
Let
, so that differentiating both sides wrt
gives

If
and
, the above reduces to

This is the slope of the tangent line, which has equation

For this problem, we use the Fundamental Counting Principle where it states that if an event has n possible outcome and another independent event has m outcomes then there will be nm total possible outcome. Therefore, there are 3x4x3 = 36 possible different lunch John can make.
Answer:
j = 21 and n = 14
Step-by-step explanation:
we have the equations:
6j + n/3 = 134
j/3 + n = 31
54j + 3n = 1206
j + 3n = 93
53j = 1113
j = 21
(21)/3 + n = 31
7 + n = 31
n = 14
Answer:
The square root of 476 is 21.8