VCE Methods Question Thread!

[silverpixeli]

TY SO MUCH I GET IT NOW! what is the likelihood of this popping up on an exam and has it before?

the identity is DEFINITELY something you should think of trying whenever you see a cos or sin squared, it can often simplify stuff (though obviously not always). That has been on exams plenty of times and it's just a cool and useful trig trick to have under your belt.

As for this specific trig question, I don't remember it from any exams, and it is harder than the usual methods exam trig equation. But that doesn't mean it will never be on an exam!

[knightrider]

For the question attached?

How would you do part b?

my working out was.









but the answer says time= 4hours.

Who is right?

[keltingmeith]

TY SO MUCH I GET IT NOW! what is the likelihood of this popping up on an exam and has it before?

Adding to silverpixelli, the "identify it's a quadratic" part will DEFINITELY be on your exam (and if it's not, this is the first time since 2011 [that I remember - might have even been on 2010] that it isn't) - VCAA love it.

For the question attached?

How would you do part b?

my working out was.









but the answer says time= 4hours.

Who is right?

The book - you've added extra segments. Try:

time = 2/3 + (14/3-10/3) + (26/3-22/3) + (12-34/3)

Note your answer also has the extra 22/3 -14/3 (which you can see defeats the point of having 14/3-10/3 and 26/3-22/3!)

[knightrider]

The book - you've added extra segments. Try:

time = 2/3 + (14/3-10/3) + (26/3-22/3) + (12-34/3)

Note your answer also has the extra 22/3 -14/3 (which you can see defeats the point of having 14/3-10/3 and 26/3-22/3!)

Thanks EulerFan101 

[knightrider]

For the picture attached.

say you want to find the equation which gives the volume of water that has flowed into the system.

When antideriving you get the c  constant on the end.

What other point can you use from the information given to find what c is ?

[qwerty101]

could someone walk em through what they have done here. I get the solve for x in terms of m with the use of quadratic formula, but not what they have done with x = m/2. I would;ve thought the discrim = 0 would be used somewhere, but dont see it.

[cosine]

For the picture attached.

say you want to find the equation which gives the volume of water that has flowed into the system.

When antideriving you get the c  constant on the end.

What other point can you use from the information given to find what c is ?

When nothing is initially given, and you are required to solve, you can usually take t=0 and V=0. This is because we assume that there is no water in the system before hand, and so at t=0 minutes, the Volume of water is also 0.

[keltingmeith]

could someone walk em through what they have done here. I get the solve for x in terms of m with the use of quadratic formula, but not what they have done with x = m/2. I would;ve thought the discrim = 0 would be used somewhere, but dont see it.

Note that the quadratic formula can be written in the form:



Where is the discriminant. So, if the equation has one solution, then:



reduces to:



Since only having one solution implies that the discriminant is 0. So, this gives us the final answer m/2

[I_I]

Hello guys!
I am struggling with a related rates question and I was hoping if you could help
Just to note: I can feel it in my bones that this question will be in my calculus sac on Monday (our theme is GYM so baseball, swimming, soccer etc.) and this is a swimming pool question.
So, please help!

[wunderkind52]

Hello guys!
I am struggling with a related rates question and I was hoping if you could help
Just to note: I can feel it in my bones that this question will be in my calculus sac on Monday (our theme is GYM so baseball, swimming, soccer etc.) and this is a swimming pool question.
So, please help!

From what I can see - it's asking for the rate when the depth is 5ft. Which, as you can see, lies in the trapezium section, so you can essentially ignore the rectangular part.
Now, it's a prism, so the volume is base area*height, or in this case area-of-trapezium*width.
Area of a trapezium is A=0.5(a+b)h, and therefore V=20*0.5(a+b)h.
Find a and b in terms of h (split the trapezoidal prism into triangles and rectangles and use similar triangles)
here, you can find dV/dh, and you already have dV/dt, and you should be able to find dh/dt.

[knightrider]

When nothing is initially given, and you are required to solve, you can usually take t=0 and V=0. This is because we assume that there is no water in the system before hand, and so at t=0 minutes, the Volume of water is also 0.

Thanks cosine 

[qwerty101]

would like some help on these questions please!

[qwerty101]

the dh/dv is from part c. But for the dv/dt, why isnt it -1/32 ? its being poured out of the first cone into the second one, and they want to find the rate of change of depth (height) in the first one, which will be decreasing over time? so why the positive 1/32 ?

[I_I]

Hello

I was hoping you could help me on related rates. I have attached question, the actual answer and the answer I got.

Please help!

[cosine]

Hello

I was hoping you could help me on related rates. I have attached question, the actual answer and the answer I got.

Please help!

Using similar triangles, we have

Transpose to make r the subject:



Plug this into your formula for the volume, and then differentiate it with respect to height:









I have no idea what to do next