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
yKpoI14uk [10]
2 years ago
11

Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12cm3/s . if the radius of the funnel is 8

cm and the altitude of the funnel is 16 cm, find
a) the depth of the salt water after 30 second

b)the rate of change of its depth at that instant
Mathematics
1 answer:
Bezzdna [24]2 years ago
7 0

Answer:

h ≅ 16.29 cm

\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}

Step-by-step explanation:

From the conical funnel;

Let the adjacent line at the base of the cone be radius (r) and the opposite ( vertical length) be the height (h)

Then;

tan  \theta= \dfrac{r}{h}

tan  \theta= \dfrac{8}{16}

tan  \theta= \dfrac{1}{2}

∴

\dfrac{r}{h} = \dfrac{1}{2}

r = \dfrac{h}{2}

The volume (V) of the cone is expressed as:

V = \dfrac{1}{3}\pi r ^2 h

V = \dfrac{1}{3}\pi (\dfrac{h}{2})^2 h

V = \dfrac{\pi h^3}{3\times 4}

\dfrac{dv}{dt} = \dfrac{3 \pi h^2}{3 \times 4} \dfrac{dh}{dt}

\dfrac{dv}{dt} = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}

Given that:

\dfrac{dv}{dt} = 12 \pi

Then:

-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}

- \int 48 \ dt = \int h^2 \ dh

\dfrac{h^3}{3}= -48 t + c

At  \ t = 0 \  ; h = 0

∴

\dfrac{0^3}{3} = -48(0) + c

c = 0

So;

\dfrac{h^3}{3}= -48 t + 0

\dfrac{h^3}{3}= -48 t

t = 30

\implies h = (-48(30))^{1/3}

h = 16.2865

h ≅ 16.29 cm

Thus;

from -12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}

\dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} } =\dfrac{dh}{dt}

\dfrac{dh}{dt} = \dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} }

\dfrac{dh}{dt}=\dfrac{-12 \times 4} { {16.29^2} }

\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}

You might be interested in
Solve -24 = 6x explain how to solve for x
stiv31 [10]

you would divide both sides by 6 to get your answer. i hope this helps :)

6 0
2 years ago
Read 2 more answers
Is 9x=270 addition property of equality or symmetric property?
Ede4ka [16]
This is the symmetric property, for you divide 9 to both sides to get x, instead of adding (addition property of equality)

So symmetric property should be your answer
Hope this helps
7 0
3 years ago
Read 2 more answers
Does anyone get this ? if so can u lmk the answer thxxxx:)
IgorLugansk [536]

Given:

In parallelogram ABCD, two of its vertices are A(-4,0) and B(0,3).

To find:

The equation that represents a line that contain CD.

Solution:

We have,

A(-4,0) and B(0,3)

Slope of AB is

m=\dfrac{y_2-y_1}{x_2-x_1}

m=\dfrac{3-0}{0-(-4)}

m=\dfrac{3}{4}

The slope of line AB is \dfrac{3}{4}.

Opposite sides of a parallelogram are parallel and slopes of parallel lines are equal.

In parallelogram ABCD, AB and CD are opposite sides. So, their slopes must be equal.

Slope of line AB = Slope of line CD = \dfrac{3}{4}

The slope intercept form of a line is

y=mx+b

Where, m is slope and b is y-intercept.

Slope of line CD is \dfrac{3}{4}, it means the line must be of the form

y=\dfrac{3}{4}x+b

Coefficient of x is \dfrac{3}{4} only in option a.

Therefore, the correct option is a.

7 0
2 years ago
Read 2 more answers
COEFFICIENTS AND VARIABLES! PLEASE SOLVE ALL ASAP! ANSWER = BRAINLIEST
sweet [91]

no hhahahahahahaahahaahahhaahha

6 0
2 years ago
Hey PLEASE HELP DUE TODAY
nadya68 [22]
What the maning of that ?
4 0
3 years ago
Other questions:
  • After a discount of 5% the sales price of a game system is $106.78 what is the original price
    7·1 answer
  • A Pythagorean triple is a triple of natural numbers satisfying the equation a^2+b^2+c^2.
    9·2 answers
  • What is the word form for 843,208,732,833?
    8·1 answer
  • A/9=-4 One-step equations
    7·1 answer
  • What is bigger 3/4 or 11/16 and why?
    5·2 answers
  • A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. she estimates that for each addit
    15·1 answer
  • There are 12 boys and 16 girls in a classroom. Which represents the simplified ratio of girls to students in the
    12·2 answers
  • 4|x-2|-12 = 0<br> Absolute Value &amp; Set in notation
    7·2 answers
  • Given the triangle below, solve for X.
    6·1 answer
  • How to change 7/10 to a percent
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!