A container is the shape of an inverted right circular cone has a radius of 4.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 2.00 inches deep, the surface level is falling at the rate of -2.00 in./s. Find the rate at which water is being drained.

The rate at which the water from the container is being drained is 24 inches per second.

Given radius of right circular cone 4 inches .height being 5 inches, height of water is 2 inches and rate at which surface area is falling is 2 inches per second.

Looking at the image we can use similar triangle propert to derive the relationship:

r/R=h/H

where dh/dt=2.

Thus r/5=2/5

r=2  inches

Now from r/R=h/H

we have to  write with initial values of cone and differentiate:

r/5=h/5

5r=5h

differentiating with respect to t

5 dr/dt=5 dh/dt

dh/dt is given as 2

5 dr/dt=5*-2

dr/dt=-2

Volume of cone is 1/3 π[tex]r^{2} h[/tex]

We can find the rate at which the water is to be drained by using partial differentiation on the volume equation.

Thus

dv/dt=1/3 π(2rh*dr/dt)+([tex]r^{2}[/tex]*dh/dt)

Putting the values which are given and calculated we get

dv/dt=1/3π(2*2*2*2)+(4*2)

=1/3*3.14*(16+8)

=3.14*24/3.14

=24 inches per second

Hence the rate at which the water is drained from the container is 24 inches per second.

Learn more about differentaiation at https://brainly.com/question/954654

#SPJ4

Question 6 (2 points)
The parabola is in intercept form.
y=(x+1)(x+7)
The vertex is
Blank 1:
Blank 2:

Rodrigo practiced playing the guitar 15 1/3 hours over the past 3 weeks.
He practiced for 5 1/4 hours during the first week and 5 2/3 hours during the second week.
How much time did Rodrigo spend practicing during the third week? Use the numbers and symbols to select the equation that represents the problem. Then solve the equation. Symbols may be used more than once or not at all.
15 1/3, 5 1/4, 5 2/3, x, =, and +.

The equation that represents the problem is
a. 15 1/3 = x - 5 1/4 - 5 2/3
b. x = 15 1/3 + 5 1/4 + 5 2/3
c. x + 15 1/3 = 5 1/4 + 5 2/3
d. 15 1/3 = 5 1/4 + 5 2/3 + x

convert 5.70 lbs to grams and explain please help

The slope is 2.92, which shows a positive relationship because it is a positive number. The
longer a person’s hair, the more it will cost to get the hair highlighted. This makes sense, as
more product is required to highlight more hair.

help please
4 − ( −12) + ( −7) =​

Which of the following correctly describes the product below?
A.
irrational

B.
rational

C.
a combination of both rational and irrational

D.
neither rational nor irrational

In ΔTUV, t = 410 cm, ∠U=27° and ∠V=78°. Find the length of v, to the nearest 10th of a centimeter.=

I need help with a/d​

x * 5 * 25 * 4 ÷ 5, if x = 813 simplified form please

Given the following parallelogram: Solve for x.
7x + 70
16x - 20

The width A rectangle is 3 cm less then its length. The perimeter of the rectangle is 30 CM. Find The length and width of the rectangle

2/3n+1/2=3/4 I need this fast pls

These two figures are the image and pre-image of a
dilation.
Find the value of x.
4 m
6 m
4 m
6 m
8 m
9 m
6 m

what's [2+(2x3)]x5.

17.
Is the relation a function? Why or why not?
{(–8, –4), (–2, 0), (1, 3), (–2, 6)}

A. Yes; only one range value exists for each domain value.

B. No; the relation passes the vertical line test.

C. No; two range values exist for domain value –2.

D. Yes; two range values exist for domain value –2.

???
[tex]( \frac{ {2x}^{3} }{ {8y}^{ - 4} }) ^{ - 3} [/tex]
​

Solve for x and show work need help just stuck on this one ☝

Which of the following are properties of the circumcenter of a triangle? Check
all that apply.
A. The circumcenter is at the intersection of the perpendicular
bisectors of the triangle's sides.
B. The circumcenter of an obtuse triangle is always outside it.
M C. The circumcenter is equidistant from each vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.

What are the coordinates of the image after a dilation
with the center at the origin and a scale factor of 2?
(0, 0) (10, 0) (10,4) (0, 4)
(-2.2) (8, 2) (8.-2) (-2,-2)
(1, 1) (6, 1) (6, 3) (1, 3)
(0, 0) (0, 2) (5.0) (5,2)

Mr. Alvarez makes a walkway of 3 cement slabs.He uses 14 cubic feet of cement to make the walkway.Each square slab has a volume of 4 cubic feet

Find the discriminant of x2-6x -10 = 0, and determine the number of real solutions of the equation.​

Consider the polynomial function h(x) = x^6 - 3x^5 - 17x^3
What is the end behavior of the graph of h?
Choose 1 answer:
PLEASE HELP

The diagram shows two right-angled triangles. PQR and QST are straight lines. It is given that sin x = [tex]\frac{15}{17}[/tex] . Find the value of cos y.

You buy 5 candy bars for $2.00. Find the cost of 18 candy bars? First
write a proportion to find the unit rate(price per one candy bar). Then use
the unit rate to to find the cost of 18 candy bars?

James has 838 feet of rope. There are 17 teams of hikers. If James gives an equal amount of rope to each team, how much rope will each team receive?

Whats 8 2.5% of 75?Write your answer as a decimal.​

please help me with this

Sara says, "If you subtract 17 from my number and multiply the difference by - 2,
the result is - 22." What is Sara's number?

PLZZ HELP ME IM DOING A TEST RNNNN.

3.

Which equation best describes the graph?


A. y = 2x + 3

B. y = 1/2x + 3

C. y = 1/2x – 3

D. y = 2x – 3