What is the mean proportional between 80 and 1/5?
Understand the Problem
The question is asking to find the mean proportional between the numbers 80 and 1/5. This involves understanding the concept of mean proportion and applying it to determine the correct answer from the given options.
Answer
4
Answer for screen readers
4
Steps to Solve
- Define mean proportional
The mean proportional $x$ between two numbers $a$ and $b$ is defined such that $a:x :: x:b$, which implies $x^2 = a \cdot b$. Therefore, $x = \sqrt{a \cdot b}$.
- Apply the formula
In this case, $a = 80$ and $b = \frac{1}{5}$. Substitute these values into the formula for the mean proportional:
$x = \sqrt{80 \cdot \frac{1}{5}}$
- Simplify the expression
$x = \sqrt{\frac{80}{5}}$
$x = \sqrt{16}$
- Calculate the square root
$x = 4$
4
More Information
The mean proportional between two numbers is also known as the geometric mean.
Tips
A common mistake is to confuse the mean proportional with the arithmetic mean. The arithmetic mean of 80 and 1/5 would be $(80 + 1/5)/2 = (400/5 + 1/5)/2 = (401/5)/2 = 401/10 = 40.1$.
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