Question

y is directly proportional to x² and y = a for a particular value of x. Find an expression for y in terms of a, when this value for x is doubled. Please help

Answer 1

Answer:

y is directly proportional to x^2 and y=a for a particular value of x. Find an expression for y in terms of a, when this value of x is doubled.

we can write

y =kx^2 where k is proportionality constant.

further

a = kx^2 ---- (1)

We have to find when x is doubled.

Let it be y1.

Hence, y1= k(2x)^2 = k*4x^2 ---- (2)

Putting value of k from 1, we get

y1 = (a/x^2)*4x^2

= 4a will be the value of when at double value.

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Answer 2

The expression for y in terms of a, when x is doubled is y = 4a.

Given:

y ∝ x².

y = a, for a particular value of x.

To Find:

We have to find the expression for y in terms of a, when this value for x is doubled.

Solution:

Given that, y ∝ x².

The proportionality can be removed by introducing a proportionality constant "k" in the above equation. Thus, we get,

y = kx².

Since y = a, the above equation can be rewritten as,

a = kx².

∴, k = $\frac{a}{x^{2} }$.

On doubling, the value of x becomes 2x. Then the expression for y is given by,

y = k × (2x²)

Substituting the value of "k" in above equation, we get,

y = $\frac{a}{x^{2} }$ × (2x²)  

i.e., y = $\frac{a}{x^{2} }$ × 4x²

On simplifying, the above expression for y becomes,

y = 4a.

Hence, the expression for y in terms of a, when this value for x is doubled is y = 4a.

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