Show that a∧6 can be written as a perfect square and as a perfect cube.

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

7 0

2 years ago

zzz [600]

The answer is B djiekljfjroeo

4 0

3 years ago

dem82 [27]

1/2 [ (3/2)y + 1/3] = -1/2 [y-5/2]

(3/2)y + 1/3 = -(1/2)y + 3

(3/2 + 1/2)y = 3 - 1/3

2y = 8/3

y = 4/3

y = 1.33

#$#HOPE YOU UNDERSTAND #$#

#$¥THANK YOU ¥$#

❤ ☺ ☺ ☺ ☺ ☺ ☺ ❤ 

5 0

2 years ago

koban [17]

9/3 is already made a fraction.

Why?

Because it is not a whole numer.

Well, this improper fraction can be simplified.

9 ÷ 3
3 ÷ 3

= 1.

4 0

2 years ago

svp [43]

Remove the radical by raising each side to the index of the radical.
x = 5/2

5 0

3 years ago