Question

if y is inversely proportional to 2x + 1 and the difference in the values of y when x = 0.5 and x = 2 is 0.9, find the value of y when x = -0.25

Answer 1

Answer:  The required value of y is 6.

Step-by-step explanation:  Given that y is  inversely proportional to 2x + 1 and the difference in the values of y when x = 0.5 and x = 2 is 0.9.

We are to find the value of y when x = -0.25.

According to the given information, we have

$y\propto\dfrac{1}{2x+1}\\\\\\\Rightarrow y=k\times\dfrac{1}{2x+1}~~~~~~~~~~~~~~~~~~~[\textup{where k is the proportionality constant}]\\\\\\\Rightarrow y=\dfrac{k}{2x+1}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Since the difference of the values of y when x = 0.5 and x = 2 is 0.9, so we get

$\dfrac{k}{2\times0.5+1}-\dfrac{k}{2\times2+1}=0.9\\\\\\\Rightarrow \dfrac{k}{2}-\dfrac{k}{5}=0.9\\\\\\\Rightarrow \dfrac{5k-2k}{10}=0.9\\\\\Rightarrow 3k=9\\\\\Rightarrow k=\dfrac{9}{3}\\\\\Rightarrow k=3.$

So, from equation (i), we get

$y=\dfrac{3}{2x+1}.$

Therefore, when x = -0.25, then the value of y is

$y=\dfrac{3}{2\times(-0.25)+1}=\dfrac{3}{-0.50+1}=\dfrac{3}{0.50}=6.$

Thus, the required value of y is 6.