, or disruption to others as abnormal.

For example, someone engaging in violent or aggressive behavior that harms others may be considered abnormal based on the distress caused to others.

4. Abnormality as unexpected behavior: This criterion defines abnormality based on behaviors that are considered atypical or unexpected in a given context or situation.

For instance, if someone starts laughing uncontrollably during a sad event, their behavior may be considered abnormal due to its unexpected nature.

5. Abnormality as highly consistent/inconsistent behavior: This criterion involves comparing an individual's behavior to both their own typical behavior and the behavior of others. Consistent or inconsistent patterns of behavior may be considered abnormal.

For example, if a person consistently engages in risky and impulsive behavior, it may be seen as abnormal compared to their own usually cautious behavior or the behavior of others in similar situations.

6. It considers behaviors that are maladaptive, causing difficulties in personal, social, or occupational areas. For instance, someone experiencing severe social anxiety that prevents them from forming relationships or attending school or work may be considered abnormal due to the disability it causes.

The medical model and classification systems used in physical illnesses have both value and limitations when applied to psychological disorders. They provide a structured framework for understanding and diagnosing psychological disorders, allowing for standardized assessment and treatment. However, they can oversimplify the complexity of psychological experiences and may lead to overpathologization or stigmatization.

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7) 4r^2- 12r + 5=0 in quadratic form​

Answers

Answer:

(2r-1)(2r-5)

Step-by-step explanation:

4r^2-10r-2r+5=0

2r(2r-5)-(2r-5)

(2r-1)(2r-5)

find the number of different ways that an instructor can choose 3 students from a class of 24 students for a field trip.

Answers

There are 2024 ways in which the instructor can choose 3 students from a class of 24 students for the field trip.

A combination is a mathematical technique for calculating the number of possible arrangements in a set of items where the order of the selection is unimportant.You can choose the items in any order in combinations.

Permutations and combinations are often confused. In permutations, however, the order of the selected items is critical. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), but different in permutations.

There is a way you can calculate combinations using a formula. This formula is:

\(nC_r = \frac{n! }{ r!(n-r)! }\)

where

n = total no. of items;

r = items selected for the combination;

"!" is the factorial

Given,

Total number of students in class , n = 24

Number of students selected, r = 3

So, the number of ways that 3 students can be selected from 24 students is

\(24C_3=\frac{24 !}{3!(24-3) !}\\\\=\frac{24 !}{3!*21 !}\\\\=\frac{3!*24*23*22*21 !}{3!*21 !}\\\\=\frac{24*23*22}{3*2*1}\\\\=2024\)

Hence, the students can be selected in 2024 ways for the field trip.

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this is my question for math ​

this is my question for math

Answers

Answer: the answer is

Step-by-step explanation: its simple bro just count the numbers inbetween 0 and

Can an acute angle be equal to 90?

Answers

No, acute angle can not be equal to 90. if an angle equal to 90 then it is a right angle.

Acute angle

An angle smaller than the right angle is called an acute angle. In other words, the angle which is less than 90 degrees forms an acute angle.

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is equal to 90 degrees). For example, ∠30o, ∠45o, ∠60o, ∠75o, ∠33o, ∠55o, ∠85o, etc. are all acute angles.

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Please draw the ray diagram! A 3.0 cm-tall object is placed at a distance of 20.0 cm from a convex mirror that has a focal length of - 60.0 cm. Calculate the position and height of the image. Use the method of ray tracing to sketch the image. State whether the image is formed in front or behind the mirror, and whether the image is upright or inverted.

Answers

The image is formed behind the mirror, and the image is upright.

Given data: Object height, h = 3.0 cm Image distance, v = ? Object distance, u = -20.0 cmFocal length, f = -60.0 cmUsing the lens formula, the image distance is given by;1/f = 1/v - 1/u

Putting the values in the above equation, we get;1/-60 = 1/v - 1/-20

Simplifying the above equation, we get;v = -40 cm

This negative sign indicates that the image is formed behind the mirror, as the object is placed in front of the mirror.

Hence, the image is virtual and erect. Using magnification formula;M = -v/uWe get;M = -(-40) / -20M = 2Hence, the height of the image is twice the height of the object.

The height of the image is given by;h' = M × hh' = 2 × 3h' = 6 cm Now, let's draw the ray diagram:

Thus, the position of the image is -40.0 cm and the height of the image is 6 cm.

The image is formed behind the mirror, and the image is upright.

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Which linear inequality represents the graph below?
O A. y >
(-3, 3)
x + 1
6
Click here for long description
B. y ≥
x + 1
C. y ≥-3x+1
O D.y > x + 1
(0, 1)

Which linear inequality represents the graph below?O A. y >(-3, 3)x + 16Click here for long descriptionB.

Answers

Based on the given options, the linear inequality that represents the graph below is C. y ≥ -3x + 1

To determine the correct option, we need to analyze the characteristics of the graph. Looking at the graph, we observe that it represents a line with a solid boundary and shading above the line. This indicates that the region above the line is included in the solution set.

Option A, y > (-3/6)x + 1, does not accurately represent the graph because it describes a line with a slope of -1/2 and a y-intercept of 1, which does not match the given graph.

Option B, y ≥ x + 1, also does not accurately represent the graph because it describes a line with a slope of 1 and a y-intercept of 1, which is different from the given graph.

Option D, y > x + 1, is not a suitable representation because it describes a line with a slope of 1 and a y-intercept of 1, which does not match the given graph.

Only Option C. y ≥ -3x + 1.

This is because the graph appears to be a solid line (indicating inclusion) and above the line, which corresponds to the "greater than or equal to" relationship. The equation y = -3x + 1 represents the line on the graph.

Consequently, The linear inequality y -3x + 1 depicts the graph.

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How do I figure out which statement is true?

How do I figure out which statement is true?

Answers

Answer:

A. if table is extendedD. if only the values in the table considered.

Step-by-step explanation:

We can see on the graph of g(x) that y-intercept is (0, 2)

The table doesn't have the value for x = 0 but we can observe that it is exponential function and has the formula:

f(x) = 3^x

We can find its y-intercept:

f(0) = 3^0 = 1

We can compare and see that:

f(0) = 1 < g(0) = 2

So the function g(x) has a greater y-intercept. This is option A.

====

Note: If only the values in the table considered, then correct option is D.

the value in dollars of recycling varies with the type of material. what is the weighted mean of this mixture of recyclables if compost is now worth twice as much?

Answers

The weighted mean of the mixture of recyclables would be (4 x $1 + 2 x $2) / 6 = $1.33.

To calculate the weighted mean of the mixture of recyclables, first identify the number of each material and their respective values. In this case, there are 4 items worth $1 each and 2 items worth $2 each. To calculate the weighted mean, multiply each item's value by the number of items and then divide by the total number of items

In this case,

4 x $1 + 2 x $2 = $6

and 6 items total, so the weighted mean is

$6 / 6 = $1.33.

This means that if compost is now worth twice as much, the weighted mean would be

(4 x $1 + 2 x $2) / 6 = $1.33.

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find the slope and y intercept of 5x-2y=-4

Answers

Answer:

Slope=2.5

Step-by-step explanation:

5x-2y=-4

-2y=-5x-4

y=2.5x+2

drop the answerrrr please and thanksssss

drop the answerrrr please and thanksssss

Answers

The slope of the line of best fit is 0. 83

What is slope?

Slope of a line can simply be described as the degree of the steepness of a line.

It measures the rise and fall of the line of best fit in a graph.

Another name for the slope of a line is referred to as the gradient of the line.

The formula for determining the slope of a line presented with the coordinates is written as;

Slope, m = y₂ - y₁/x₂ - x₁

From the diagram shown, we have;

Slope, m = 13 - 8/10 - 4

Subtract the values

Slope, m = 5/6

Divide the values, we get;

Slope, m = 0. 83

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This season, the probability that the Yankees will win a game is 0. 61 and the probability that the Yankees will score 5 or more runs in a game is 0. 48. The probability that the Yankees lose and score fewer than 5 runs is 0. 32. What is the probability that the Yankees would score fewer than 5 runs when they lose the game? Round your answer to the nearest thousandth

Answers

Answer:

0.238

Step-by-step explanation:

This season, the probability that the Yankees will win a game is 0. 61 and the probability that the Yankees

Find the length of the hypotenuse in the following right triangle

Find the length of the hypotenuse in the following right triangle

Answers

Answer:

25

Step-by-step explanation:

take the square root of 24^2+7^2

The length of the hypotenuse in the right triangle is 25 units.

Hence the correct option is B.

Given is a right triangle with base length b = 24 and the perpendicular a = 7.

We need to find the length of the hypotenuse c.

To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

The Pythagorean theorem can be expressed as:

c² = a² + b²

Substituting the given values:

c² = 7² + 24²

c² = 49 + 576

c² = 625

To find the length of c, we need to take the square root of both sides:

c = √625

c = 25

Therefore, the length of the hypotenuse (c) is 25.

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Find the perimeter of the figure
where the length is 4x + 7,
the width is 2x - 5.

Answers

4x+7+2x-5=0
6x+2=0
x=-1/3

Now put the value of which is -1/3 in length and breadth .

I had done like this , May be it’s right or wrong ,

May be it might helps you!

I WILL MARK BRAINLIST TO WHO IS RIGHT PLS HELP ME!.

Answers

Answer:

Your answer would be 1 x10^6.

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the.

The sign of the exponent will depend on the direction you are moving the decimal.

Hope that makes sense.

If A = {4, 7, 10, 13, 17) and B = {3, 5, 7, 9), then which of the following statements Is true?
BCA
AUB=(7)
BCB

If A = {4, 7, 10, 13, 17) and B = {3, 5, 7, 9), then which of the following statements Is true?BCAAUB=(7)BCB

Answers

The answer is the last one.

B isn’t a proper subset of A because A doesn’t have elements 3, 5, and 9. A U B = {4, 7, 10, 13, 17, 3, 5, 9}, not {7}. Only B is a subset of B is true because every set is a subset of itself.

Students in school - how do we pay taxes? Get a job? Raise children?
Schools- solve for x
Plz help me With number 8 don’t get it thx

Students in school - how do we pay taxes? Get a job? Raise children?Schools- solve for xPlz help me With

Answers

How to solve the problem is

1) Factor out the common term which is 2.

2(1+2b)/2_>3b+6


2) Cancel 2.

1+2b_>3b+6

3) Subtract 1 from both sides.

2b_>3b+6-1

4) Simplify 3b+6 -1 to 3b+5

2b_> 3b+5

5) Subtract 3b from both sides.

2b-3b_>5

6) Simplify 2b-3b to -b.

-b_>5

7) Multiply both sides by -1

b_< -5


Hope this helps :)
Students in school - how do we pay taxes? Get a job? Raise children?Schools- solve for xPlz help me With

A=4ℼR2 solve for R
SHOW ALL STEPSSSSSSSSSSSSS

Answers

Given problem;

  A  = 4 π R²

  To solve for R, we have to make it the subject of the expression.

Since

      A  = 4 π R² , follow these steps to find R;

    Multiply both sides by \(\frac{1}{4\pi }\)  

 A x \(\frac{1}{4\pi }\)  =  \(\frac{1}{4\pi }\) x 4 π R²

          \(\frac{A}{4\pi }\)   = R²

Then find the square root of both sides

        √R²  = \(\sqrt{\frac{A}{4\pi } }\)  

            R  = \(\sqrt{\frac{A}{4\pi } }\)

The solution is \(\sqrt{\frac{A}{4\pi } }\)

common multiples for 3,6 and 8​

Answers

24 is the common multiple *\(^o^)/*

which situation can be modeled by equation y=3x25​

which situation can be modeled by equation y=3x25

Answers

i believe the answer is a

Identify if the question is
statistical or non statistical.
"How many students at your
school play soccer?"

Answers

Answer: Statistical

Step-by-step explanation:

I think its statistical because its quantitative data, meaning you can count it.

Estimate 1188+405+848 by first rounding each number to the nearest hundred

Answers

Answer:

about 2300

Step-by-step explanation:

Pls help me ill mark brainliest and more

Pls help me ill mark brainliest and more

Answers

Answer: i believe its yes

Step-by-step explanation:

Answer:

B. Yes

Step-by-step explanation:

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