VCE Methods Question Thread!

[Planck's constant]

Hardest Methods Trial Exam

[Eugenet17]

f: [-pi,2pi] --> R, f(x) = 3/2sin(2x/3)

Can someone help me sketch this graph please? The one i did was different to the answer :<

[fleet street]

Because of the 3/2 in the front, amplitude = 3/2, so your turning points will have y-coordinates 3/2 or -3/2
Period =
So, x-intercepts are and
Maximum turning point at
Minimum turning point at
Endpoints:
And:
If you haven't seen what it looks like yet, then put it into your CAS and you should be able to see it there.

[aestheticatar]

Help would be great!

Thanks in advance

[SocialRhubarb]

Use linear approximation formula.

That is, .

[09Ti08]

A. is approximately
h=xtan(a)

Now notice that alpha is measured in degrees, we want dh/da, but the formula that we get d(tanx)/dx=sec^2(x) works for radians only, so we have to convert alpha degrees into a*pi/180 radians
So dh/da=sec^2(a)*pi*x/180. Use chain rule here if you're confused
Finally, multiply this by delta a and you're done

B. i think you can do this.
C. Just plug in x=50 and delta a=0.02 and you'll get what you need.

[zvezda]

Hey,
How would i got about finding the variance of a prob dens. function whose rule is a modulus expression? Say, for example, if the rule is |1/9(3-x)|, how would i find the variance?
Cheers

[lzxnl]

Hey,
How would i got about finding the variance of a prob dens. function whose rule is a modulus expression? Say, for example, if the rule is |1/9(3-x)|, how would i find the variance?
Cheers

I'm assuming the 3-x is in the numerator.

For this, split the function into two parts for x>=3 and x<3. Then compute the integral.

[zvezda]

I'm assuming the 3-x is in the numerator.

For this, split the function into two parts for x>=3 and x<3. Then compute the integral.

Yeah sorry i should havw cleared that up. Yeah i did that however i got the wrong answer. I might need to re-check my working then. Thanks

[Essendon2013]

The equation of the graph is y = A sin (Bx + C). Find the values of A, B and C.

I have found A very easily, can't seem to find B & C.

I have attached a file that has a rough sketch of the graph.

Help would be greatly appreciated!

[b^3]

Pick the value that orients the curve the right way up, since our curve is a shift of units in the negative direction from the standard sine curve, we will take (remember shift left is positive, also you could just get this last part from looking at the graph and noticing the shift).

[Essendon2013]

Pick the value that orients the curve the right way up, since our curve is a shift of units in the negative direction from the standard sine curve, we will take (remember shift left is positive, also you could just get this last part from looking at the graph and noticing the shift).

Thanks so much! The thing I was doing wrong was excluding the 1/2. Can I ask why the 1/2 must be included?

[b^3]

The section of the curve shown only covers half the period of the function. Remember, the period of the function will correspond to how long it takes for the function to go through one complete cycle and get back to it's starting point. In this case our function only goes through half of this (because we don't see the whole curve in the image above).
The whole curve looks like the below.

I.e. The lines show half the period and a whole period.

[JieSun92]

Anyone please help me with part b) ii of this question. I'm so confused 

[09Ti08]

I think that's a typo.
h=0???
Now I think the real problem is the value of h 
From the answer at the back of essential, I got the value of h as approximately 10 cm.