Final answer:
To calculate the value of x for which the geometric mean of 10 and x is 30, we solve the equation 30 = √(10 × x), which results in x equaling 90.
Step-by-step explanation:
To find the value of x when the geometric mean of 10 and x is 30, we use the formula for the geometric mean of two numbers:
Geometric Mean = √(first number × second number)
In this case, we want to set up the equation as follows:
30 = √(10 × x)
Squaring both sides to eliminate the square root gives us:
900 = 10 × x
Dividing both sides by 10 to solve for x gives:
x = 90
Therefore, the value of x that makes the geometric mean of 10 and x equal to 30 is 90.