Question

Find constant of variation and write equation of variation for every example given below:
1)p a 1/q ; if p=15 then q=4
2)z a 1/w ; when z= 2.5 then w=24

Answer 1

Answer:

1). 3.75 and 2).0.141...

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given:

1)$p \propto \frac{1}{q}$ ; if p=15 then q=4

2)$z \propto \frac{1}{w}$ ;when z= 2.5 then w=24

To find: Find constant of variation and write equation of variation in each case.

Solution 1:

Step 1: Write the proportionality.

$p \propto \frac{1}{q}$

Step 2: Remove the sign of proportionality.

We can remove the sign of proportion by a constant.

Let the Proportionality constant is k.

Equation of variation is:

$p = \frac{k}{q}$

Step 3: Put the given values of p and q.

Put p=15 and q=4

$15 = \frac{k}{4}$

$k = 15 \times 4$

$\bf \green{k = 60}$

Solution 2:

Step 1: Write the proportionality.

$z \propto \frac{1}{w}$

Step 2: Remove the sign of proportionality.

We can remove the sign of proportion by a constant.

Let the Proportionality constant is k'.

Equation of variation is:

$z = \frac{k'}{w}$

Step 3: Put the given values of z and w.

Put z=2.5 and w=24

$2.5 = \frac{k'}{24}$

$k' = 2.5 \times 24$

$\bf \pink{k' = 60}$

Final answer:

Constant of variation, k=60 in equation $p= \frac{k}{q}$ ,if p=15, q=4.

Constant of variation, k'=60 in equation $z= \frac{k'}{w}$ ,if z=2.5 and w=24.

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