Answer:
a) See figure attached
b) 
c) 
So then the heigth for the building is approximately 30 ft
Step-by-step explanation:
Part a
We can see the figure attached is a illustration for the problem on this case.
Part b
For this case we can use the sin law to find the value of r first like this:
Then we can use the same law in order to find the valueof x liek this:
And that represent the distance between Sara and Paul.
Part c
For this cas we are interested on the height h on the figure attached. We can use the sine indentity in order to find it.
And if we solve for h we got:
So then the heigth for the building is approximately 30 ft
He is not making a valid inference because he is assuming the student populations interest based on a small part/ group of the student population, his class.
Answer:
Yes, it does
Step-by-step explanation:
let's notice something, the parabola is a vertical one, so the squared variable is the x, and is opening downwards, meaning the x² will have a negative coefficient.
the distance from the vertex to the directrix/focus is the amount of "p" units, let's see in the graph, the distance from the vertex to the directrix is 2, and since the parabola is opening downwards, "p" is a negative 2, p = -2. The vertex is of course at (0, 2).
![\bf \textit{parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=2\\ p=-2 \end{cases}\implies 4(-2)(y-2)=(x-0)^2\implies -8(y-2)=x^2 \\\\\\ y-2=\cfrac{x^2}{-8}\implies \blacktriangleright y=-\cfrac{1}{8}x^2+2 \blacktriangleleft](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%0A%5C%5C%5C%5C%0A4p%28y-%20k%29%3D%28x-%20h%29%5E2%0A%5Cqquad%0A%5Cbegin%7Barray%7D%7Bllll%7D%0Avertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%0A%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0Ah%3D0%5C%5C%0Ak%3D2%5C%5C%0Ap%3D-2%0A%5Cend%7Bcases%7D%5Cimplies%204%28-2%29%28y-2%29%3D%28x-0%29%5E2%5Cimplies%20-8%28y-2%29%3Dx%5E2%0A%5C%5C%5C%5C%5C%5C%0Ay-2%3D%5Ccfrac%7Bx%5E2%7D%7B-8%7D%5Cimplies%20%5Cblacktriangleright%20y%3D-%5Ccfrac%7B1%7D%7B8%7Dx%5E2%2B2%20%5Cblacktriangleleft%20)
2y+5=y+10
y+5=10
y=5
KN=15
2x+6=3x-1
6=x-1
7=x
NM=20
