y varies inversely with x. If y = 2.4 and k (the constant of variation) = 8.88, what is x? Round to the nearest tenth, if necessary.

Accepted Solution

Answer:3.7Step-by-step explanation:Inversely means we are taking the constant and dividing it.So y varies inversely with x means "y=k/x".k is a constant.  We can find the constant if they give us a point on this curve.The constant is a number that doesn't change no matter your input and output.[tex]y=\frac{k}{x}[/tex] So they actually give us k=8.88 and y=2.4 so let's input this:[tex]2.4=\frac{8.88}{x}[/tex]We need to solve this equation for x.  You can do your favorite thing in cross-multiply. But how, Freckles?  Well just slap a 1 underneath that 2.4.  You can do that because 2.4/1 is still 2.4.[tex]\frac{2.4}{1}=\frac{8.88}{x}[/tex]Cross-multiply:[tex]2.4x=8.88(1)[/tex][tex]2.4x=8.88[/tex]Divide both sides by 2.4:[tex]x=\frac{8.88}{2.4}[/tex][tex]x=3.7[/tex] when [tex]y=2.4[/tex].