1. By the chain rule,

I'm going to switch up the notation to save space, so for example,
is shorthand for
.

We have




Similarly,

where



To capture all the partial derivatives of
, compute its gradient:


2. The problem is asking for
and
. But
is already a function of
, so the chain rule isn't needed here. I suspect it's supposed to say "find
and
" instead.
If that's the case, then


as the hint suggests. We have



Putting everything together, we get


Answer:
about 52 feet
Step-by-step explanation:
The figure is omitted--you may draw it to confirm my answer.
sin (38°) = 32/x
x sin (38°) = 32
x = 32 / sin (38°) = about 52 feet
Answer:
The expression f(200) depicts the value of the concentration of the pollutant, which when substituted in the expression T = f(P) will give the value of the thickness of the pelican eggs.
Step-by-step explanation:
Since we are given that T = f(P)
Where T = thickness of the eggs
P = concentration in ppm ((parts per million))
Considering f(200) comparing to f(P)
The expression f(200) depicts the value of the concentration of the pollutant, which when substiuted in the expression T = f(P) will give the value of the thickness of the pelican eggs.
i.e substituted the value of the concentration in ppm to get the thickness of the pelican eggs in mm. since the expression shows thickness of pelican eggs as a function of the concentration. for every 200ppm of concentration, the numerical value of the thickness of pelican eggs can be gotten.
-105
Multiply first, then subtract, then add.
Answer: 9 remainder 2
Explanation: 9 is the closest 6 can get to 56 without going over. Since 9•6=54, and 56-54=2 , 2 is the remainder.