Question

If y varies directly as the square of x, find the percentage increase in y when x is increased by 5%

Answer 1

Answer:

The change in percentage of y when x increases by 5% will be 25%

Step-by-step explanation:

Y varies directly as the square of x.

We start off by forming a general equation to show the direct variation

Y=kx ²

Let the value of x be any desired value ,say 25

25 will be x as 100% . therefore when x is 100%  the value of y will be

Y=25²k

  =625k

Increasing the value of x by 5%,  

Say if 25 is 100%

What will be its 105%?

(105*25)/100 =26.25

Therefore 105% of 25 becomes  26.25.

Lets now find the value of y when x is 105%,

Applying the variation equation ,we obtain

Y=(26.25)²k

  =689.0625k

We now find the percentage change in y caused by an increase of x by 5%

Say 625k is 100%,

What percentage will 689.0625 be?

(689.0625*100)/625 = 110.25%

Therefore to find the percentage change in y when x increases by 5% will be  

$New percentage value of y – initial percentage value of Y= percentage change$

(110.25-100)% =10.25%

Therefore the change in percentage of y when x increases by 5% will be 25%

Answer 2

Step-by-step explanation:

The change in percentage of y when x increases by 5% will be 25%

Step-by-step explanation:

Y varies directly as the square of x.

We start off by forming a general equation to show the direct variation

Y=kx ²

Let the value of x be any desired value ,say 25

25 will be x as 100% . therefore when x is 100% the value of y will be

Y=25²k

=625k

Increasing the value of x by 5%,

Say if 25 is 100%

What will be its 105%?

(105*25)/100 =26.25

Therefore 105% of 25 becomes 26.25.

Lets now find the value of y when x is 105%,

Applying the variation equation ,we obtain

Y=(26.25)²k

=689.0625k

We now find the percentage change in y caused by an increase of x by 5%

Say 625k is 100%,

What percentage will 689.0625 be?

(689.0625*100)/625 = 110.25%

Therefore to find the percentage change in y when x increases by 5% will be

New percentage value of y – initial percentage value of Y= percentage changeNewpercentagevalueofy–initialpercentagevalueofY=percentagechange

(110.25-100)% =10.25%

Therefore the change in percentage of y when x increases by 5% will be 25%