Question

y is inversely proportional to the square of x.
y = 8 when x = 3.5
8
Find the negative value of x when y= 8/9

Answer 1

Step-by-step explanation:

x²y = k, where k is a real constant.

When x = 3.5, y = 8.

=> (3.5)²(8) = k, k = 98.

When y = 8/9,

we have x²(8/9) = (98).

=> x² = 110.25

=> x = 10.5 or x = -10.5.

Since we want the negative value,

the answer is x = -10.5.

Answer 2

The required negative value of variable x when y = 8/9 is -10.5. To understand the calculations, check below.

Proportion:

Important information:

• y is inversely proportional to the square of x.
• y=8 when x=3.5.

Using the given inverse proportional statement, we get

$y\propto \dfrac{1}{x^2}$

$y=\dfrac{k}{x^2}$     ...(i)

Substitute $x=3.5,y=8$.

$8=\dfrac{k}{3.5^2}$

$8=\dfrac{k}{12.25}$

$8\times 12.25=k$

$98=k$

Substitute $k=98$ in (i).

$y=\dfrac{98}{x^2}$

Substitute $y=\dfrac{8}{9}$.

$\dfrac{8}{9}=\dfrac{98}{x^2}$

$x^2=98\times \dfrac{9}{8}$

$x^2=110.25$

$x=\pm \sqrt{110.25}$

$x=\pm 10.5$

We need only negative value.

$x=-10.5$

Therefore, the required value of variable x is -10.5.

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