# Thread: VCE Maths questions help

1. ## Re: VCE Maths questions help Originally Posted by InteGrand Answer to your last question: yes.

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

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.  Reply With Quote

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  Reply With Quote

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  Reply With Quote

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  Reply With Quote

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?  Reply With Quote

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  Reply With Quote

8. ## Re: VCE Maths questions help

Bump
Can somebody PLEASE ANSWER all my questions above?  Reply With Quote

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 .

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.

.

When we go in the positive direction, the first angle for which is .

So that means that when we go in the negative direction, the first angle for which is .

But is outside the range of , so it's not a solution to the equation.  Reply With Quote

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 is . So,

Also, . So, 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  Reply With Quote

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)  Reply With Quote

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   Reply With Quote

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 with and to shift it right you would replace with , in that order.

Dilate:

Shift graph: 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

Reflect across x axis:

Dilate:  Reply With Quote

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  Reply With Quote

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  Reply With Quote

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

Can someone please help me with this?  Reply With Quote

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)  Reply With Quote

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?  Reply With Quote

19. ## Re: VCE Maths questions help

Bump
Can somebody PLEASE ANSWER all my questions above?  Reply With Quote

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  Reply With Quote

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  Reply With Quote

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.  Reply With Quote

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  Reply With Quote

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  Reply With Quote

25. ## Re: VCE Maths questions help Originally Posted by boredsatan Bump
Bump!  Reply With Quote

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