So in order to find the line you’ll have to submit the point (3,5) and the slope into the point slope formula : y-y1= m(x-x1)

Y-5= 1/3(x-3)

Solve(turn to y intercept form):

Y-5= 1/3x -1

6 0

3 years ago

Two numbers have a difference of 24. What is the sum of their squares if it is a minimum?

seraphim [82]

Let "a" and "b" be some number where:

a - b = 24

We want to find where a^2 + b^2 is a minimum. Instead of just logically figuring out that the answer is where a=b=12, I'll just use derivatives.

So we can first substitute for "a" where a = b+24

So we have (b+24)^2 + b^2 = b^2 +48b +576 + b^2
And that equals 2b^2 +48b +576

Then we take the derivative and set it equal to zero:

4b +48 = 0
4(b+12) = 0
b + 12 = 0
b = -12

Thus "a" must equal 12.

So:
a = 12
b = -12

And the sum of those two numbers squared is (12)^2 + (-12)^2 = 144 + 144 = 288.

The smallest sum is 288.

3 0

3 years ago