1) How do you express a vector as a linear combination of i and j unit vectors?

For example, v = <2,-2> and w = <0,3>.

2) How do you solve tricky radical equations like this? When trying to repeatedly square both sides to get rid of the root, the equation doesn’t check.

I.E. sqrt(5x-3) – 2sqrt(x)=6

3) When determining profit from a cost equation and a revenue equation, do you set both equations to be equal to each other in order to find the break even point?

I.E.

C = 70 – 11p

R = 14p – 2p^2

4) How do you solve questions of force and magnitude using vectors? I learned about solving questions of direction and heading using vectors, but never force.

For example, a truck weighing 6578 pounds is on a driveway inclined 17.5 degrees to the ground. Neglecting friction, what’s the magnitude of the force parallel to the driveway that will keep the truck from rolling down the incline?

Thanks in advance