Sem2Answers

Hey guys, the link with answers that Mr A posted doesn't work b/c its not actually a link to a server, but just a download for the webpage itself. So i thought maybe we could just post our answers here. :D i figured we r gonna be asking each other for answers anw so y not :D

Also, just in case we get one of the questions wrong, while you are checking answers, if you have the same answer as the one given, just add a comment next to it (confirmed or something). but obviously if it already has lots of people, don't add another one (:

1) **Ans: 240**. for convenience, i'll call the angle y. (confirmed)

tan y = 3 / x. differentiating implicitly: d(tan y) / dy * dy / dt = d(3/x) / dx * dx / dt (sec y)^2 * dy / dt = -3x^-2 * dx / dt

rearranging gives dx / dt = [ (sec y)^2 * dy/dt ] / (-3x^-2) subbing in values for theta, dy/dt, and x, we get -0.067 km/s which is equal to 240 km/h

2) **Ans: y=(4/3)x-(5/3)** (confirmed) Use implicit differentiation to get dy/dx: d(x^3*y^2)/dx=0 (3x^2*y^2)+(2x^3*y)*(dy/dx)=0 (dy/dx)=-(3x^2*y^2)/(2x^3*y^2) (dy/dx)=-3y/2x Substitute y=1 and x=2 to get -3/4

The slope of normal is then 4/3. y-1=(4/3)(x-2) y=(4/3)x-(5/3)

3) **Ans: y=x^2 + cosx + 1** (confirmed) Integrate dy/dx to get y. When we integrate 2x - sinx we get (2x^2)/2 + cosx + c =x^2 + cosx + c Now we sub in (0, 2) as given: 2 = 0 + cos0 + c 2 = 1 + c, c = 1. y=x^2 + cosx + 1

4) **Ans: (a, b, c) = (2, -18, -7)** point (1,7) on the graph: f(1) --> a + b + c = -23 (eq 1) point (1,7) is a max --> f'(x) = 0 at x = 1: f'(x) = 3ax^2 + 2bx + 30 f'(1) --> 3a + 2b = -30 (eq2) inflection pt at x = 3 --> f(x) = 0 at x = 3: f(x) = 6ax + 2b f''(3) --> 18a + 2b = 0 (eq3)

plug these three equations into a matrix on ur calculator (: could be typoes i typed that rather fast without checking.