Find the values of k so that the geometric mean between 25/2 and 2 is k+1. I need the answer right now.
k+1 = √(25/2 * 2) = √25 = 5
Well, I'm no math whiz, but I do know how to have a good laugh! Let's see if we can figure this out together.
To find the geometric mean, we need to find the number that, when multiplied by itself, gives us the product of the two numbers we have. In this case, the numbers are 25/2 and 2.
So, let's set up the equation: (25/2) * 2 = (k+1) * (k+1)
Simplifying that expression, we get: 25 = 4 * (k+1)^2
Now, let's divide both sides of the equation by 4: 25/4 = (k+1)^2
Taking the square root of both sides, we get: √(25/4) = k+1
Simplifying that further, we have: 5/2 = k+1
Subtracting 1 from both sides gives us: 5/2 - 1 = k
After some arithmetic, we find that k = 3/2.
So, the value of k that makes the geometric mean between 25/2 and 2 equal to k+1 is 3/2. Ta-da!
To find the values of k that satisfies the given condition, let's set up the equation for the geometric mean:
√((25/2) * 2) = k + 1
First, let's simplify the expression inside the square root:
√(25) = k + 1
Solving for k:
5 = k + 1
Subtracting 1 from both sides:
k = 5 - 1
Therefore, the value of k is 4.
To find the values of k, we need to find the geometric mean between 25/2 and 2, and set it equal to k+1.
The geometric mean between two numbers a and b is given by the equation:
√(a * b)
In this case, a = 25/2 and b = 2. Let's substitute these values into the equation:
Geometric mean = √((25/2) * 2)
Simplifying the expression further:
Geometric mean = √(25)
Taking the square root of 25, we find that the geometric mean is 5.
Now, we can set the geometric mean equal to k + 1:
5 = k + 1
Solving for k, we subtract 1 from both sides of the equation:
k = 5 - 1
Hence, the value of k is 4.
Therefore, the values of k that make the geometric mean between 25/2 and 2 equal to k+1 are k = 4.