The point A has coordinates (1, 1) and the point B has coordinates (5, k).
The line AB has equation 3x+4y=7.
a. (i) show that k=2
(ii) hence find the coordinates of the mid-point of AB
b. (i) find the gradient of AB
c. The line AC is perpendicular to the line AB.
(i) Find the gradient of AC.
(ii) Hence find an equation of the line AC.
(iii)Given that the point C lies on the x-axis, find its x-coordinate.
Part II
The line L has equation y+2x=12 and the curve C has equation y=x^{2} -4x +9.
(i) Show that the x-coordinates of the points of intersection of L and C satisfy the equation x^{2} - 2x - 3 = 0
(ii) Hence find the coordinates of the points of intersection of L and C

Which term best describes the association between variables a and b

Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is π cubic inches.

The school track has eight lanes. each lane is 1.25 meters wide. the arc at each end of the track is 180. the distance of the home straight and the radii for the arcs in the 1st 4 lanes are given. s=85m r1=36.5m r2=37.75m r3=39m r4=40.25m part one: find the radii of lanes 5 through 8 of the track. show your work. part two: if max ran around lane one, how far did he run? show your work and explain your solution. part three: max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. show your work and round to the hundredths. part 4: based on your lane choices in part three, what was the total distance max ran in the three laps around the track?