Small mathematics (P1) questions

[XWTBSILT]

First question

P1
May / June 2006
Question 11 (i)
Functions f and g are defined by
f : x → k − x for x ∈ R, where k is a constant,
g : x →9 / x + 2 for x ∈ R, x ≠ −2.

(i) Find the values of k for which the equation f(x) = g(x) has two equal roots and solve the equation f(x) = g(x) in these cases. [6]

I equated them and i got this

kx + 2k - x^2 - 2x = 9
x^2 + 2x - kx + 2k +9 = 0
x^2 + x(2 - k) + 2k + 9 = 0

form this point can some continue please try to include evry single step in solving.

Second question

P11
October / November 2009

The equation of a curve is y = 3 cos 2x. The equation of a line is x + 2y = pi. On the same diagram,
sketch the curve and the line for 0 ≤ x ≤ pi.

Ok i know how to draw 3 cos 2x, can some one draw and show x+ 2y = pi

Thanx in advance for your replies

 

[Mohammad Aamer]

First question...
since the eqn has two equal roots b^2-4ac=0
thus (2-k)^2 - 4(1)(2k+9)= 0...solve.......youll get 2 values for k.

Second question....
this is pretty easy..
x+2y = pi
2y = pi-x
y=pi/2 - x/2
thus the pi/2 is the y intercept and -1/2 is the gradient
now u should be able to draw the line...

 

[XWTBSILT]

Got it
Thanx

 

[1992]

how do u draw 3cos2x ??? what does the 3 mean??

 

[Mohammad Aamer]

how do u draw 3cos2x ??? what does the 3 mean??

Let y = 3cos2x
Use different values of x to find y and draw a table....for ex: x=0, x=pi/6, x=pi/3, x= pi/2, etc etc to pi.
When the mode is in degrees u can use 0,30,60,90,120,150,180.
The 3 is the amplitude of the graph.

 

[XWTBSILT]

thanx, sorry for the delay

 

[1992]

how do u draw 3cos2x ??? what does the 3 mean??

Let y = 3cos2x
Use different values of x to find y and draw a table....for ex: x=0, x=pi/6, x=pi/3, x= pi/2, etc etc to pi.
When the mode is in rads u can use 0,30,60,90,120,150,180.
The 3 is the amplitude of the graph.

so to draw graphs for sin, cos tan etcc... We can just use the values of x and then substitute them, right?
like making a table. and then plot them.will that always work??

 

[Mohammad Aamer]

how do u draw 3cos2x ??? what does the 3 mean??

Let y = 3cos2x
Use different values of x to find y and draw a table....for ex: x=0, x=pi/6, x=pi/3, x= pi/2, etc etc to pi.
When the mode is in rads u can use 0,30,60,90,120,150,180.
The 3 is the amplitude of the graph.

so to draw graphs for sin, cos tan etcc... We can just use the values of x and then substitute them, right?
like making a table. and then plot them.will that always work??

You sure can.its handy to know the general shape of graphs though..it can help you to determine whthr ur graph is correct.

 

[1992]

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