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
leonid [27]
2 years ago
10

A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1

ft. If the trough is being filled with water at a rate of 15 ft3/min, how fast is the water level rising when the water is 8 inches deep
Mathematics
1 answer:
Anna11 [10]2 years ago
7 0

Answer:

7.5 ft³/min

Step-by-step explanation:

Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.

Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²

So, V = Ah = 2h = 2(10 - x)

The rate of change of volume is thus

dV/dt = d[2(10 - x)]/dt = -2dx/dt

Since dV/dt = 15 ft³/min,

dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min

Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt

= -dx/dt

= -(-7.5 ft³/min)

= 7.5 ft³/min

And the height at this point when x = 8 inches = 8 in × 1 ft/12 in  = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft

You might be interested in
A color printer prints 18 pages in 8 minutes.<br>How many minutes does it take per page?​
Sav [38]

Answer:

2.25 pages per minute

Step-by-step explanation:

Step 1:

18 ÷ 8

Step 2:

2.25

Answer:

2.25 pages per minute

Hope This Helps :)

4 0
3 years ago
What is the volume of this figure?
AysviL [449]
What figure , are you trying to figure the volume for
4 0
3 years ago
I need help with Spanish
Colt1911 [192]
Ana es diseñadora
nosotros somos muy delgados
El -es- astronauta

:))
8 0
3 years ago
Heeelllppppp
Andrei [34K]

Answer:

Hmm. I'm not sure... But I just wanted to say I love your profile picture.

Step-by-step explanation:

8 0
2 years ago
Name the property used in the equation 1=6n then find the value of n​
shusha [124]

Answer:

1/6

Step-by-step explanation:

Divide both sides of the equation by the same term

1=6

7 0
3 years ago
Other questions:
  • Chelsea has a beginning balance of $715 in her checking account. She writes two checks for $320 and $640. She has a deposit of $
    9·2 answers
  • You're supposed to simplify these, but for the last one, isn't it simplified enough?
    15·1 answer
  • Can somebody help me
    7·1 answer
  • Degree 3, zeros: 1,-3-i, find the remaining zeros
    13·1 answer
  • Brainliest for the correct ANSWER!!! Help ASAP
    6·2 answers
  • In a linear Pair angles are?
    8·2 answers
  • Order the angles in each triangle from smallest to largest.
    7·1 answer
  • Use the figure below to answer the question. What is the measure of ∠ABC? *
    12·1 answer
  • 6/5 s = -2 <br><br> whats the answer solve the (s)
    11·2 answers
  • PLEASE HELP Please quick quick help
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!