VCE Methods Question Thread!

[Bhootnike]

I'd imagine so since you end up with the same values for x as you would if the 3 wasnt there!

[ashoni]

Hey just stuck on a question guys! show working out please

8 A herbalist wishes to prepare a mixture from two herbs, A and B. The mixture costs
$6 per kilogram. If herb A costs $5 per kilogram and herb B costs $8 per kilogram and
60 kilograms of the mixture is to be prepared, how many kilograms of each herb should be
used?

answer is A = 40 ; B = 20

[IndefatigableLover]

The total cost of the mixture will be 60kg x $6=$360

Let's say 'x' represents the number of kilograms of Herb A used so the number of kg Herb B will be (60-x)

Since it's $5 for Herb A, and $8 for Herb B, our equation is:

5x + 8(60-x)=360
5x+480-8x=360
-3x=-120
x=40

Therefore A=40 and sub in 40 into Herb B to get:

A=40;B=20

[ashoni]

ohhh alright cool! thanks for your help Henry!

[IndefatigableLover]

ohhh alright cool! thanks for your help IndefatigableLover!

No problems

[ashoni]

hey again, today i got a question on a methods sat... still kind of remember it so i'll try to get all the info i have...
anyways!

The question was like the moons orbit around the earth is given as the function x^2+y^2=360000^2 where the earth is situated at the centre, which is obviously (0,0). Then there was a hyperbolic function representing the path of an asteroid which was y=2000000/x with a restricted domain of [0, infinity) . Then there was a scale factor of 10000 so the numbers would be reasonable to work with i.e equations would be x^2+y^2=36^2 and y=200/x respectively.

Alright so the real question was, Bruce Willis (lol this was actually in the sat) was given the task of protecting Earth (again lol) and he had to find when the asteroid is closest to Earth (also hinted to use symmetry). So find when the asteroid is closest to the Earth which is at (0,0). Then the next question was like how far in kilometres would this asteroid be.

hope i gave you guys enough information, if it's too confusing i'll wait to get my paper back and ill send the actual question!
thanks!

[Phy124]

hey again, today i got a question on a methods sat... still kind of remember it so i'll try to get all the info i have...
anyways!

The question was like the moons orbit around the earth is given as the function x^2+y^2=360000^2 where the earth is situated at the centre, which is obviously (0,0). Then there was a hyperbolic function representing the path of an asteroid which was y=2000000/x with a restricted domain of [0, infinity) . Then there was a scale factor of 10000 so the numbers would be reasonable to work with i.e equations would be x^2+y^2=36^2 and y=200/x respectively.

Alright so the real question was, Bruce Willis (lol this was actually in the sat) was given the task of protecting Earth (again lol) and he had to find when the asteroid is closest to Earth (also hinted to use symmetry). So find when the asteroid is closest to the Earth which is at (0,0). Then the next question was like how far in kilometres would this asteroid be.

hope i gave you guys enough information, if it's too confusing i'll wait to get my paper back and ill send the actual question!
thanks!

If I've interpreted this correctly, you are trying to find the point at which is closest to the origin .

This will occur at the intersection between the graphs and







But as the graph of is restricted to positive values we are left with



To find the distance from the origin we need to use and such also need the y-value of this coordinate



Thus;





I assume that the moons orbit is 360000 km.

Therefore using the scale factor

[ashoni]

hey again, today i got a question on a methods sat... still kind of remember it so i'll try to get all the info i have...
anyways!

The question was like the moons orbit around the earth is given as the function x^2+y^2=360000^2 where the earth is situated at the centre, which is obviously (0,0). Then there was a hyperbolic function representing the path of an asteroid which was y=2000000/x with a restricted domain of [0, infinity) . Then there was a scale factor of 10000 so the numbers would be reasonable to work with i.e equations would be x^2+y^2=36^2 and y=200/x respectively.

Alright so the real question was, Bruce Willis (lol this was actually in the sat) was given the task of protecting Earth (again lol) and he had to find when the asteroid is closest to Earth (also hinted to use symmetry). So find when the asteroid is closest to the Earth which is at (0,0). Then the next question was like how far in kilometres would this asteroid be.

hope i gave you guys enough information, if it's too confusing i'll wait to get my paper back and ill send the actual question!
thanks!

If I've interpreted this correctly, you are trying to find the point at which is closest to the origin .

This will occur at the intersection between the graphs and







But as the graph of is restricted to positive values we are left with



To find the distance from the origin we need to use and such also need the y-value of this coordinate



Thus;





I assume that the moons orbit is 360000 km.

Therefore using the scale factor

that looks pretty right to me! thanks heaps! abit too late now though wish i knew this during the sat....

[ligands]

quick question about linear approximation

with f(x)= using f(x+h) = f(x) + hf'(x) find an approximation for correct to 5 decimal places

thanks

[TrueTears]

[ligands]

thank you truetears

[depressedchild]

so the formula is 20sin(pi times t /6)=25 where t is the number of hours after 7 am
this formula is the distance from water to the sand dune

from the tip of my head, the question asked if a girl left her sandals 6 m away from the sand dune, will her sandals get wet and if so what time?

the other question was when and where can she leave her sandals so it doesn't get wet

please help me, this question is related to my SAC and I'm struggling in methods

[#1procrastinator]

1) In the Essential book, it says for the composition of g with f to be defined, the range of has to be a proper subset of the domain of g. Does this mean that the range has to be a subset of the domain of g but it can't EQUAL the domain of g?

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2) Let a be a positive number, let f: [2, infinity) -> R, f(x) = a-x and g: (-infinity, 1] -> R, g(x) = x^2+a. Find all values of a for which f o g and g o f both exist.

I got the correct answer but not after three tries and I'm looking for a more systemic way of doing it. The way I did it involved a bit of guessing and plugging in different numbers to check.

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3) For f: (-infinity, 2] -> R, f(x) = (x-2)^2

To find the inverse, how do you know to take the negative square root? Is the only way to tell just to look at the domain of f and hopefully realise that it must be the negative root to have as its range?

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4) Why is the horizontal translation in y=2^(-x+2) two units to the right and not left?

[ashoni]

Simplify
(x - 1)^(1/2) - x/(x - 1)^(1/2)

[ligands]

Simplify
(x - 1)^(1/2) - x/(x - 1)^(1/2)