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:
42
Step-by-step explanation:
for one cup 28/12
for 18 cup,
(28/12)×18
=42
9514 1404 393
Answer:
3. C(−1, −5), D(2, −5)
Step-by-step explanation:
The given points are 2 -(-1) = 3 units apart horizontally, so the remaining points will need to be 18/3 = 6 units below, vertically. Translating the given points down 6 gives ...
D = A -(0, 6) = (2, 1) -(0, 6) = (2, -5)
C = B -(0, 6) = (-1, 1) -(0, 6) = (-1, -5)
The two points required to make a rectangle with an area of 18 square units are ...
C(-1, -5), D(2, -5)
_____
The area of a rectangle is the product of length and width. If the area is 18 square units, and the width is 3 units, then the length must be 6 units. 3×6=18.
#1 √ 75
Answer : 5√3 or ≈ 8.66025
#2 √ 48
Answer : 4√3 or ≈ 6.9282
#3 √ 128
Answer : 8√2 or ≈ 11.31371
#4 √ 300
Answer : 10√3 or ≈ 17.32051
~~
#5 √⅔
Answer :

#6 √16/4
Answer : 2
#7 √ 6/8
Answer :

#8 √27/9
Answer : √ 2 or ≈ 1.73205
~~
I hope that helps you out!!
Any more questions, please feel free to ask me and I will gladly help you out!!
~Zoey