Find the quotient, when the mean proportional of 71⁄5 and 245 is divided by an even prime number.
21
Step 1: Convert the mixed fraction to an improper fraction
7⅕ = (7 × 5 + 1) ÷ 5 = 36 ÷ 5
Step 2: Find the mean proportional of 36 ÷ 5 and 245
The formula for the mean proportional of two numbers, a and b, is:
Mean Proportional = √(a × b)
Here, a = 36 ÷ 5, and b = 245.
Mean Proportional = √(36 ÷ 5 × 245)
= √(36 × 245) ÷ √5
= √8820 ÷ √5
Step 3: Simplify the mean proportional
The mean proportional simplifies to 42.
Step 4: Divide by the even prime number
The only even prime number is 2.
Quotient = 42 ÷ 2 = 21.
Thus, the correct answer is 21.
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