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
Angelina_Jolie [31]
3 years ago
15

A trough is 8 feet long and has perpendicular cross section in the shape of an isosceles triangle (point down) with base 1 foot

and height 2 feet. The trough is being filled with water at a rate of 1 cubic foot every 5 minutes. How fast is the water level rising whenthe water is 1/2 foot deep?
Mathematics
1 answer:
murzikaleks [220]3 years ago
4 0

Answer:

Dh/dt  = 0.082 ft/min

Step-by-step explanation:

As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of  1 feet and height     h = 2 feet.

The volume of a circular cone is:

V(c)  = 1/3 * π*r²*h

Then differentiating on both sides of the equation we get:

DV(c)/dt   = 1/3* π*r² * Dh/dt   (1)

We know that DV(c) / dt   is  1 ft³ / 5 min      or     1/5  ft³/min

and  we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment

By proportion we know

r/h  ( at the top of the cone  0,5/ 2)   is equal to  r/0.5  when water is 1/2 foot deep

Then      r/h   =   0,5/2   =  r/0.5

r  =  (0,5)*( 0.5) / 2        ⇒   r  =  0,125 ft

Then in equation (1) we got

(1/5) / 1/3* π*r² =  Dh/dt

Dh/dt  = 1/ 5*0.01635

Dh/dt  = 0.082 ft/min

You might be interested in
The sum of two numbers is 40, and their difference is 8. Find the numbers.
Fudgin [204]
x+y=40\\
x-y=8\\
-----\\
2x=48\\
x=24\\\\
24+y=40\\
y=16
3 0
3 years ago
Read 2 more answers
Sam is proving the product property of logarithms.
Charra [1.4K]

Answer: c

Step-by-step explanation: edge 2021

8 0
3 years ago
determine the volume of a rectangular container van with length,width, and height of 52m,13 m and 20m respectively.
icang [17]

\huge \boxed{ \green{ANSWER}}

\underline{v = 13 \: 520 \:  {m}^{3}  }

\huge \boxed{ \red{SOLUTION}}

v = lwh \\  = (52m) \: (13m) \: (20m) \\  \implies \underline{v = \: 13 \: 520 \:  {m}^{3}  }

<h3>#CarryOnLearning</h3>

\mathfrak{WatanabeHaruto}

6 0
2 years ago
Help please and thank you
Juliette [100K]

Answer:

infinity

Step-by-step explanation:

you can change x and then every answer will be different

8 0
3 years ago
What is qualitative data? Give an example.
Margarita [4]

Answer:

it is data that you can see or describe such as he is a boy

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • What is the value ?????
    12·1 answer
  • Given f ( x ) = x ^2 - 1, find the value f ( p ).
    5·1 answer
  • Yan has already finished 3/5 of the 45 math problems he was assigned today. Each math problem took him 1 4/5 of a minute to comp
    5·1 answer
  • Would you use a boxplot or a histogram to estimate the mean? Why In complete sentence use statistics terms
    6·1 answer
  • How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square
    5·1 answer
  • Choose the correct x-intercepts for the following quadratic fiction
    10·1 answer
  • Please help QUICK!! TY LOVES!!
    8·2 answers
  • Find the value of x.​
    13·2 answers
  • Expand (x-y)^4 “expand each binomial”
    14·1 answer
  • I need help finding the slope and what m=
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!