Inverse Variation and Square Roots

The video tutorial explains the concept of inverse variation, specifically when y is inversely proportional to the square root of x. It demonstrates how to find the constant of proportionality (k) using given values of y and x, and how to write the variation equation. The tutorial also shows how to calculate y for a specific x value using the derived equation, rounding results to three decimal places.

What does it mean when y is inversely proportional to the square root of x?

• y increases as the square root of x increases

• y decreases as the square root of x increases

• y is constant regardless of x

• y is directly proportional to x

Which equation represents y being inversely proportional to the square root of x?

• y = k * sqrt(x)

• y = k / x

• y = k / sqrt(x)

• y = k * x

If y = 15 when x = 7, how do you find the constant k?

• Multiply 15 by the square root of 7

• Divide 15 by the square root of 7

• Add 15 and the square root of 7

• Multiply 15 by 7

What is the exact value of k when y = 15 and x = 7?

• 7 * sqrt(15)

• 15 / sqrt(7)

• 15 * sqrt(7)

• 15

After rounding, what is the approximate value of k to three decimal places?

• 39.685

• 39.686

• 39.687

• 39.688

How do you write the inverse variation equation using the rounded value of k?

• y = 39.686 / sqrt(x)

• y = 39.686 * sqrt(x)

• y = 39.686 / x

• y = 39.686 * x

What is the next step after substituting x = 18 into the inverse variation equation?

• Multiply 39.686 by 18

• Divide 39.686 by 18

• Multiply 39.686 by the square root of 18

• Divide 39.686 by the square root of 18

What is the approximate value of y when x = 18, rounded to three decimal places?

• 9.356

• 9.353

• 9.354

• 9.355

Why do we round the value of y to three decimal places?

• To simplify calculations

• To avoid using a calculator

• To match the precision of k

• To make the number smaller

What is the purpose of using a calculator in this problem?

• To round numbers accurately

• To find the square root

• To perform division

• To check the work