There are infinite multiples of 1/5
multiply 1/5 by a number "n"
where n = all real numbers
(1/5)*n
n = 1 --> 1/5
n = 2 --> 2/5
n = 3 -->3/5
and so on
You're looking for the extreme values of
subject to the constraint
.
The target function has partial derivatives (set equal to 0)


so there is only one critical point at
. But this point does not fall in the region
. There are no extreme values in the region of interest, so we check the boundary.
Parameterize the boundary of
by


with
. Then
can be considered a function of
alone:



has critical points where
:



but
for all
, so this case yields nothing important.
At these critical points, we have temperatures of


so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.
Take 6.5 divided by 2.75 which equals 2.36, 2.36 times 2.75 equals 6.5
Let's solve your equation step-by-step.
Question 1: −2(6−2x) =4(−3+x)
Step 1: Simplify both sides of the equation.
−2(6−2x) =4(−3+x)
(−2) (6) +(−2) (−2x) =(4)(−3)+(4)(x)(Distribute)
−12+4x=−12+4x
4x−12=4x−12
Step 2: Subtract 4x from both sides.
4x−12−4x=4x−12−4x
−12=−12
Step 3: Add 12 to both sides.
−12+12=−12+12
0=0
Answer: All real numbers are solutions.
Question 2:
Let's
solve your equation step-by-step.
5−1(2x+3)
=−2(4+x)
Step 1:
Simplify both sides of the equation.
5−1(2x+3)
=−2(4+x)
5+(−1)
(2x) +(−1) (3) =(−2) (4)+(−2)(x)(Distribute)
5+−2x+−3=−8+−2x
(−2x)
+(5+−3) =−2x−8(Combine Like Terms)
−2x+2=−2x−8
−2x+2=−2x−8
Step 2:
Add 2x to both sides.
−2x+2+2x=−2x−8+2x
2=−8
Step 3:
Subtract 2 from both sides.
2−2=−8−2
0=−10
Answer: There are no solutions.