VCE Methods Question Thread!

[Homer]

Consider the function f(x) = x^3 - 6x^2 + 12x + p, where p is a real constant. Find the values of b and c in terms of p if necessary such that f(x)=(x+b)^3 + c.

[pi]

(x+b)^3 + c
= (x+b)(x^2 + 2xb + b^2) +c
= x^3 + 3x^2b + 3xb^2 + b^3 +c
= f(x)
= x^3 - 6x^2 + 12x + p

Hence, using coefficients:
(1) 3b = -6 -> b = -2
(2) b^3 + c = p -> c = p +8

[Homer]

Thanks again!

[Homer]

Find the area of the largest rectangle that has each of its sides touching a vertex of the given rectangle (4cm by 3 cm).

[nisha]

Was doing some CAT questions for methods (apparently thats what they used to call it before SACS), and I came across two questions which seem easy (and they probably are) but i couldn't do them. Help would be appreciated:::

1/ A random sample of 100 people were asked for an opinion about the Australian flag and of those asked 27 believed that the flag should be changed. An approximate 95 percent confidence interval for the proportion of the population who would like the flag changed is?

2/Of the 200 cars travelling down the Great western Freeway, 60 of them were exceeding 100km/hr. Let p denote the proportion of the cars travelling along the Great Westerm Freeway that exceeded 100km/hr. A 95 per cent confidence interval for p is given by?

[BubbleWrapMan]

Find the area of the largest rectangle that has each of its sides touching a vertex of the given rectangle (4cm by 3 cm).

Here.

I used a double angle formula, but you don't have to, though it saves time.

[Homer]

I am not sure about these but yolo
1) 18.12 to 35.88
2) 47.04 to 72.96

[catwoman101]

what are the transformations in
4(1-x)2
(the 2 is a squared)

[Homer]

Reflection in the y- axis?
Dilation of 4 from the x-axis?
Translation of 1 unit to the right?

[Jenny_2108]

Reflection in the y- axis?
Dilation of 4 from the x-axis?
Translation of 1 unit to the right?

yep

[catwoman101]

Reflection in the y- axis?
Dilation of 4 from the x-axis?
Translation of 1 unit to the right?

thanks

[FlorianK]

Is cos(x)*sin(x)=.5*sin(2x) ?

[WhoTookMyUsername]

yes, although i don't think you can use that in methods.
It's a double angle formula where sin(2x) = 2 (cox(x)sin(x))


edit: oops

[monkeywantsabanana]

yes, although i don't think you can use that in methods.
It's a double angle formula where sin(2x) = 1/2) (cox(x)sin(x))

2cosxsinx?

and yeah, i'm pretty sure you can.

[pi]

You won't need to use it unless it's on your formula sheet.