1answer.
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
inna [77]
3 years ago
7

A trough has ends shaped like isosceles triangles, with width 5 m and height 7 m, and the trough is 12 m long. Water is being pu

mped into the trough at a rate of 6 m3/min. At what rate (in m/min) does the height of the water change when the water is 1 m deep?
Mathematics
2 answers:
Svet_ta [14]3 years ago
6 0

Answer:

\dfrac{dh}{dt}=21 \text{m/min}

the rate of change of height when the water is 1 meter deep is 21 m/min

Step-by-step explanation:

First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)

V = \dfrac{1}{2}(bh)\times L

here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).

As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:

\dfrac{b}{h} = \dfrac{5}{7}

b=\dfrac{5}{7}h this can be substituted back in the volume equation

V = \dfrac{5}{14}h^2L

the rate of the water flowing in is:

\dfrac{dV}{dt} = 6

The question is asking for the rate of change of height (m/min) hence that can be denoted as: \frac{dh}{dt}

Using the chainrule:

\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}

the only thing missing in this equation is dh/dV which can be easily obtained by differentiating the volume equation with respect to h

V = \dfrac{5}{14}h^2L

\dfrac{dV}{dh} = \dfrac{5}{7}hL

reciprocating

\dfrac{dh}{dV} = \dfrac{7}{5hL}

plugging everything in the chain rule equation:

\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}

\dfrac{dh}{dt}=\dfrac{7}{5hL}\times 6

\dfrac{dh}{dt}=\dfrac{42}{5hL}

L = 12, and h = 1 (when the water is 1m deep)

\dfrac{dh}{dt}=\dfrac{42}{5(1)(12)}

\dfrac{dh}{dt}=21 \text{m/min}

the rate of change of height when the water is 1 meter deep is 21 m/min

evablogger [386]3 years ago
3 0

Answer:

0.7 m3/min.

Step-by-step explanation:

Volume of a 3D triangle (prism) = area * length

= 1/2 * (b * h) * l

b = width

= 5/7 * h

Volume = 5/14 * h^2 * l

Volume flow rate of the trough;

dv/dt = area of trough * dh/dt

Area = l * b

= 5/7*h*l * dh/dt

Therefore,

dh/dt = 7/(5*l*h) * dv/dt

= 7/(5*12*1) * 6

= 0.7 m3/min.

You might be interested in
Which equation can be used to find the measure of angle LJK?
Alexxandr [17]

Answer: cos(x)= 10/15

Step-by-step explanation:

Trust

3 0
3 years ago
I need help with this question. Can someone please help me with it. Thanks in advance
trasher [3.6K]
Okay, 72 degrees is equal to (5x-98), so
72=5x-98
5x=170
x=34

So now that we know that x=34, we can put 34 into (5x-98), so 170-98
170-98 and y are supplementary, so they add up to 180 degrees. So the equation is 
170-98+y=180
72+y=180
y=180-72
y=108
8 0
3 years ago
What is the sum of all of the odd numbers from 1 to 59? <br> Answer 900
jasenka [17]
The sum of all the odd numbers from 1 to 59 is 900.
5 0
3 years ago
Read 2 more answers
three different accounts are described below. order the accounts to their values after 10 years, from greatest to least.
Sedbober [7]

Answer

You deposit $800 in an account that earns 7.5% annual interest compounded quarterly.

Step-by-step explanation:

From the close eye, this seems to me the best and most factual answer to be found!! Goodluck with your quiz!

6 0
3 years ago
Read 2 more answers
Help help help help
gtnhenbr [62]
The answer is 4. 2x plus 7 is equal to 15. First you subtract 7 from both sides then divide by 2 to get the answer 4. Hope this helps!
4 0
3 years ago
Other questions:
  • What is the sum of the first 20 terms of a finite geometric series where a1 =3 and r = 3/2
    9·1 answer
  • Unit rate of 9 strikes in 3 innings
    6·1 answer
  • Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 70 mph and the o
    13·2 answers
  • Corey bought 2 1/2 litters of paint for $60.<br> What was the cost per liter of paint?
    9·2 answers
  • Help please with this question
    15·1 answer
  • The auditorium holds 200 people. Tickets cost $12 at the door and $8.50 if purchased in advance. The Honor Society has a goal of
    7·1 answer
  • H(8) = 40,000 • 1.05^8
    6·1 answer
  • Does this shape have 4 Right Angles​
    8·1 answer
  • URGENT!! I WILL GIVE BRAINLIEST TO CORRECT ANSWER!!
    15·1 answer
  • In a savings canister, Tom has a total of $2.85 in pennies and quarters. If the number of pennies Tom has in 5 more than three t
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!