VCE General & Further Maths Question Thread!

[Einstein]

Could someone please tell me how i would go about doing these questions

[Einstein]

please 

[Paulrus]

disclaimer, i haven't started geo and trig yet (going off year 11 knowledge here), so could be wrong
basically to find how far O is from the chord, you want to find the measurements of that triangle within the circle.
if the radius is 14cm, we know that the distance from A to O is 14cm. and chord AB is 4cm, but we only want half of that (from A to the middle). so we know the measurements of the triangle are 14cm and 4cm. using pythag, you calculate 14²-4², which gives you 180. the square root of 180 is 13.416407865, so the chord should be 13.42cm away from O.

i'm about to eat but i'll do the other ones and edit this post after i get back lol

[Duyyy11]

disclaimer, i haven't started geo and trig yet (going off year 11 knowledge here), so could be wrong
basically to find how far O is from the chord, you want to find the measurements of that triangle within the circle.
if the radius is 14cm, we know that the distance from A to O is 14cm. and chord AB is 4cm, but we only want half of that (from A to the middle). so we know the measurements of the triangle are 14cm and 4cm. using pythag, you calculate 14²-4², which gives you 180. the square root of 180 is 13.416407865, so the chord should be 13.42cm away from O.

i'm about to eat but i'll do the other ones and edit this post after i get back lol

So very very close!

You said yourself, we only want half of cord AB which is 4cm, therefore we want 2cm².

Therfore we have 14²-2² which equals 192. Square root 192 would give you 13.86 or 13.9 depending on the amount of decimals you want!

Hope I helped!

[Paulrus]

oh whoops, i really need to proofread my posts. yeah, that should have been 2², thank you for that

as for question 13 a:
i'm going to use a lot of decimal values for each number here just for the sake of being more accurate, hopefully it doesn't make it more confusing
your calculator tell you that 8 square root 2 is equivalent to 11.3137. you can find that out just by typing it into your calculator and pressing CTRL+Enter. that lets you split the square into two triangles with the diagonal of 11.3137 acting as the hypotenuse. we know that a²+b²=c², and because it's taken from a square we know that both a and b will be the same. so basically a²+b² will equal 11.3137², which is 127.99980769.
127.99980769 divided by 2 is 63.999903845, which is both our a² and b² cos they're the same. remember that we need to square root these to find the length of the sides, so we end up with 7.99999399031.

now we can put the triangles back together, and we're left with a square that has sides of 7.9999939901cm. we want to find the area of the square, which has the formula of length². so you take the value we found for the length of the side, and square it, which will give you 63.999903845. if you round up, that means the square will have an area of 64cm².

hopefully that helped! tbh i think i might have used more steps than necessary, but i looked over it and i'm pretty sure that should get you the right answer. i'm not sure which textbook you're using but if you check the answers section i think it should hopefully be right haha. using that you should be able to solve 13b as well, cos it's basically the same question. if this explanation is too confusing i can try rephrase some of it 

[Billion]

oh whoops, i really need to proofread my posts. yeah, that should have been 2², thank you for that

as for question 13 a:
i'm going to use a lot of decimal values for each number here just for the sake of being more accurate, hopefully it doesn't make it more confusing
your calculator tell you that 8 square root 2 is equivalent to 11.3137. you can find that out just by typing it into your calculator and pressing CTRL+Enter. that lets you split the square into two triangles with the diagonal of 11.3137 acting as the hypotenuse. we know that a²+b²=c², and because it's taken from a square we know that both a and b will be the same. so basically a²+b² will equal 11.3137², which is 127.99980769.
127.99980769 divided by 2 is 63.999903845, which is both our a² and b² cos they're the same. remember that we need to square root these to find the length of the sides, so we end up with 7.99999399031.

now we can put the triangles back together, and we're left with a square that has sides of 7.9999939901cm. we want to find the area of the square, which has the formula of length². so you take the value we found for the length of the side, and square it, which will give you 63.999903845. if you round up, that means the square will have an area of 64cm².

hopefully that helped! tbh i think i might have used more steps than necessary, but i looked over it and i'm pretty sure that should get you the right answer. i'm not sure which textbook you're using but if you check the answers section i think it should hopefully be right haha. using that you should be able to solve 13b as well, cos it's basically the same question. if this explanation is too confusing i can try rephrase some of it 

For Q 13 a and b, I think it's easier to use this method:
We know that the lengths of a square are equal, thus a diagonal cut would leave us with an isosceles triangle.
For part a), the diagonal length represents the hypotenuse, and we know that the hypotenuse is always sqrt(2) x one of the lengths of the sides.
That means that the two other sides must be 8 cm each.
Therefore you can figure out the area of the square by multiplying 8 by 8 = 64 cm squared. Or calculating the area of the triangle and doubling it. So half base x height will leave us with 4 x 8 = 32 cm squared, times 2 = 64 cm squared.

Part b) is essentially using the same concept.
We can use the above rule to find out the side lengths, however, I think it's easier to just use Pythagorean's theorem.
So we know that we have a square cut diagonally with the cut measuring 8 cm.
That means we're left right an isosceles right angled triangle.
From a² + b² = c²
We know that x² + x² = 8²
Therefore 2x² = 64
x² = 32
x = sqrt(32)

And to find the area of the square, it's simple l x w.
so sqrt(32) times sqrt(32) = 32 cm²
Hopefully I didn't make this more confusing, but I think that's how they're trying to make you work it out. Hope it helps.

[plato]

When doing transition matrices, how do you find initial state if it isn't given to you but the transition matrix is???

Here's the question attached:
Further Question Thread!

I assume you mean question 7.
Although you are not given an initial state matrix, you are told that there were 2800 birds nesting at site C in 2008.
The transition matrix states that 20% of these birds will nest at site A in 2009. This is the transition matrix element (1, 3)
So 20% of 2800 = 560 Answer A

[darklight]

When a question asks to 'plot' points, do you draw a line through the points or not?

[~V]

When a question asks to 'plot' points, do you draw a line through the points or not?

No, you literally only 'plot' points on the graph. When they ask eg.'add a line of best fit' or 'sketch linear regression line' then you draw a line through the points with the given equation or line of best fit by eye. Read the questions carefully and if they want to fit a line in, they'll tell you.

[Einstein]

could someone please help me with these two.

10 A and B
13A

Answers

10 A) 192 m2
10 B) 160 m3

13A) 892.70 cm2

im probably asking for too much , thanks to anyone who can help

[Billion]

Not sure how to explain it well, so I'll just show my working out I guess?

10 a)
First we'll do the bottom (shaded shape)
Front = 5x2 = 10. x2 because there's one at the back as well. 20.
Side = 2x10 = 20 x2 because there's one on the other side. 40.
Base = 5x10 = 50.
Now for the top.
Calculate the area of both triangles.
1/2 base x height. 0.5x3x4 = 6. x2 because there's 2 = 12.
Now the sides are both different.
So 4x10 = 40.
and 3x10 = 30.

Add them altogether; = 192 cm²

10 b) The volume of the bottom shaded area is 5x2x10 = 100cm³
The volume of the top is half base x height x length
1.5x4x10 = 50cm³

Add them both together = 160cm³

13a) Hopefully you can bear with me here.
We'll do the top first (half cylinder).
The area of both the front and back semi-cirlces add to equal just a normal circle.
So pi*r² = pix5² = 78.54
Now for the half round shape around the cylinder;
We need the circumference (2*pi*r) of the circle x the length and then divide by 2, since it's only half.
so 2 x pi x 5 x 20 = ..., then divide this answer by 2.
= 314.16
Now for the bottom shaded area.
10x5x2 = 100 (both front and back)
5x20x2 = 200 (both sides)
10x20 = 200 (base)

Add them altogether = 892.70 cm³

Hope this helps.

[Einstein]

Thanks very much

[Einstein]

With 10a, how did you get a base of 3?

and with 10b, how did you get 1.5 x 4 x 10. if its half base x height.

Thanks

[Billion]

For 10a, If you look at the triangles tilting your head right, you can see that 3 becomes the base and 4 is now the height.
We have to do this because we are unable to calculate the other side of the triangle because we don't know if it's a right angled triangle (even though it looks like one), so we can't be sure that Pythagorean's theorem can be used.

10b,  The volume is half base x height x length.
The area is only half base x height.
So using 3 as the base of the triangle again, halving it gives us 1.5
Now we times this by the height (4), then again by the length (10.

[Einstein]

alright, thanks for that

still unsurehow 3 is base when i tilt my head to the right. to see from right hand side view