26,) If y varies inversely as x, and y = 5 as x = 6, find y for the x-value of 10.

3

Step-by-step explanation:

the initial statement is

y ∝ 1 / x

to convert to an equation multiply by k the constant

of variation

y = k * 1 / x = k / x

to find k use the given condition

y = 5 when x = 6

y = k / x ⇒ k = y x = 5 * 6 = 30

y = 30 / x

when

x = 10

then

y = 30 / 10 = 3

Answer: y = 3

Step-by-step explanation:

In inverse variation, as one variable increases, the other variable decreases and as one variable decreases, the other increases.

We would introduce a constant of proportionality, k. Therefore,

y = k/x

When y = 5, x = 6

Therefore,

5 = k/6

Cross multiplying by 6, it becomes

k = 6 * 5 = 30

The expression becomes

y = 30/x

Therefore, when x is 10,

y = 30/10

y = 3