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Write an equation that expresses the following relationship. p varies directly with d and inversely with the square root of u In your equation, use k as the constant of proportionality.

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tiara143
The equation given as p varies directly with d and inversely with the square root of u is written as:

p = k1d
k1 is the proportionality constant.
and p = k2[tex]\frac{1}{ \sqrt{u} } [/tex]
here k2 is the proportionality constant.

Thus,
 combining both equations we get, p = C[tex] \frac{d}{ \sqrt{u} } [/tex]
where K = K1*K2, K is the proportionality constant.

P varies directly proportional with d and inversely proportional with the square root of u in your equation. Then the equation is

[tex]\rm P = k\dfrac{d}{\sqrt{u}}[/tex].

What are ratio and proportion?

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0.

A proportion is an equation in which two ratios are set equal to each other.

An equation that expresses the following relationship. P varies directly proportional with d and inversely proportional with the square root of u in your equation.

P varies directly proportional with d that is given by

[tex]\rm P \propto d[/tex] ...1

P varies inversely proportional with the square root of u that is given by

[tex]\rm P \propto \dfrac{1}{\sqrt{u}}[/tex] ...2

From equations 1 and 2, we have

[tex]\rm P \propto \dfrac{d}{\sqrt{u}}\\[/tex]

Whenever the proportionality is removed then a constant comes.

[tex]\rm P = k\dfrac{d}{\sqrt{u}}[/tex]

Where, k is proportionality constant.Thus, the equation is

[tex]\rm P = k\dfrac{d}{\sqrt{u}}[/tex].

More about the ratio and proportion link is given below.

https://brainly.com/question/14335762