Is density exponentially proportional to volume or inversely?

1 answer:

8 0

An exponential relationship takes the form y = k(a^x), where a and b are constants. Often the value of a turns out to be Euler's number, e = 2.718281828..., because it has the special property that d/dx(e^x) = e^x. Exponential growth might model how the population of a bacterium which divides every 5 seconds increases, and exponential decay might model how the mass of a radioactive isotope sample decreases with time.

Inverse proportion takes the form

An inverse proportion takes the form y = k/x, for a constant k. This kind of relationship might model how the time taken to complete a job varies as the number of workers varies, for example.

We know the formula for density is mass over volume (d = m/v). We therefore see that when mass is considered an arbitrary constant, substitute y = d, k = m and x = v, and we have our inverse proportion.

Intuitively this makes sense. Double the volume for the same mass and the density halves. Quarter the volume for the same mass and the density quadruples.

I hope this helps you :)

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3 0

3 years ago

Please help Need good grade

ivann1987 [24]

Answer:

The other angle is 120°.

Explanation:

Given that,

Angle = 60

Speed = 5.0

We need to calculate the range

Using formula of range

$R=\dfrac{v^2\sin(2\theta)}{g}$ ...(I)

The range for the other angle is

$R=\dfrac{v^2\sin(2(\alpha-\theta))}{g}$ ....(II)

Here, distance and speed are same

On comparing both range

$\dfrac{v^2\sin(2\theta)}{g}=\dfrac{v^2\sin(2(\alpha-\theta))}{g}$

$\sin(2\theta)=\sin(2\times(\alpha-\theta))$

$\sin120=\sin2(\alpha-60)$

$120=2\alpha-120$

$\alpha=\dfrac{120+120}{2}$

$\alpha=120^{\circ}$

Hence, The other angle is 120°

6 0

4 years ago

A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?

dolphi86 [110]

To solve this problem we will derive the expression of the precession period from the moment of inertia of the given object. We will convert the units that are not in SI, and finally we will find the precession period with the variables found. Let's start defining the moment of inertia.

$I = MR^2$