A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 feet deep at its deepest point. If the pool is being filled at a rate of 0.8ft3/min, how fast is the water level rising when the depth at the deepest point is 5 ft

Answers

Answer 1

Using implicit differentiation, it is found that the water level is rising a rate of 0.001 ft/sec.

The volume of a pool of length l, width w and height h is given by:

[tex]V = lwh[/tex]

Applying implicit differentiation, the rate of change of the volume is given by:

[tex]\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}[/tex]

Neither the width nor the length changes, hence [tex]\frac{dl}{dt} = \frac{dw}{dt} = 0[/tex], and:

[tex]\frac{dV}{dt} = lw\frac{dh}{dt}[/tex]

We are given that:

[tex]\frac{dV}{dt} = 0.3, l = 20, w = 40[/tex], hence:

[tex]\frac{dV}{dt} = lw\frac{dh}{dt}[/tex]

[tex]0.8 = 20(40)\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt} = \frac{0.8}{800}[/tex]

[tex]\frac{dh}{dt} = 0.001 [/tex]

Water level is rising at rate of 0.001 ft/sec.

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Related Questions

what is the solution set for this inequality?
-6x + 30 < -18
□ x > -2
□ x < 8
□ x > 8
□ x < -2
pls answer​

Answers

Answer:

x > 8

Step-by-step explanation:

= > -6x + 30 < - 18

= > 30 + 18 < 6x

= > 48 < 6x

= > x > 48/6

= > x > 8...ans

Hope it Helps you!!

Fighting for my life rn

Answers

Answer:

I think the other side on top is 129 degrees

Step-by-step explanation:

Im not 100 percent sure sorry if im wrong!!!

11/6= 1/p



Pls help!!

Answers

Answer:

p = 6/11

Step-by-step explanation:

11/6 = 1/p

=> 11p = 6

=> p = 6/11

Hoped this helped.

So There Are 3 Dogs In 25 Parks How Many Dogs In Parks Are There So This Is 3×25=? I mean It's Ez ​

Answers

Answer: You are right! Just multiply for your answer!

Step-by-step explanation:

The answer is 25•3 is 75

The monthly rent for an 800 square foot office is $975. For an 1100 square foot office, the rent is $1125. WRITE AND SOLVE A LINER EQUATION to find the monthly rent for a 1500 square foot office.

I need help and pls do it in The liner equation way which is also given two points.

Answers

Answer:

$1325

Step-by-step explanation:

Translate the given into two pairs of coordinates:

(800, 975) and (1100, 1125)

Work out the equation of the line passing through both of the points.

Find the slope:

m = (1125 - 975) / (1100 - 800) = 0.5

Find the y-intercept:

975 = 0.5*800 + b975 = 400 + bb = 975 - 400b = 575

The line is:

y = 0.5x + 575

Find the value of y when x = 1500:

y = 0.5*1500 + 575 = 1325

Please look at picture for question.

Answers

Answer:

The answer is D ane B

Step-by-step explanation:

The expression [tex](8z-4)(-7)[/tex] you would have to distribute -7 to get [tex]-56z+28[/tex]

The same goes for 40 in the expression [tex](-1.4z+0.7)*40[/tex]

Find the accumulated value of an investment of $2000 at 8% compounded continuously for 4 years

Answers

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000e^{0.08\cdot 4}\implies A=2000e^{0.32}\implies \boxed{A\approx 2754.26}[/tex]

Share 7.20 naira between Tayo and Visit,so that Tayo gets 70 Kobo more than Bisi. how much does Tayo get?​

Answers

Answer:

4.30 naira

Step-by-step explanation:

Splitting in half, we have that they both get 3.60 naira each. Adding 70 kobo to 3.60 naira, we have 4.30 naira. Since we need Tayo's share to be 70 kobo more than Bisi's, we give Tayo the bigger share and the left cash to Bisi (2.90 naira).

Tayo will get 3.95 more than the naira of the given shares.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that can be evaluated to obtain a value.

Let's call the amount that Visit gets "x".

According to the problem, Tayo gets 70 kobos (0.70 nairas) more than Visit. So, Tayo gets:

x + 0.70

The total amount of money shared between them is 7.20 naira. So, we can set up an equation:

x + (x + 0.70) = 7.20

Simplifying this equation, we get:

2x + 0.70 = 7.20

Subtracting 0.70 from both sides, we get:

2x = 6.50

Dividing both sides by 2, we get:

x = 3.25

To find out how much Tayo gets, we can use the equation we came up with earlier:

x + 0.70

Substituting x = 3.25, we get:

3.25 + 0.70 = 3.95

Therefore, Tayo will get 3.95 more than the naira.

To know more about an expression follow

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#SPJ2

What is the difference between (2.4x10^8) and (9.2x10^6)

Answers

Answer:

  2.308×10^8

Step-by-step explanation:

Your calculator can tell you what the difference is.

  2.4×10^8 -9.2×10^6 = (2.4 -0.092)×10^8 = 2.308×10^8

_____

Additional comment

If this is a problem where you're expected to round the answer to an appropriate number of significant figures, you will notice the largest contributor has a resolution of 0.1×10^8. That will be the resolution required in the answer: 2.3×10^8.

please help this is for my study guide thanks! ​

Answers

The volume is 29.32 <3

Simplify this expression:

Answers

[tex](-3c^8)(2c^6d^8)\implies (-3)(2)c^8c^6d^8\implies -6c^{8+6}d^8\implies -6c^{14}d^8[/tex]

Which expression finds the length of side y in this right triangle?

Answers

Answer:

y = [tex]\sqrt{19^2} + \sqrt{8.2^2}[/tex]

Step-by-step explanation:

Pythagorean Theorem : a² + b² = c²

19² + 8.2² = c²

c = [tex]\sqrt{19^2 + 8.2^2}[/tex]

c = [tex]\sqrt{19^2} + \sqrt{8.2^2}[/tex]

-Chetan K

PAGE 77/215 #1A-C
What percentage of a dollar is the value of each coin combination?

a. 4 dimes
b. 1 nickel and 3 pennies
c. 5 quarters and 1 dime
?

Answers

Answer:4 dimes = 40 cents

1 nickel 3 pennies =8 cents

5 quarters and 1 dime = $1 and 35 cents

step explanation:

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

Fertilizer puts nitrogen into the soil, so using fertilizer puts more nitrogen into the carbon cycle.

When you use fertilizer, its because a certain plant you are planting uses all the nitrogen in the soil, so it won't grow next time. Too much fertilizer, though, would burn up your plant (not literally). Some plants put their own nitrogen into the soil. I can't think of one off the top of my head, but I believe potatoes do. Anyways, this is where crop rotation came into play.

Things like corn take a lot of nitrogen, so the next time you had to plant whatever plant potatoes, which again may be wrong, in order to get nitrogen for the corn to grow next season. Today we have fertilizer, so we can give them nitrogen while they grow, instead of putting in other plants, taking more time.

So really, it doesn't do much, because your plant takes all the nitrogen that the Fertilizer adds.

Answer:

People have been converting atmospheric nitrogen into nitrogen fertilizers and then applying the fertilizers to plants in to grow more crops. This has previously been quite effective, allowing individuals to farm on previously unproductive lands, and provide adequate food for expanding populations of people. Unfortunately, fertilizers are frequently overused, which can lead to issues.

Nitrogen from fertilizers excretes into soils, typically promoting the growth of weeds rather than native vegetation. Nitrogen then washes into streams, resulting in a nutrient overload, a phenomenon known as eutrophication.

Eutrophication causes aquatic weeds to proliferate excessively in freshwater lakes. These aquatic weeds  occasionally occupy entire lakes, streams, or rivers. Green algae cloud the water, and gooey algal slime covers the shallow rocks. 

When nitrogen-rich waters flow down into the ocean, they worsen the situation. High nitrogen concentrations in the Mississippi River Delta have generated a 'dead zone' where the water flows into the Gulf of Mexico. This has occurred every summer for over 30 years. In 2001, this dead zone, where oxygen levels are too low for species to thrive, encompassed over 8000 square miles of water. It occurs when nitrogen in the water enables algae to quickly grow out of control.

Step-by-step explanation:

Great article to look at for more information -

https://www.nytimes.com/2017/07/27/climate/nitrogen-fertilizers-climate-change-pollution-waterways-global-warming.html

what is the prime number of 30 to 59​

Answers

Answer:

the prime numbers between 30 and 59 are 31, 37, 41, 43, 47, 53

Function or not a function?

Answers

Answer: Not Function

Step-by-step explanation:

The pattern is not consistent.

Which is greater, -6.4 or -6.5? please explain !!

Answers

Answer:

-6.4 is GREATER.

The number closest to 0 is greater.

f(x) = 2/3x + 3 what is the value of f(12)? ​

Answers

Answer:

11

Step-by-step explanation:

    f(12) means that we plug 12 into our x value since the function is f(x) which will be solved as the following:

2/3x + 3

2/3(12) + 3

8 + 3

11

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

90 people apply for job, 10 have no sales or publishing experience, 65 have sales, 58 have publishing, how many have both?

Answers

                     No sales | Sales

No Publishing |      10      __       __

Publishing       |      __       x        58

                              __      65       90

Fill in spots

                    No sales | Sales

No Publishing |      10      22       32

Publishing       |      15      43       58

                              25     65       90

43 applicants have both sales and publishing experience

Which of the following best describes the equation below?

y^2=x

A.
both a relation and function
B.
function only
C.
neither a relation nor a function
D.
relation only

Answers

Answer:

I believe it's a relation

Answewant to be allies?

Step-by-step explanation: lol

What would the answer be

Answers

Answer:

B.

Step-by-step explanation:

process of elimination. the red dot is not a 1/4 of the number of lines, so it cant be 12.25, 13.625 is impossible because it has a value less than 13, and 12.625 is impossible as well because it has a value less than 12.5 therefore 12.375 is the best answer, and the only correct answer

If z=15, what would the expression z2 – 2z + 15 be equal to?
A 205
B 210
C 215
D
220

Answers

None of those are correct.

Find the value of x that makes the equation true:

x + 3 = 4

a. x = 12
b. x = 2
c. x = 1
d. x = 7

Answers

Answer to this question is option C

What are the equivalent ratios to 6:5

Answers

Ratio of 6 to 5

A ratio of 6 to 5 can be written as 6 to 5, 6:5, or 6/5. Furthermore, 6 and 5 can be the quantity or measurement of anything, such as students, fruit, weights, heights, speed and so on.

A ratio of 6 to 5 simply means that for every 6 of something, there are 5 of something else, with a total of 11

Below is a list of equivalent ratios of 6:5 that we created using our 6:5 ratio calculator above.

6:5

12:10

18:15

24:20

30:25

36:30

42:35

48:40

54:45

60:50

66:55

72:60

How do the expressions 5h2−3g and 3(g+h)h compare when g = 10 and h = 3?

Drag a symbol into the box to correctly complete the statement.

5h2−3g Response area 3(g+h)h when g = 10 and h = 3.

Answers

Answer:

the answer is >

Step-by-step explanation:

I took the test

Find the equation of a line that passes through the point (2,5) and has a gradient of 2. Leave your answer in the form y = m x + c

Answers

Answer:

y=2x+1

Step-by-step explanation:

y-5/x-2=2

2x-4=y-5

y=2x+1

Encuentra las coordenadas del punto P(x,y) que divide al segmento P1P2 con coordenadas
de sus extremos P1(x1,y1) y P2(x2,y2) dada la razón r.
P1(-1,6) P2(3,-3) r = ¾

Answers

Usando segmentos de línea, se encuentra que el punto es [tex]P\left(2, -\frac{3}{4}\right)[/tex]

El punto P1 es dado por (-1,6).El punto P2 es dado por (3, -3).

El punto P divide el segmento en la razón [tex]r = \frac{3}{4}[/tex], o sea:

[tex]P - P_1 = \frac{3}{4}(P_2 - P_1)[/tex]

La coordenada x de P1 es -1.La coordenada x de P2 es 3.La coordenada x de P es x.

[tex]P - P_1 = \frac{3}{4}(P_2 - P_1)[/tex]

[tex]x + 1 = 3[/tex]

[tex]x = 2[/tex]

La coordenada y de P1 es 6.La coordenada y de P2 es -3.La coordenada y de P es y.

[tex]P - P_1 = \frac{3}{4}(P_2 - P_1)[/tex]

[tex]y - 6 = -\frac{27}{4}[/tex]

[tex]y = -\frac{27}{4} + \frac{24}{4}[/tex]

[tex]y = -\frac{3}{4}[/tex]

El punto es [tex]P\left(2, -\frac{3}{4}\right)[/tex]

Un problema similar es dado por https://brainly.com/question/4854238

9. A cheetah is located 100 yards away from an antelope. The cheetah begins running on a straight path toward the antelope at a constant speed of 30 yards per second. At the same time, the antelope begins running away from the cheetah at a constant speed of 25 yards per second. If both animals continue to run on a straight path at the same speeds, how long will it take for the cheetah to catch up to the antelope?​

Answers

It takes 20 seconds for the cheetah to catch up to the antelope

Speed is the ratio of distance to time taken. It is given by:

Speed = distance / time

Let d represent the distance covered by the cheetah at time t, hence:

30 = d / t

t = d / 30

The antelope is 100 yards away, hence:

25 = (d - 100) / t

t = (d - 100)/25

d/30 = (d - 100)/25

25d = 30d - 3000

d = 600 yards

t = d/30 = 600/30 = 20 seconds

It takes 20 seconds for the cheetah to catch up to the antelope

Find out more at: https://brainly.com/question/22610586

can someone plz help

Answers

Answer:

77

Step-by-step explanation:

I think that's the answer, lemme know if i'm right.

Which lines are parallel? Why?
A) a || b by same side interior angles
B) c || d by same side interior angles
C) c || d by converse of corresponding angles
D) a || b by converse of same side interior angles
E) a || b by converse of corresponding angles
F) a || b by corresponding angles
G) c || d by converse of same side interior angles
H) c || d corresponding angles

Answers

9514 1404 393

Answer:

  C) c || d by converse of corresponding angles

Step-by-step explanation:

Only corresponding angles where transversal b crosses lines c and d are shown. All answer choices involving a||b or interior angles can be eliminated from consideration.

The "corresponding angle" theorem tells you corresponding angles are congruent if the lines are parallel.

The converse of that theorem tells you the lines are parallel if the corresponding angles are congruent. Here, the angles are shown congruent, so the "converse" theorem applies.

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