Let

. Then

, and differentiating both sides with respect to

gives


Now, when

, you get

You have

, so

and

. So
Answer:
The questions and problem can be chosen in 1260 ways.
Step-by-step explanation:
Given that, a physics exam consists of 6 open-ended problem and 9 multiple choice questions.
The order of choosing does not matter.
So,we use combination to find ways.
The ways to choose 6 multiple choice from 9 is= 

=84
The ways to 2 open-ended question from 6 is= 

=15
Since pick 6 multiple choice out of 9 and 2 open-ended question out of 6 both are independent we have multiply both to find required ways.
Total number of ways is =(84×15)
=1260.
Answer:
Step-by-step explanation:
Your problem setup is correct. The triangle is isosceles, so the marked segments are the same length.
3x - 8 = 2x
You can solve this by subtracting 2x (from both sides) ...
x - 8 = 0
Then adding 8 (to both sides):
x = 8
MB = MA = 2x = 16.
3x+4y=12
9x-2y=15
we will use elimination
multiply 3x+4y=12 by -3
-9x-12y=-36
9x-2y=15
_________ add
-14y=-21
÷-14 both sides
y=1.5
find x
3x+4 (1.5)=12
3x+6=12
-6 both sides
3x=6
÷3 both sides
x=2
x=2
y=1.5