Answer:
x = 60°
Step-by-step explanation:
Use special triangles.
Starting with an equilateral triangle (all angles at 60°) with the side length of 2. Drop an altitude from one of the vertices to cut in half and make a right - triangle.
The hypotenuse length is 2. The base length, because it was cut in half, is 1. The height can be found with the Pythagorean theorem, which is √3.
The ratio for tangent is opposite over adjacent.
Since √3 = √3 / 1, the angle must be the one as marked in the picture.
Remember this triangle came from an equilateral triangle, so that angle is 60°. It was not cut in half, unlike the top angle which is 30°.
; where a = 1, b = -4 and c = 8
from the provided focus point and directrix, we can see that the focus point is above the directrix, meaning is a vertical parabola and is opening upwards, thus the squared variable will be the "x".
keeping in mind the vertex is half-way between these two fellows, Check the picture below.
![\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] ~\dotfill](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~%5Cdotfill)
Answer:
$9.89
Step-by-step explanation:
Increasing the amount of fuel by 28 gallons from 10 to 38 increased the weight by 154 pounds from 2155 to 2309 pounds.
The increase to 52 gallons of fuel is an increase of 14 gallons from 38, which is half the previous increase of 28 gallons. Thus, we expect the increase in weight from 2309 pounds to be half the previous increase, or 154/2 = 77 pounds.
2309 + 77 = 2386 . . . pounds
We expect the airplane to weigh 2386 pounds when it is carrying 52 gallons of fuel.
