Ask question

Ask question

All categories

3 years ago

10

A machine starts dumping sand at the rate of 35 m3/min, forming a pile in the shape of a cone. The height of the pile is always

one and one half the length of the base diameter. After 7 minutes, how fast is the radius increasing? And the height?

1 answer:

juin [17]3 years ago

6 0

We are given with the following given
dV/dt = 35 m3/min
h = (3/2)D

What is asked is
dr/dt at t = 7 min

The volume of a cone is
V = (1/3)πr²h

From the given
h = (3/2)D
since D = 2r
h = 3r

Subsituting
V = πr³

At t = 7 min, the volume is
V = 35(7)
V = 245
and the radius is
245 = πr³
r = 4.27

Differentiating the volume
dV/dt = 3πr² dr/dt
From the given
dV/dt = 35

Subsituting
35 = 3πr² dr/dt
So,
dr/dt = 0.20 m/s
and
dh/dt = 0.60 m/s

You might be interested in

Sin =9/15 . Find tan 0

ELEN [110]

Answer:

c. 9/12

Step by step explanation.

Given: sin = 9/15

and,

$sin = \frac{opp.}{hyp.}$

$tan = \frac{opp.}{adj.}$

thus, find adj. side

by using Pythagoras theorem

${c }^{2} = {a}^{2} + {b}^{2}$

then,

let adj. side be a^

${a}^{2} = {c}^{2} - {b }^{2} \\ {a}^{2} = {15 }^{2} - {9}^{2} \\ {a}^{2} = 144 \\ a = 12$

thus,

adj. side is 12

then,

tan of the angle = 9/12

3 0

3 years ago

Which represents the inverse of the function f(x) = 4x?

irga5000 [103]

Answer:

y = x/4

Step-by-step explanation:

First, replace f(x) with y, so it's easier to find the inverse:

y = 4x

To find the inverse of this function, you would replace all the y's with x's and all the x's with y's, and then solve for y. That would be:

x = 4y

y = x/4

Therefore, the inverse function of y = 4x is y = x/4.

4 0

3 years ago

kakasveta [241]

C. 17 r 1 is the correct answer

6 0

3 years ago

The circumference of the hub cap of a tire is 83.96 centimeters. Find the area of this hub cap. Use 3.14 for . Use pencil and pa

Bess [88]

Answer:

Area = $561.2485$ square centimeter

If the circumference of the hub cap would have been smaller, then its radius would have been smaller and subsequently its area would also have been less.

Step-by-step explanation:

As we know the circumference of a circle is $2\pi r$

The radius of the hub cap needs to be devised to determine the area

$83.96$ $= 2* 3.14*r$

$r = \frac{83.96}{2*3.14}$

$r = 13.37$ centimeters

Area of the hub cap = $\pi r^{2}$

Substituting the devised value of r in the above equation, we get -

$3.14 * 13.37^2\\$

$561.2485$ square centimeter

If the circumference of the hub cap would have been smaller, then its radius would have been smaller and subsequently its area would also have been less.

5 0

3 years ago

Due tomorrow Please help!!

anastassius [24]

Answer:

A

$\frac{1}{8}$ = $\frac{b}{4^{2} }$

b = $\frac{1}{8}$ × $4^{2}$

b = $\frac{4^{2} }{8}$

then b = $\frac{c^{2} }{a}$ that is ORANGE

B

-2 - v = -7

v = -7 +2

then v = k + m that is BROWN

C

$\frac{14}{q}$ = $\frac{-7}{-4}$

q = $\frac{14 * -4 }{-7}$

then q = $\frac{ps}{r}$ that is YELLOW

D

4m + 2(n) = 5 (n)

4m = 5 (n) - 2n

4m = 3n

m = $\frac{3n}{4}$

then m = $\frac{3n}{4}$ that is RED

E

-8 = $\frac{x}{-5}$ - 6

$\frac{x}{-5}$ = -8 + 6

x = -5 (-8 + 6)

then x = y( w + z ) that is LIGHT GREEN

7 0

3 years ago