What is a common factor for the two fractional terms

A tank in the form of a right-circular cylinder of radius 2 feet and height 10 feet is standing on end. If the tank is initially

k0ka [10]

Answer:

$\frac{dh}{dt} = -3.48 \times 10^{-3}\sqrt{h}$ feet per second is the differential equation

Step-by-step explanation:

Given:

The radius of the cylindrical tank= 2 feet

The height of the cylindrical tank = 10 feet

The radius of the circular hole = 3/4 inches

To Find:

The differential equation for the height h of the water at time t.

Solution:

<u>Finding the surface area(A) of the tank</u>

Surface area = $\pi R^2$

On substituting the values

Surface area = $\pi(2)^2$

= $4\pi$ square feet

<u>Finding the surface area(a) of the hole</u>

The radius is given in inches, so converting into feet we have

1 inch = 0.083 foot

similarly

$\frac{3}{4} = 0.75 inches = 0.75 \times 0.083$ = 0.0625 feet.

Now the surface area,

= $\pi \times 0.0625$

= $0.0625 \pi$ square feet

Now let the velocity of water through the hole is v

According law of conservation of energy, the penitential energy due to the height h of the water gets converted into kinetic energy.

$\frac{1}{2}mv^2 =mgh$

$v^2 = \frac{2mgh}{m}$

$v^2 = 2gh$

$v= \sqrt{2gh}$

The rate of water flowing through the hole is = $a\times v$

= > $a \times \sqrt{2gh}$

At any time t

$V(t) = A \times h(t)$

$\frac{dV}{dt} = -a\sqrt{2gh}$

$\frac{d(Ah(t))}{dt} = -a\sqrt{2gh}$

$A \frac{d(h(t))}{d(t)} = -a\sqrt{2gh}$

$\frac{dh}{dt} = -\frac{a}{A} \sqrt{2gh}$

On substituting the values, we get

$\frac{dh}{dt} = -\frac{0.0625\pi}{4\pi}\sqrt{2\times 32 \times 10$

$\frac{dh}{dt} = -3.48 \times 10^{-3}\sqrt{h}$ feet per second

3 0

3 years ago

- Is this a function? Why or why not?

tensa zangetsu [6.8K]

9514 1404 393

Answer:

a) yes (a function)

b) no (not a function)

Step-by-step explanation:

A functional relationship will have only one value of dependent variable for each value of independent variable. That is, the column on the left can only have one arrow tail per item.

__

a) is a function. Each independent variable maps to one dependent value

b) not a function. Independent variable values 7 and 30 map to two values each.

7 0

3 years ago

!!URGENT!!WILL GIVE BRAINLIEST!! GEOMETRY DILATIONS!!! PLEASE INCLUDE EXPLANATION

Sergeu [11.5K]

Unless otherwise specified we usually assume the dilation is about the origin. That is you can tell the scale factor by the way the distance to the origin changes.

Point C, for example, is 6 units from the origin. Its image, C' is 4 units from the origin. Then the scale factor image/original is 4/6 = 2/3.

Your green question mark gets filled with 3 to make the fraction 2/3.

_____

To find the translation, pick any point on A'B'C' and find the corresponding point A'', B'', or C''. Count the squares you have to go left to get from A' to A'', for example. That will be 5 to the left. Similarly, count the squares you have to go down to get from A' to A''. That will be 4 down.

7 0

3 years ago

How to fiind the area of a sqare that say 2 6 6

rewona [7]

Answer:
Since we don’t know which side is which length, I’m going to tell you the two possible answers. The first possible answer is 2 * 6 = 8 and the second possible answer is 6 * 6 = 36

8 0

3 years ago

Simplify 2x + 5(2x - 3)

Thepotemich [5.8K]

Step-by-step explanation:

= 2x + 10x - 15

=12x - 15

I think this is the answer

7 0

3 years ago