Prelim 2016 Maths Help Thread (1 Viewer)

[davidgoes4wce]

Can someone show the steps for solving these questions... I am not getting these:
View attachment 33231

I answered those questions in this thread:

http://community.boredofstudies.org...unit-cambridge-question-answer-thread-52.html

 

[davidgoes4wce]

Also how do I sketch the following inverse functions

1. y=2-e^x

To determine the inverse function

 

[davidgoes4wce]

Also how do I sketch the following inverse functions


2. y=sinx

 

[davidgoes4wce]

Q:

Two model rockets launched from two different launch pads G & D. From an observation site, O, rocket A has been launched at N28 degrees WEST and rocket B has been luanched at N40 degrees EAST. The angle of elevation from the observation location is 29 degrees for rocket A and 37 degrees for rocket B. If the distance between the observation site and launch pad G is 120m and the distance from observation site to a launch pad D is 80m, what is the distance between the two rockets AFTER THE LAUNCH.

Do you have an answer I just want to compare my answer?

 

[davidgoes4wce]

Also how do I sketch the following inverse functions


3. y=cos2x, 0≤x≤π/2

Here is my graph:

 

[InteGrand]

At the HSC level (since you don't know what a codomain is yet) a function is one-to-one iff every one value of x carries only ONE value for y.

If x and y happen to equal to the same thing that means jack shit. It's that for every x-value, there can be at most one y-value.

If x=0 then y=0 and y=1 SIMULTANEOUSLY then it's no longer one-to-one

This is essentially referring to the definition of a function (no input has more than two outputs).

For one-to-one, it's basically reverse: every y-value in the range has one and only one x-value in the domain. Or equivalently, we don't have two different x-values getting mapped to the same y-value.

For eyeseeyou's one, since no two different x-values map to the same y-value (as all the y-values are different), it's one-to-one.

 

[eyeseeyou]

Thanks for the help guys

Was greatly appreciated

 

[eyeseeyou]

Q:

Two model rockets launched from two different launch pads G & D. From an observation site, O, rocket A has been launched at N28 degrees WEST and rocket B has been luanched at N40 degrees EAST. The angle of elevation from the observation location is 29 degrees for rocket A and 37 degrees for rocket B. If the distance between the observation site and launch pad G is 120m and the distance from observation site to a launch pad D is 80m, what is the distance between the two rockets AFTER THE LAUNCH.

Unfortunately I do not. I got it from yahoo answers

 

[eyeseeyou]

Might post some more inverse function Q's later tonight and tomorrow morning

 

[eyeseeyou]

Can someone please help me with Induction (maths). I really suck at it

1. 1+2+3+...+n=(n(n+1))/2
2. 1/(x^n(x-1)=1/(x-1)-1/x-1/x^2-...-1/x^n

 

[InteGrand]

Can someone please help me with Induction (maths). I really suck at it

1. 1+2+3+...+n=(n(n+1))/2
2. 1/(x^n(x-1)=1/(x-1)-1/x-1/x^2-...-1/x^n

 

[eyeseeyou]

Not much

Tried it but always trip up on the 3rd step of induction

 

[eyeseeyou]

3. 1^2+3^2+5^2+...+(2n-1)^2=((n(4n^2-1)/3)
4. 1.1!+2.2!+3.3!+...+n.n!=(n+1)!-1

 

[InteGrand]

 

[eyeseeyou]

Could you do an example?

 

[InteGrand]

Could you do an example?

I pretty much did in that post. Just simplify that to show that it equals (k+1)*((k+1)+1)/2.

 

[eyeseeyou]

The steps i follow are

1. Show true for n=1 (or whenever it starts)
2. Assume true for n=k
3. Show true for n=k+1 (this step always annoys me) Always involve assumption
4. Conclusion

Using my 4 steps could you please help me

 

[InteGrand]

The steps i follow are

1. Show true for n=1 (or whenever it starts)
2. Assume true for n=k
3. Show true for n=k+1 (this step always annoys me) Always involve assumption
4. Conclusion

Using my 4 steps could you please help me

All the steps are trivial here apart from 3. And I already helped you with 3.

 

[eyeseeyou]

All the steps are trivial here apart from 3. And I already helped you with 3.

Yeah I think I know ths jist of things now

Anyways thanks

BTW when you answer my "why" science questions (phys and chem) could you please not say "By inspection" because it really annoys me. This is like...showing you have no pure knowledge to phys/chem at all

 

[InteGrand]

Yeah I think I know ths jist of things now

Anyways thanks

BTW when you answer my "why" science questions (phys and chem) could you please not say "By inspection" because it really annoys me. This is like...showing you have no pure knowledge to phys/chem at all

You're welcome.