Question

y = k√x
complete the table to describe the pattern between x and y:

x	y
2	30
8	yellow cell

Explanation:

Step1: Find the value of k

We know that when \( x = 2 \), \( y = 30 \) and the equation is \( y=k\sqrt{x} \). Substitute these values into the equation:
\( 30 = k\sqrt{2} \)
To find \( k \), we solve for \( k \): \( k=\frac{30}{\sqrt{2}} \), rationalize the denominator: \( k = \frac{30\sqrt{2}}{2}=15\sqrt{2} \)

Step2: Calculate y when x = 8

Now that we have \( k = 15\sqrt{2} \), substitute \( x = 8 \) and \( k = 15\sqrt{2} \) into the equation \( y = k\sqrt{x} \):
\( y=15\sqrt{2}\times\sqrt{8} \)
Simplify \( \sqrt{8}=\sqrt{4\times2} = 2\sqrt{2} \), so:
\( y=15\sqrt{2}\times2\sqrt{2} \)
Multiply the coefficients and the square roots: \( y = 30\times(\sqrt{2}\times\sqrt{2}) \)
Since \( \sqrt{a}\times\sqrt{a}=a \) (for \( a\geq0 \)), \( \sqrt{2}\times\sqrt{2} = 2 \), so:
\( y=30\times2 = 60 \)

Answer:

60