Find two positive integers such that their sum is 10, and minimize and maximize the sum of their squares.

Two numbers whose sum is 10 is required.

The answer is

Minimum: 5, 5

Maximum: 9, 1

Let and be two numbers

The sum of the squares would be

Differentiating with respect with x

Equating with zero

Double derivative of f(x)

So, at the value of the function is minimum.

Therefore, at and the function has minimum value of

For the finding the maximum values of and we have to use trial and error method

0 and 10 will not be considered as 0 is neither positive nor negative.

So, the maximum value of the numbers is 9 and 1 and the maximum value of the function is 82.

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answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq