Answer:
D. Yes,because every x-value corresponds to exactly one y-value.
Step-by-step explanation:
The given ordered pairs are;
{
}
We do not have the same x-value corresponding to more than one y-value.
We can see from the ordered pairs that every x-value corresponds to exactly one y-value.
Therefore the graph of this relation will pass the vertical line test.
Check the picture below.
so the volume will simply be the area of the hexagonal face times the height.
![\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B4%7Dns%5E2%5Cstackrel%7B%5Cqquad%20degrees%7D%7B%5Ccot%5Cleft%28%20%5Cfrac%7B180%7D%7Bn%7D%20%5Cright%29%7D~~%20%5Cbegin%7Bcases%7D%20n%3D%5Cstackrel%7Bnumber~of%7D%7Bsides%7D%5C%5C%20s%3D%5Cstackrel%7Blength~of%7D%7Bside%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20n%3D6%5C%5C%20s%3D12%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B4%7D%286%29%2812%29%5E2%5Ccot%5Cleft%28%20%5Cfrac%7B180%7D%7B6%7D%20%5Cright%29%20%5C%5C%5C%5C%5C%5C%20A%3D216%5Ccot%2830%5Eo%29%5Cimplies%20A%3D216%5Csqrt%7B3%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20hexagon%7D%7D%7B%28216%5Csqrt%7B3%7D%29%7D~~%5Cstackrel%7Bheight%7D%7B%2810%29%7D%5Cimplies%202160%5Csqrt%7B3%7D~~%5Capprox%20~~3741.2~cm%5E3)
Answer:
b. slope: -5; y-intercept: 7
Step-by-step explanation:
We are given the equation:
y + 5x = 7
To find the slope and y-intercept of the line, it would be helpful to get the equation into slope-intercept form. The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
Lets get the given equation into slope-intercept form.
y + 5x = 7
Subtract 5x from both sides.
y = -5x + 7
Now we have the equation in slope-intercept form. By looking at the equation, we can see that the slope is -5 and that the y-intercept is 7.
The correct answer choice would be b.
I hope you find my answer and explanation to be helpful. Happy studying.
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

