Thesumoftwopositivenumbersis16.whatisthesmallest possible value of the sum of their squares?

1 answer:

5 0

X+y=16
the sum of the squares is
x^2+y^2=sum

solve for y in first equation
x+y=16
y=16-x
subsitiute that for y in other equation

x^2+(16-x)^2=sum
x^2+x^2-32x+256=sum
2x^2-32x+256=sum
take derivitive to find the minimum value (or just find the vertex because the parabola opens up)
derivitive is
4x-32=derivitve of sum
the max/min is where the derivitive equals 0
4x-32=0
4x=32
x=8

at x=8
so then y=16-8=8

the smallest value then is 8^2+8^2=64+64=128

You might be interested in

Please help I have a sucky teacher and don’t know what to do

Katyanochek1 [597]

Answer:

1, 4, 3, 6, 2, 7, 5

Step-by-step explanation:

The circle operator in $f\circ g$ means that the function named on the left (f) operates on the result of the function named on the right (g). So, the notation

$(f\circ g)(x)$

means

$f(g(x))$

That is, g(x) is computed and used as input to the function f. When the function definitions are as shown, the evaluation proceeds in these steps.

$(f\circ g)(-4)\\\\=f(g(-4))\quad\text{write as function of a function}\\\\=f(-2(-4)^2)\quad\text{put -4 for x in $g(x)$}\\\\=f(-2(16))\quad\text{evaluate $(-4)^2$}\\\\=f(-32)\quad\text{evaluate $g(-4)$}\\\\=2(-32-1)\quad\text{put -32 for x in $f(x)$}\\\\=2(-33)\quad\text{first step evaluating $f(-32)$}\\\\=-66\quad\text{value of $(f\circ g)(-4)$}$