Question

If y is directly proportional to x²,and y=8 when x=4,then find y when x=5(explain in detail with correct method)​

Answer 1

The first statement (“y is inversely proportional to x”) can be written in mathematical shorthand as:

y = a*(1/x)

Where a is the coefficient of proportionality.

It follows that:

a = x*y

Substituting the known values gives

a = 4*8 = 32

So, if x = 5, then y = 32/x = 32/5 = 64/10
=6.4

Answer 2

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Given:

• y is directly proportional to x^2
• When x = 4, then y = 8

To Find:

• Value of y when x = 5

Solution:

According to the question,

$:\longrightarrow y \propto x^2 \\:\implies y = ax^2 ('a'\:is\: proportionality\: constant) \\\text{Also,} \\:\implies 8 = a(4)^2 \\:\implies 8 = 16a \\:\implies a = \dfrac{8}{16} = \dfrac{1}{2}. \\\text{So, } \\:\implies y = \dfrac{x^2}{2} \\\text{So, we have to find value of y at x = 5}\\:\implies y = \dfrac{5^2}{2} \\:\implies y = \dfrac{25}{2} \\\bf{:\implies y = 12.5}$

Hope it Helps!!!