Example 3.7.4: The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares

The smallest possible value of the sum of their squares is 128.

Step-by-step explanation:

Let the first number = x

let the the second number = y

x +  y = 16

y = 16 -x

minimum value, f = x² + y²

f(x) = x² + (16-x)²

f(x) = x² + 256 - 32x + x²

f(x) = 2x² - 32x + 256

f(x)' = 4x - 32

4x - 32 = 0

4x = 32

x = 32 / 4

x = 8

The absolute minimum value of x = 8

y = 16 - x

y = 8

The smallest possible value of the sum of their squares is given by x² + y²;

=  (8)² + (8)²

= 128

Therefore, the smallest possible value of the sum of their squares is 128.

6 hours 48 min

step-by-step explanation:

68÷5=13.6

13.6×30=408min=6 hours 48 min.

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12.5 feet

step-by-step explanation: