Question

Suppose that y varies directly as the square root of x, and that y = 45 when x = 225. What is y when x

places if necessary.
AnswerHow to enter your answer (opens in new window) 2 Points
= 12? Round your answer to two decimal
Keypa
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Answer 1

To find the value of y when x = 12 in a direct variation equation with the square root of x, we substitute the given values into the equation and solve for the constant of variation. Then, we substitute the constant and the given value of x to find the value of y. In this case, y ≈ 10.39 when x = 12.

Step-by-step explanation:

To determine the value of y when x = 12, we need to use the given information that y varies directly as the square root of x. This means that we can write an equation in the form y = k(sqrt(x)), where k is the constant of variation. To find the value of k, we can substitute the given values y = 45 and x = 225 into the equation and solve for k.

When we substitute y = 45 and x = 225 into the equation, we get:

45 = k(sqrt(225))

Simplifying the right side of the equation:

45 = k(15)

Dividing both sides of the equation by 15:

k = 3

Now that we know the value of k is 3, we can substitute it into the equation and solve for y when x = 12:

y = 3(sqrt(12))

Calculating the square root of 12:

y = 3(3.464)

Rounding the answer to two decimal places:

y ≈ 10.39

Therefore, when x = 12, y ≈ 10.39.

Learn more about direct variation, square root, solving equations