Suppose that H(x) varies inversely with x and H(x) = 50 when x = 0.25.What is H(x) when x = 2?A. 0.5B. 6.25C. 12.5D. 24

Accepted Solution

we know thatA relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]so[tex]H(x)*x=k[/tex]Step 1Find the value of kIn this problem  we have[tex]H(x)=50[/tex]  for [tex]x=0.25[/tex]Substitute[tex]k=50*0.25[/tex][tex]k=12.5[/tex]The equation of the inverse variation is equal to[tex]H(x)=\frac{12.5}{x} [/tex]Step 2Find the value of H(x) for [tex]x=2[/tex]Substitute in the formula[tex]H(2)=\frac{12.5}{2}=6.25[/tex]thereforethe answer is the option B[tex]6.25[/tex]