Y varies inversely with the square of x, Given that y= 1/3 when x= -2, how do you express y in terms of x?

3 Answers
Apr 6, 2017

Answer:

#y=4/(3x^2)#

Explanation:

Since #y# varies inversely with the square of #x#, #y prop 1/x^2#, or #y=k/x^2# where #k# is a constant.

Since #y=1/3ifx=-2#, #1/3=k/(-2)^2#. Solving for #k# gives #4/3#.

Thus, we can express #y# in terms of #x# as #y=4/(3x^2)#.

Apr 6, 2017

Answer:

#y=4/(3x^2)#

Explanation:

Inverse means #1/"variable"#

The square of x is expressed as #x^2#

#"Initially " yprop1/x^2#

#rArry=kxx1/x^2=k/x^2# where k is the constant of variation.

To find k use the given condition #y=1/3" when " x=-2#

#y=k/x^2rArrk=yx^2=1/3xx(-2)^2=4/3#

#rArr color(red)(bar(ul(|color(white)(2/2)color(black)(y=4/(3x^2))color(white)(2/2)|)))larr" is the equation"#

Apr 6, 2017

Answer:

#Y = 4/(3 x^2)#

Explanation:

Y varies inversely with square of x means

#Y = k (1/x^2)# where #k# is a constant

plug in #Y = 1/3# and #x = -2# in the above equation.

#1/3 = k (1/(-2)^2)#

#1/3 = k (1/4)#

multiply with #4# to both sides.

#4/3 = k#

therefore,
#Y = 4/3 (1/x^2) = 4/(3 x^2)#