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
Leto [7]
3 years ago
15

PLEASE SHOW WORK

Mathematics
1 answer:
CaHeK987 [17]3 years ago
7 0

(C)

Step-by-step explanation:

The volume of the conical pile is given by

V = \dfrac{\pi}{3}r^2h

Taking the derivative of V with respect to time, we get

\dfrac{dV}{dt} = \dfrac{\pi}{3}\dfrac{d}{dt}(r^2h)

\:\:\:\:\:\:\:= \dfrac{\pi}{3}\left(2rh\dfrac{dr}{dt} + r^2\dfrac{dh}{dt}\right)

Since r is always equal to h, we can set

\dfrac{dr}{dt} = \dfrac{dh}{dt}

so that our expression for dV/dt becomes

\dfrac{dV}{dt} = \dfrac{\pi}{3}\left(3r^2\dfrac{dh}{dt}\right)

\:\:\:\:\:\:\:= \pi r^2\dfrac{dh}{dt}

Solving for dh/dt, we get

\dfrac{dh}{dt} = \dfrac{1}{\pi r^2}\dfrac{dV}{dt}

\:\:\:\:\:\:\:= \dfrac{1}{9\pi\:\text{m}^2}(36\:\text{m}^3\text{/s})

\:\:\:\:\:\:\:= \dfrac{4}{\pi}\:\text{m/s}

You might be interested in
Solve the equation 18=-5(4x+3)+21x
AlexFokin [52]
-5(4x+3)+21x=18\\\\(-5)(4x)+(-5)(3)+21x=18\\\\-20x-15+21x=18\ \ \ |+15\\\\x=33
5 0
3 years ago
What is one of the solutions to the following system of equations? y2 x2 = 53 y − x = 5 (−10, −5) (−7, −2) (7, 2) (5, 10).
Aliun [14]

The solution of the system of equation is (-7, -2).

<h2>Given</h2>

The system of the equations;

\rm y^2 + x^2 = 53 \\\\y -x = 5

From equation 1

\rm  y -x=5\\\\y = 5+x

Substitute the value of y in equation 1

\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0     \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2

Hence, the solution of the system of equation is (-7, -2).

To know more about System of Equation click the link given below.

brainly.com/question/1495351

6 0
2 years ago
What equation describes the circle that is centered at (8, 3) and has a radius of 9
Sloan [31]

Answer:

<h3> (x-8)²+(y-3)² = 81</h3>

Step-by-step explanation:

The general equation of a circle is expressed as;

(x-a)²+(y-b)² = r² where;

(a, b) is the centre of the circle

r is the radius

Given the centre (8, 3) and the radius of 9, the equation of the circle will be;

(x-a)²+(y-b)² = r²

(x-8)²+(y-3)² = 9²

(x-8)²+(y-3)² = 81

hence the required equation is  (x-8)²+(y-3)² = 81

5 0
2 years ago
A mapping diagram showing a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negat
VladimirAG [237]

Answer:

The correct option is A)  {x | x = –5, –3, 1, 2, 6}

Step-by-step explanation:

Consider the provided diagram.

Here the left side represents the input (X) values and the right side represents the output (Y) values.

The domain refers to the set of possible input values.

Now consider the provided figure, the set of input value is:

{x | x = –5, –3, 1, 2, 6}

Hence, the correct option is A)  {x | x = –5, –3, 1, 2, 6}

5 0
3 years ago
Read 2 more answers
Look at the expression 15 + 75. Write an expression that shows the GCF multiplied by the sum of the other factors. 
skelet666 [1.2K]
The answer to that question would be 15
8 0
3 years ago
Other questions:
  • 8 less than 5 times a number
    12·2 answers
  • Less expensive and cleaner than power plants that use fossil fuels, why are they not used on a larger scale?
    9·2 answers
  • What is the slope for <br> y=-1/3x+4
    13·1 answer
  • Please help! Plot any 6 points with x-coordinate equal to 3.
    9·1 answer
  • Two-ninths of a number is less than or equal to negative thirteen
    8·1 answer
  • Complete the square to determine the minimum or maximum value of the function defined by the expression. −x2 + 18x − 99
    10·2 answers
  • Does this graph show a function? Explain how you know.
    6·1 answer
  • The following graphs show the performance of two stocks over the first five months of the year. A graph titled Stock A B C has m
    6·2 answers
  • On the coordinate plane below, quadrilaterals TRAP and HELP are similar to each other.
    7·2 answers
  • 3. Quincy has 0.926 m of string. Suppose he cuts the string into 4 equal lengths. What is the length of each piece of string? 4.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!