answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Natasha_Volkova [10]
2 years ago
14

Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a

height of 12 ft and a radius of 10 ft. How fast does the depth of the water change when the water is 10 ft high if the cone leaks at a rate of 8 cubic feet per minute?
Mathematics
1 answer:
Artyom0805 [142]2 years ago
6 0

Answer:

\frac{dh}{dt} = \frac{216}{1875\pi}

Step-by-step explanation:

Given

Represent radius with r and height with h

h = 12ft

r = 10ft

Rate = \frac{8ft^3}{min} when h = 10ft

Express radius in terms of height

\frac{r}{h} = \frac{10}{12}

\frac{r}{h} = \frac{5}{6}

r = \frac{5}{6}h

First, we need to determine the volume of the cone in terms of height.

Volume = \frac{1}{3}\pi r^2h

Substitute r = \frac{5}{6}h

V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h

V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h

V = \frac{1}{3} * \pi * \frac{25}{36}h^3

V = \frac{25}{108} \pi h^3

Differentiate both sides w.r.t time (t)

\frac{dV}{dt} = 3 *  \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}

\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}

Solve for \frac{dh}{dt}

\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}

At this point, h = 10 and \frac{dv}{dt} = \frac{8ft^3}{min}

So, we have:

\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}

\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}

\frac{dh}{dt} = \frac{864}{7500\pi}

\frac{dh}{dt} = \frac{216}{1875\pi}

Hence:

The rate is \frac{216}{1875\pi} ft/min

You might be interested in
A grocer bought 70 cans of corn. She sold 10 cans that day and 15 cans the next day. How many did she have left?
e-lub [12.9K]

answer

45

step-by-step explanation

total = day1 + day2 + remaining

total = 70

day1 = 10

day2 = 15

plug in values

70 = 10 + 15 + remaining

remaining = 70 - 10 - 15

remaining = 45 cans

3 0
2 years ago
Evaluate e − 1 2 f e− 2 1 ​ fe, minus, start fraction, 1, divided by, 2, end fraction, f when e = 15 e=15e, equals, 15 and f = 2
ivolga24 [154]
The answer 456 fe
Because it the benefit is doing today
7 1
2 years ago
Read 3 more answers
Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $5
ANTONII [103]
How you would set this up would be as follows:

(50*30)+4,596*.03

The 50*30 is her earning $50 a day for 30 days. Then to find her commission earnings you multiply her sales of 4,596 times the commission rate of 3%(when you move the decimal place you get .03)

Add them together and you get her total amount earned of $1,637.88

Hope this helped!


6 0
2 years ago
Read 2 more answers
What do the symbols of mirrors and glass represent in this
luda_lava [24]

Question:

Read the excerpt from Julius Caesar, act 1, scene 2.

CASSIUS: ‘Tis just; And it is very much lamented, Brutus, That you have no such mirrors as will turn Your hidden worthiness into your eye, That you might see your shadow. I have heard 5 Where many of the best respect in Rome– Except immortal Caesar‐speaking of Brutus, And groaning underneath this age’s yoke, Have wished that noble Brutus had his eyes.

BRUTUS: Into what dangers would you lead me, Cassius, 10 That you would have me seek into myself For that which is not in me?  

CASSIUS: Therefore, good Brutus, be prepared to hear. And since you know you cannot see yourself So well as by reflection, I, your glass, 15 Will modestly discover to yourself That of yourself which you yet know not of.

Answer:

The correct choice is D)

Explanation:

Cassius speaks of Brutus as one who is unable to see or know his own value and presumes to help him therewith. He does this by pointing out that many of the well respected people in Rome wish that he were in Caesars shoes as King.

Cheers!

7 0
2 years ago
n the previous problem, Ken predicted a drop in temperature. Explain why a drop in temperature would lead to adding a negative i
Alex
Adding a negative interference is the same as subtracting a positive integer
7 0
2 years ago
Other questions:
  • bo has 23 video games for sale he plans to donate the money he makes from each sale to a local charity what is the least amount
    5·2 answers
  • The sum of two consecutive odd numbers is 284
    11·1 answer
  • To graph x ≥ 2, place a(n) on a number line at , and shade to the .
    5·2 answers
  • The price of a box of 15 cloud markers is $12.70. The price of a box of 42 cloud markers is $31.60. All prices are without tax,
    5·2 answers
  • A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf that la
    14·1 answer
  • Which of the following is the radical expression of a to the four ninths power?
    15·2 answers
  • Which of the following rational functions is graphed below?
    5·2 answers
  • In a school of 2100 students, the ratio of teachers to students is 1:14. Some teachers join the school and the ratio changes to
    14·1 answer
  • On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The numb
    8·2 answers
  • Which fractions have a LCD of 30? A. 3/4 1/7 16 B.2/3 1/5 1/15 C. 2/15 1/4 1/3 D. 2/3 1/5 1/6
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!