VCE Specialist 3/4 Question Thread!

[Planck's constant]

In the storeroom of a fruit shop there were two boxes of apples, one of Golden Delicious and the other of Jonathons, which were to be sold at $2.80 and$3.50/kg, respectively. The apples were accidentally mixed together and, instead of sorting them out, the owner decides to sell them as they were. So as not to make  a loss, he sold the mixed apples at $3.10/kg. How many kilograms of each type of apple were there if together they weighed 35kg in total?

thanks..

Let G be the original quantity of Golden Delicious apples [Kg]
Let J be the original quantity of Jonathon apples [Kg]

J + G = 35   (1)

2.80*G + 3.50*J = 3.10*(J + G)     (2)

[Mr. Study]

since we don't know what F3 is, let's assign the variable x and y to describe it

so let F3 = xi + yj

we know that the resultant force, F1 + F2 + F3 = 0
So:
13i -5j - 4i + 9j + xi +yj = 0
9i + 4j + xi + yj = 0
(9 + x)i + (4+y)j = 0

so 9 + x and 4 + y both have to equal 0
so x = -9 and y = -4
now we can sub these values back into F3 = xi + yj
F3 = -9i - 4j

You had already done most of the work when you found the resultant force of F1 and F2 to equal 9i + 4j, F3 just had to be a vector that cancelled them out to equal 0 when added together, so straight away you can tell from that that F3 needed to equal -9i -4j

Ah! That makes sense!

Thank you.

[powerrrr]

I received my specialist sac marks last week and I just passed. 51%. This is terrble relative to other students. Have I already failed this course?

I've lost hope for a good SS.

[abd123]

I received my specialist sac marks last week and I just passed. 51%. This is terrble relative to other students. Have I already failed this course?

I've lost hope for a good SS.

Naaah man, theres still a few more sacs that can make up your 51%.

It seems like an average score in spesh, after all spesh is one of the hardest subjects in school.

Anyways good luck, my brotheren.

[domislong]

Hey I'm doing a spec-type unit at uni, mostly Methods revision at the moment, but I can't quite figure this question out. It asks to find values of x for which g(x) is positive, g(x) = (2x^2-1)/(x^2+6x-7).

I've already solved for the inequality g(x) > 0, but after looking at a graph that appears to be only a partial solution, I only found g(x) between the vertical asymptotes.

My question is, how can I find these x values analytically, i.e. without a graph? It is a multi-part question with asymptotes, limits and intercepts asked in later questions so I assume I can't use those.

[TrueTears]

Solve 2 cases:

1. 2x^2-1 > 0 and x^2+6x-7>0

2. 2x^2-1 < 0 and x^2+6x-7<0

[domislong]

Ah because the equation will be positive if numerator and denominator are both +ve or -ve., so simple yet I couldn't think of it!

Thanks TT

[Dominatorrr]

OK, probably a very easy question but I forgot how to do it.

If tan(y)=5/12 y=[pi,3pi/2] how do you figure out tan(2y)?

[Dominatorrr]

Never mind, I got it, double angle formulas.

[Mr. Study]

Two vector questions that are doing my head in.

a=3i-6j+4k and b=2i+j-2k.
a) Find c, the vector component of a perpendicular to b

If I can understand how to get part a), I can do the rest of the question.

a=2I+3j-4k and b=2i-j+2k. c=2i+(1+3t)j+(-1+2t)k.
b) Find the values of t for which angle BCA=90 degrees

This is what I have so far:
CA=(2-3t)i+(-3-2t)k
CB=(-2-3t)j+(3-2t)k.

I'm guess we have to use the costheta=a.b/|a||b|. But I know the formula 'works' for two vectors, not the position vectors, and I guess we would use CA and CB. However, I did that and obtained a loooong quartic and I guess I did something wrong.

Could someone show me what I should be doing?

(Sorry for not putting it in LaTeX).

[generalkorn12]

Could anyone explain differential equations the 'k' value and the 'a' value?

Thanks.

[Greatness]

Two vector questions that are doing my head in.

a=3i-6j+4k and b=2i+j-2k.
a) Find c, the vector component of a perpendicular to b

If I can understand how to get part a), I can do the rest of the question.

a=2I+3j-4k and b=2i-j+2k. c=2i+(1+3t)j+(-1+2t)k.
b) Find the values of t for which angle BCA=90 degrees

This is what I have so far:
CA=(2-3t)i+(-3-2t)k
CB=(-2-3t)j+(3-2t)k.

I'm guess we have to use the costheta=a.b/|a||b|. But I know the formula 'works' for two vectors, not the position vectors, and I guess we would use CA and CB. However, I did that and obtained a loooong quartic and I guess I did something wrong.

Could someone show me what I should be doing?

(Sorry for not putting it in LaTeX).

90 degrees = perpendicular, so use dot product = 0 and solve for t. Or is that too simple.... lol

[Dominatorrr]

If sin(A)=1/sqrt(5) and A=[0,pi/2] then how do you workout sin(3A)?

[pi]

Use double angle formulas to get sin(2A) and then use sin(2A + A) to find sin(3A) N.B. you can find cos(A) by drawing a triangle and using Pythagoras' theorem.


(I would solve it but I don't remember the relevant formulas lol)

[Mr. Study]

Two vector questions that are doing my head in.

a=3i-6j+4k and b=2i+j-2k.
a) Find c, the vector component of a perpendicular to b

If I can understand how to get part a), I can do the rest of the question.

a=2I+3j-4k and b=2i-j+2k. c=2i+(1+3t)j+(-1+2t)k.
b) Find the values of t for which angle BCA=90 degrees

This is what I have so far:
CA=(2-3t)i+(-3-2t)k
CB=(-2-3t)j+(3-2t)k.

I'm guess we have to use the costheta=a.b/|a||b|. But I know the formula 'works' for two vectors, not the position vectors, and I guess we would use CA and CB. However, I did that and obtained a loooong quartic and I guess I did something wrong.

Could someone show me what I should be doing?

(Sorry for not putting it in LaTeX).

90 degrees = perpendicular, so use dot product = 0 and solve for t. Or is that too simple.... lol

I did that but doesn't a dot product give only a magnitude and no direction.

This is referring to Question 1, so If I did a.b is would be -8 but what would I do with the -8? :S