
Help for exam in 6 hours
Hi all,
I have an exam in 6 hours, which I know nothing about. You can see I'm doing well already. All I know is that the questions are always the same, but the numbers change. From the past papers, I know the following questions (apart from the numbers being different) are going to be on there. If anyone could give me the solutions to the following, step by step, I would bake them a cake and ship it to them. Or, y'know, something else:
1. A line passes through the points (2,7) and (6,1).
Find the equation of the line.
*I'm guessing just yb = m(xa) here? Obviously finding m through m=(y2y1)/(x2x1)
2.A line makes an angle of 50 degrees with the positive direction of the xaxis., where the scales on the axis are equal.
Find the gradient of the line.
*Huh?
3. (a) write down the gradient of any line parallel to y=1/2x +3
(b) write down the gradient of a line perpendicular to y = 3x1
A few of the other questions have diagrams, which I'm not sure how to put in. I'll leave those ones, and try and figure them out....
8 (a) Two functions f and g are givem by f(x) = x(squared) 1 and g(x) = 3x1.
Obtain an expression for f(g(x))
*I seriously have no idea for this one.
(b) Functions h and k, defined on suibtable domains, are given by h(x) = 4x and k(x) = cos x. Find k(h(x))
*once again, no idea.
9. Given y= 1+x4/x2
find dy/dx
any help would be great, thank you so much
Matthew

(1) correct (use pointslope form)
(2) the slope is equaled to $\displaystyle \tan \alpha = \tan 50 $
8(a) $\displaystyle f(x) = x^{2}  1, \ g(x) = 3x1 $
So $\displaystyle f \circ g = (3x1)^2  1 $, same for (b)
9. $\displaystyle y = 1 + \frac{x^4}{x^2} $
$\displaystyle \frac{dy}{dx} = 2x $ (use power rule)