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:
Total number of children = 70
Step-by-step explanation:
Given:
Number of kids buy popcorn = 42
Percent of kids buy popcorn = 60% = 0.6
Find:
Total number of children
Computation:
Total number of children = Number of kids buy popcorn / Percent of kids buy popcorn
Total number of children = 42 / 0.6
Total number of children = 70
Answer:
or
Step-by-step explanation:
3/5 actually can't be simplified, so it will stay as
The decimal form is
Answer:
Step-by-step explanation:
Let h be the number of hats Elliott makes and s be the number of scarves she makes.
Each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats. This is expressed as
h = 2s
The total number of hats and scarves that she wants to make is 20. This is expressed as
h + s = 20
Therefore, the system of equations that represents this situation are
h = 2s
h + s = 20
Answer:
(-∞,∞)
Step-by-step explanation:
It is positive for all x