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3 years ago

The difference between a positive and negative association?

1 answer:

4 0

<em><u>Answer:</u></em><em> </em>Two variables have a positive association when the values of one variable tend to increase as the values of the other variable increase.

Two variables have a negative association when the values of one variable tend to decrease as the values of the other variable increase.

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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

A small box of raspberries costs $2. A large box of raspberries costs $6. Use this information to complete the sentence below.

Sunny_sXe [5.5K]

What sentence below

5 0

4 years ago

Please help!!!!! I have no idea what to do!

Phantasy [73]

Answer:

$f(x)=-\frac{1}{2}x +1$

Step-by-step explanation:

Slope intercept form is: $f(x)=mx+b$

<h2>Find the Slope:</h2>

Choose 2 points on the graph:

(0,1) (2,0)

Find the slope of the two points:

$\frac{0-1}{2-0}=-\frac{1}{2}$

$m=-\frac{1}{2}$

<h2>Find the Y-Intercept</h2>

The y-intercept, or the point that the line crosses on the y axis, is (0,1).

$b=1$

$f(x)=-\frac{1}{2}x +1$

4 0

3 years ago

Read 2 more answers

Find the solutions <br><br> question is pasted on the question

Anna71 [15]

Answer:

1=(5,-2) 2=(1,4)

Step-by-step explanation:

6 0

3 years ago

The function G(x)=-x+5 is compressed horizontally to form F(x). Which of the following could be the equation of F(x)?

Y_Kistochka [10]

The horizontal compression of a graph means that the graph has come closer to the y-axis. Horizontal stretching and compression occur when a factor is multiplied to the original equation. If the factor being multiplied is greater than 1, then the graph is compressed. If the factor being multiplied is less than 1, the graph is stretched. Therefore, in this case, a number greater than 1 must be multiplied to -x + 5.
The answer is B. F(x) = -2(x-5)

3 0

3 years ago