Mathematics
Grade10
Easy

Question

Suppose y varies inversely as the square of x. If x is multiplied by 4 , which of the following is true for the value of y?

  1. It is multiplied by 4 
  2. It is multiplied by 16
  3. It is multiplied by 1 fourth
  4. It is multiplied by 1 over 16 

Hint:

Mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

The correct answer is: It is multiplied by 1 over 16


    We have to find the value of y  when y varies inversely to the square of x.
    We have, y = straight k over straight x squared
    If x becomes 4x, then:
    y = straight k over left parenthesis 4 straight x right parenthesis squared = fraction numerator straight k over denominator left parenthesis 16 space cross times space 2 right parenthesis end fraction
    So, y is multiplied by 1 over 16.
    Hence, the correct option is D.

    Instead of taking y= k/x², we could also have taken yx² = k, where k is a constant.

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