# Thread: VCE Maths questions help

1. ## Re: VCE Maths questions help

Originally Posted by InteGrand

Thanks. Also, do you know how to find the general solutions to the equations I posted above?
Thanks

2. ## Re: VCE Maths questions help

Originally Posted by boredsatan
Thanks. Also, do you know how to find the general solutions to the equations I posted above?
Thanks
Yes, I do.

3. ## Re: VCE Maths questions help

Originally Posted by InteGrand
Yes, I do.
Could you please explain how to do it as read my textbook but got confused with it's explanation

4. ## Re: VCE Maths questions help

Originally Posted by boredsatan
Also, can someone please explain how to find the general solution to the following equations.
Cos 2(x+pi/3) = 1/2

2 tan 2(x+pi/4) = 2√(3)

2 sin(x+pi/3) = -1

Thanks

Silly question, but is
sin 2(x+pi/3) the same as sin(2x+2pi/3)
Originally Posted by boredsatan
Could you please explain how to do it as read my textbook but got confused with it's explanation
$\noindent Are you able first of all to find the general solution to$

$\cos \theta = \frac{1}{2}?$

$\noindent If you can do this, you should be able to easily do the questions you wrote. But if you \emph{can't} do this, you should probably work on this first.$

5. ## Re: VCE Maths questions help

If (x-1)^3 = 8
then would x-1 = +- cube root of 8, or just + cube root of 8 and why?

Also, does anyone know how you would work out sin(11pi/4), which is sin(2.75pi), and is in quadrant 2, and the rule for quadrant 2 is pi - base, but since it's 2.75, would you do (2pi) + (pi-base)?
And how would you work out the value of the base?

How would you find the basic angle for a negative value?
For instance cos(x) = -1/2

How would you work out (x+1)^3 = -2 without a calculator?
Thanks

6. ## Re: VCE Maths questions help

Originally Posted by boredsatan
If (x-1)^3 = 8
then would x-1 = +- cube root of 8, or just + cube root of 8 and why?

Also, does anyone know how you would work out sin(11pi/4), which is sin(2.75pi), and is in quadrant 2, and the rule for quadrant 2 is pi - base, but since it's 2.75, would you do (2pi) + (pi-base)?
And how would you work out the value of the base?

How would you find the basic angle for a negative value?
For instance cos(x) = -1/2

How would you work out (x+1)^3 = -2 without a calculator?
Thanks
Anyone?

7. ## Re: VCE Maths questions help

Bump!
Any one know how to do the above questions?

Also, does anyone know how to solve the equation sin x = 1/2 for [-pi, to 2pi]
I'm confused with the negative domain
Thanks

Bump

9. ## Re: VCE Maths questions help

Originally Posted by boredsatan
Also, does anyone know how to solve the equation sin x = 1/2 for [-pi, to 2pi]
I'm confused with the negative domain
Thanks
The sine wave has symmetry across the origin, so it's an odd function, which means that $f(-x) = f(-x)$.

Basically that implies that the sine of a negative angle is the same as reversing the sign of the sine of the positive angle, i.e.

$\sin -\theta = -\sin \theta$.

When we go in the positive direction, the first angle $x$ for which $\sin x = -0.5$ is $7\pi / 6$.

So that means that when we go in the negative direction, the first angle $-x$ for which $\sin -x = 0.5$ is $-7\pi / 6$.

But $-7\pi / 6$ is outside the range of $[-\pi, 2\pi]$, so it's not a solution to the equation.

10. ## Re: VCE Maths questions help

Originally Posted by boredsatan
Also, does anyone know how you would work out sin(11pi/4)
The period of $\sin(x)$ is $2\pi$. So,

$\sin\left(\frac{11\pi}{4}\right) = \sin\left(\frac{11\pi}{4} - 2\pi \right) = \sin\left(\frac{3\pi}{4}\right)$

Also, $\sin(x) = \sin(\pi-x)$. So,

$\sin\left(\frac{3\pi}{4}\right) = \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt 2}{2}$

Originally Posted by boredsatan
How would you work out (x+1)^3 = -2 without a calculator?
Thanks
If you want the answer in exact form, then

$x+1 = \sqrt[3]{-2}$

$x+1 = -\sqrt[3]{2}$

$x = -1 -\sqrt[3]{2}$

11. ## Re: VCE Maths questions help

The equation of the image of the graph of y = sin x under a transformation of a dilation of factor 1/2 from the y-axis followed by a translation of pi/4 units in the positive direction of the x axis is:
I'm narrowed it down two 2 options, but don't know which one is correct. Can someone please explain which one is correct and why
y = sin(2x - pi/4) or y = sin2(x-pi/4)

12. ## Re: VCE Maths questions help

let f: [0, pi/2] → R, where f(x) = cos(3x) -2. The graph of f is transformed by a reflection in the x-axis followed by a dilation of factor 3 from the y-axis. How would you work out the resulting graph, super confusing so wold greatly appreciate if someone helped out

13. ## Re: VCE Maths questions help

Originally Posted by boredsatan
The equation of the image of the graph of y = sin x under a transformation of a dilation of factor 1/2 from the y-axis followed by a translation of pi/4 units in the positive direction of the x axis is:
I'm narrowed it down two 2 options, but don't know which one is correct. Can someone please explain which one is correct and why
y = sin(2x - pi/4) or y = sin2(x-pi/4)
I'm not familiar with that specific terminology, but if "dilation of factor 1/2 from the y-axis" means compressing the function horizontally, then you replace $x$ with $2x$ and to shift it right you would replace $x$ with $x - \pi/4$, in that order.

$y = \sin x$

Dilate:

$y = \sin 2x$

Shift graph:

$y = \sin 2\left(x-\frac{\pi}{4}\right)$

Originally Posted by boredsatan
let f: [0, pi/2] → R, where f(x) = cos(3x) -2. The graph of f is transformed by a reflection in the x-axis followed by a dilation of factor 3 from the y-axis. How would you work out the resulting graph, super confusing so wold greatly appreciate if someone helped out
$f(x) = \cos 3x -2$

Reflect across x axis:

$f(x) = -(\cos 3x -2)$

Dilate:

$f(x) = -\left(\cos 3\left(\frac{x}{3}\right) -2\right)$

$= 2 - \cos x$

14. ## Re: VCE Maths questions help

An open tank is to be made from a sheet of metal 84 cm by 40 cm by cutting congruent squares of side length x cm from each of the corners.
I've found the volume to be = (84-2x)(40-2x)(x)

State the maximal domain for V when it is considered as a function of x. Confused how to do this part
Any help would be appreciated

15. ## Re: VCE Maths questions help

Originally Posted by boredsatan
An open tank is to be made from a sheet of metal 84 cm by 40 cm by cutting congruent squares of side length x cm from each of the corners.
I've found the volume to be = (84-2x)(40-2x)(x)

State the maximal domain for V when it is considered as a function of x. Confused how to do this part
Any help would be appreciated
bump

16. ## Re: VCE Maths questions help

A rectangle is defined by vertices N and P(x,y) on the curve with equation y = 16-x^2 and vertices M and Q on the x axis
a.i. Find the area, A of the rectangle in terms of x
ii. state the implied domain for the function defined by the rule given in part i

17. ## Re: VCE Maths questions help

A metal worker is required to cut a circular cylinder from a solid sphere of radius 5 cm. Express r in terms of h, where r cm is the radius of the cylinder and h cm is the height of the cylinder. Hence show that the volume, V cm^3, of the cylinder is given by V = (1/4)(pi)(h)(100-h^2)

18. ## Re: VCE Maths questions help

n a tidal river, the time between high tides and low tides is 12 hours. The average depth of water at a point in the river is 5m. At high tide the depth is 8 m. Assume that the depth of the water, h(t) m, at this point is given by
h(t) = A sin(nt+e)+b, where t is the number of hours after noon. At noon there is a high tide.

a. find the values of A, n,b, and e

b. at what times is the depth of the water 6 m?

Bump

20. ## Re: VCE Maths questions help

A new TV lottery game consists of the random selection, with replacement, of 3 marbles from a barrel. The 3 marbles are drawn from a group of 8 identical marbles except for colour. 3 of the marbles are blue and 5 are yellow. If X represents the number of blue marbles in the sample of 3, complete the probability distribution for X. The above is a binomial distribution, would n be 3 or 8? (please give reasong as well) Thanks﻿
I'm really confused as to weather the sample size is 3 or 8, i checked the answer they said the sample size was 3, but I don't understand why

21. ## Re: VCE Maths questions help

Originally Posted by boredsatan
A new TV lottery game consists of the random selection, with replacement, of 3 marbles from a barrel. The 3 marbles are drawn from a group of 8 identical marbles except for colour. 3 of the marbles are blue and 5 are yellow. If X represents the number of blue marbles in the sample of 3, complete the probability distribution for X. The above is a binomial distribution, would n be 3 or 8? (please give reasong as well) Thanks﻿
I'm really confused as to weather the sample size is 3 or 8, i checked the answer they said the sample size was 3, but I don't understand why

bump

22. ## Re: VCE Maths questions help

Originally Posted by boredsatan
bump
marblesin the sample of 3

It gives you the answer in the question, how many marbles are being chosen is the sample size.

23. ## Re: VCE Maths questions help

Originally Posted by BLIT2014
marblesin the sample of 3

It gives you the answer in the question, how many marbles are being chosen is the sample size.
Thanks
Also, how do you tell if something is conditional?

The length of music pieces (in minutes) played daily on Classical FM from 12 noon is a continuous random
variable X with pdf given by
f(x) = 0.025e^(-0.025x), x>=0
0, elsewhere
a. Find the probability, correct to 4 decimal places, that the first piece played on Monday is shorter than 12
minutes.
b. Find the average length of a piece of music on Classical FM.
c. Rachel turns on her radio at a quarter past twelve and hears a familiar tune being played. What is the
probability, correct to 4 decimal places, that she is listening to the first piece played on Monday?

I know how to do part a and b, but how do we know if part c is conditionl or not?
Thanks again

24. ## Re: VCE Maths questions help

Originally Posted by boredsatan
Thanks
Also, how do you tell if something is conditional?

The length of music pieces (in minutes) played daily on Classical FM from 12 noon is a continuous random
variable X with pdf given by
f(x) = 0.025e^(-0.025x), x>=0
0, elsewhere
a. Find the probability, correct to 4 decimal places, that the first piece played on Monday is shorter than 12
minutes.
b. Find the average length of a piece of music on Classical FM.
c. Rachel turns on her radio at a quarter past twelve and hears a familiar tune being played. What is the
probability, correct to 4 decimal places, that she is listening to the first piece played on Monday?

I know how to do part a and b, but how do we know if part c is conditionl or not?
Thanks again
Bump

25. ## Re: VCE Maths questions help

Originally Posted by boredsatan
Bump
Bump!

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