Question

The quantity of p varies directly as q. When the value of p is 17, then the value ofq is 3.4. Find the proportionality constant. What is the equation of variation?

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Answer 1

$\huge\bold{\mathtt{Question⇒}}$

The quantity of $\mathtt{p}$ varies directly as $\mathtt{q}.$ When the value of $\mathtt{p}$ is $\mathtt{17},$ then the value of $\mathtt{q}$ is $\mathtt{3.4}.$ Find the proportionally constant. What is the equation of variation?

$\huge\bold{\mathtt{Given⇒}}$

• The quantity of $\mathtt{p}$ varies directly as $\mathtt{q}.$

• When the value of $\mathtt{p}$ is $\mathtt{17},$ then the value of $\mathtt{q}$ is $\mathtt{3.4}.$

$\huge\bold{\mathtt{To\:find⇒}}$

• The proportionally constant.

• The equation of variation.

$\huge\bold{\mathtt{Solution⇒}}$

The quantity of $\mathtt{p}$ varies directly as $\mathtt{q}.$

• $\mathtt{p=17}$

• $\mathtt{q=3.4}$

Let $\mathtt{k}$ is the proportionally constant.

So, we can say-

$\large\mathtt{p = k × q}\:\:\:\:\:$ $[\mathtt{k≠0}]$

Substituting $\mathtt{p}$ and $\mathtt{q}$ with their values respectively.

$\large\mathtt{ 17 = k × 3.4 }$

$\large\mathtt{➳\:{\frac{17}{3.4}} = k}$

$\large\mathtt{➳\:k = {\frac{17}{3.4}}}$

$\large\mathtt{➳\:k = {\frac{(17×10)}{(3.4×10)}}}$

$\large\mathtt{➳\:k = {\frac{170}{34}}}$

$\large\mathtt{➳\:k = 5 }$

$\huge\bold{\mathtt{Hence⇒}}$

$\mathtt{k = 5}$

Proportionally constant $\mathtt{= k = 5 }$

Equation $⇒{\mathtt{( p = k × q)}}$

$\huge\bold{\mathtt{Therefore⇒}}$

The proportionally constant is $\mathtt{5}$ and the equation of variation is $\mathtt{(p = k × q)}$.

$\huge\bold{\mathtt{Done࿐}}$

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