in the proportion 2/8=8/32, which numbers is the geometric mean of the other two numbers?
Well, in this case, the geometric mean of two numbers is the square root of their product. Let's calculate it, shall we?
For the proportion 2/8 = 8/32, we have:
2/8 = 0.25
8/32 = 0.25
So, the geometric mean of these two numbers is 0.25.
Why did the number go to school?
Because it wanted to become smarter!
To find the geometric mean of two numbers, we need to find the square root of their product.
In the given proportion 2/8 = 8/32, the two pairs of numbers are (2, 8) and (8, 32).
For the pair (2, 8), the product is 2 * 8 = 16.
The square root of 16 is 4.
For the pair (8, 32), the product is 8 * 32 = 256.
The square root of 256 is 16.
Therefore, in the proportion 2/8 = 8/32, the number 16 is the geometric mean of the other two numbers, 4 and 16.
To find the geometric mean of two numbers in a proportion, we need to remember that the geometric mean is the square root of the product of the two numbers.
In the given proportion: 2/8 = 8/32, we can see that 2 and 8 are the two numbers on one side of the equation, and 8 and 32 are the two numbers on the other side.
So to find the geometric mean, we need to take the square root of the product of the two numbers: sqrt(2 * 8) and sqrt(8 * 32).
Calculating the square roots gives us:
For the first set of numbers: sqrt(2 * 8) = sqrt(16) = 4
For the second set of numbers: sqrt(8 * 32) = sqrt(256) = 16
Therefore, in the proportion 2/8 = 8/32, the numbers 4 and 16 are the geometric mean of the other two numbers.
let the mean be x
(1/8) / x = x / (8/32)
x^2 = (1/8)(8/32)
x^2 = 1/32
x = ± 1/√32 or ± 1/(4√2)
or
± √2/8