![\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvertical%20parabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%204p%28y-%20k%29%3D%28x-%20h%29%5E2%20%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bfocus~point%7D%7B%28h%2Ck%2Bp%29%7D%5Cqquad%20%5Cstackrel%7Bdirectrix%7D%7By%3Dk-p%7D%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22p%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22p%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
something noteworthy is that the squared variable is the "x", thus the parabola is a vertical one, the "p" value is negative, so is opening downwards, and the h,k is pretty much the origin,
vertex is at (0,0)
the focus point is "p" or 5 units down from there, namely at (0, -5)
the directrix is "p" units on the opposite direction, up, namely at y = 5
the focal width, well, |4p| is pretty much the focal width, in this case, is simply yeap, you guessed it, 20.
From what I'm understanding of these questions, the biggest thing you need to answer these is the formulas for cylinders and triangular prisms. I'm not sure what the quantities are for either question so I'm going to work with made up numbers to give examples for the formulas. For number 2 with the cylinder, let's consider the formula first:
π × r2 × h <em>OR </em>pi (3.14) times radius squared times height
If you have the height and you have pi, all you need to take is the doubled radius (aka multiply it by 2) and plug that back into the formula. For the sake of an example, I'm going to make up the number 2 for the radius and 6 for the height. Here's what that would look like:
r = 2; double it, resulting in 4
pi x 4^2 x 6
3.14 x 16 x 6
= 301.44
Work with the actual numbers you have and you're good to go.
For number 3, reducing something by 1/2 means dividing by 2. Let's consider the formula and then work through another example:
1/2 x b x h x l <em>OR </em> 1/2 times base times height times length
For the sake of an example, I'll use 10 for the height, 15 for the base, and 20 for the length:
h = 10; reduce by 1/2, resulting in 5
1/2 x 15 x 5 x 20
= 750
Plug in your actual quantities, and remember your volume units. Hope this helps!
The axis of symmetry would be -3 because it is always the (x) of the vertex
Answer:
20.5g in protein
427.55mg in sodium
Step-by-step explanation:
Add the amount or proteins he ate first for all the food he ate, and then the sodium for the food and there is your answer.
