+0

# The temperature of a point in the plane is given by the expression . What is the temperature of the coldest point in the pla

0
684
5

The temperature of a point  in the plane is given by the expression . What is the temperature of the coldest point in the plane?

Nov 2, 2014

#2
+101741
+10

\$\$\\T=x^2+y^2-4x+2y\\\\
T+4+1=(x^2-4x+4)+(y^2+2y+1)\\\\
T+5=(x-2)^2+(y+1)^2\\\\
T=(x-2)^2+(y+1)^2\;-5\\\\\$\$

Now anything squared has to be  greater or equal to zero so T has to be greater to or equal to -5 degrees.

This will occur when x=2 and y=-1

Nov 3, 2014

#1
0

Nov 3, 2014
#2
+101741
+10

\$\$\\T=x^2+y^2-4x+2y\\\\
T+4+1=(x^2-4x+4)+(y^2+2y+1)\\\\
T+5=(x-2)^2+(y+1)^2\\\\
T=(x-2)^2+(y+1)^2\;-5\\\\\$\$

Now anything squared has to be  greater or equal to zero so T has to be greater to or equal to -5 degrees.

This will occur when x=2 and y=-1

Melody Nov 3, 2014
#4
+101149
0

Very nice, Melody........no Calculus required !!!!

Nov 3, 2014
#5
+101741
0

Thanks Chris  :))

Nov 3, 2014