onur369's Methods Question Thread :)

[onur369]

Hey guys after having a break for methods (1.5 weeks) I got some questions.

VCAA 2007:
P is the point on the line 2x+y-10=0 such that the length of OP, the line segment from the origin O to P is a minimum. Find the coordinates of P and this minimum length.

VCAA 2006:
A normal to the graph of y=x^.5 has the equation y=-4x+a, where a is a real constant. Find the value of a.

[luken93]

Rearrange to make y = -2x + 10

The shortest distance will always occur when the gradient is a normal to the line in question

ie, gradient = 1/2

Since you know it goes thru the origin, the equation is y = 1/2x

Finally, find point, the point in which they intersect;
1/2x = -2x + 10
5/2x = 10
5x = 20
x = 4
(4, 2)

The length is sqrt{ (y2- y1)^2 + (x2 - x1)^2)
= sqrt(4 + 16)
= sqrt(20)
= 2sqrt(5)

[luken93]

If -4 is the gradient of the normal, then 1/4 is the gradient of the tangent

y = sqrt(x)
y' = 1/(2sqsrt(x))

Find when y' = 1/4
x = 4

Hence, y = -4x + a passes thru (4, 2)
a = 18

Hopefully I haven't made any mistakes

[onur369]

Hey guys Im having trouble with some type of question.

In exam 2 type questions, multiple choice there are questions like.
i.e: where p and q are real constants, have a unique solution provided or when no solution.

What do I do for each ? Like when it asks for a unique solution or no solution, Im assuming we use the discriminant?

[xZero]

yeah, unique solution discriminant =/= 0, no or infinite solution discriminant = 0

[onur369]

Hey guys, Im stuck on a few more questions: Now half way through Integration.

Question 1: Find f(x), if f'(x)=5sin(2x) and f(pi)=-1
- I do the first section correct, I integrate it and get -2.5cos(2x) its just the f(pi)=-1 part of the question

Question 2: A curve has the gradient dy/dx=ksin(3x)-3 where k is a constant. and a stationary point (pi/2,-2)
Find: a) the value of k, I attempted this I got -3, I am not sure if that is correct
         b) Find the equation of the curve.

[xZero]

1. -2.5cos(2x)+c, sub f(pi)=-1 to find c
2.a) correct b)anti diff it, sub in (pi/2,-2) to find c

[onur369]

For the 2nd question finding c I got 3pi -1 ? Is that correct?

[b^3]

2b



sub in

[onur369]

thanks alot xzero and b^3

[onur369]

Worst question coming up, shame
I am not good with memorising the exact values and now it has come across in integration. How do you remember the values?

[tony3272]

Before i actually learnt the values off by heart, i used to just draw this equilateral triangle (in the attachments) and then cut it in half. You're left with your base angles and side lengths and can just work off of that.

[david10d]

Look at the exact values table and you can see the pattern of square roots ascending (sin) or descending (cos).

[pi]

Look at the exact values table and you can see the pattern of square roots ascending (sin) or descending (cos).

That's what I do, and then sin/cos for tan (or memorise)

[onur369]

I'm stuck with an integral question, only problem here is how to deal with the denominator :/