2u Mathematics Marathon v1.0 (1 Viewer)

[B35tY]

It's solving the equation sin²3@ - sin²@ = sin2@ for the range 0 < x < pi, not proving it

Ah, of course.

 

[zeek]

Show that 1-1=0

Hence, give the result of 0/0 and explain why.

 

[zeek]

lol wat r u talking about?
prove it

 

[drynxz]

well whats wrong with this proof ?

first..let a=b
1) ab=a^2
2) ab-b^2=a^2-b^2
3) b(a-b)=(a+b)(a-b)
4) b=a+b
5) b=2b
6) 1=2.

which line has a error and why...?

 

[Riviet]

Yeah, try to stick to questions that aren't too fundamental ie are potential questions in the 2u HSC.

LottoX was on a bit of a roll tonight in terms of jokes. See my sig for more details.

 

[Riviet]

well whats wrong with this proof ?

first..let a=b
1) ab=a^2
2) ab-b^2=a^2-b^2
3) b(a-b)=(a+b)(a-b)
4) b=a+b
5) b=2b
6) 1=2.

which line has a error and why...?

Dividing by zero from line 3 to 4: a=b <=> a-b=0

 

[SoulSearcher]

well whats wrong with this proof ?

first..let a=b
1) ab=a^2
2) ab-b^2=a^2-b^2
3) b(a-b)=(a+b)(a-b)
4) b=a+b
5) b=2b
6) 1=2.

which line has a error and why...?

That's some nice illegal maths there, unfortunately Riviet's question still needs answering

 

[Riviet]

For everyone's convenience of not having to go back to the previous page:

Next Question:

In a complex pulley system, the length of rope L needed for operation and the distance x m from a specific pulley to the centre of the system is defined by:

L=(x²-20x+136)^1/2 + (x²+64)^1/2

Find the distance x m that the pulley should be from the centre of the system that minimises the length of rope required.

 

[SoulSearcher]

50 posts per page ftw

 

[Riviet]

50 posts per page ftw

I tried that for a day once. Felt like too much overloaded in a page so I switched back to default. Okay, no more spam please (unless you're posting to answer a question), otherwise I'll have to bump my question to the next page.

 

[Aaron06]

For everyone's convenience of not having to go back to the previous page:

Next Question:

In a complex pulley system, the length of rope L needed for operation and the distance x m from a specific pulley to the centre of the system is defined by:

L=(x²-20x+136)^1/2 + (x²+64)^1/2

Find the distance x m that the pulley should be from the centre of the system that minimises the length of rope required.

Spoiler

M + x = (x²-20x+136)^1/2 + (x²+64)^1/2

M = (x²-20x+136)^1/2 + (x²+64)^1/2 - x

For distance (lets just put the x for distance n haha )

N² = {sqrt (x² - 20x + 136)² + sqrt ( x² + 64)² } - x²

= x² - 20x + 136 + x² + 64 - x²

= 2x² - 20x + 200 m

thus distance that the pulley should be from the centre of the system that minimises the length of rope is equal to = 2x² - 20x + 200 m

Ah, I think that is right. Is it?
I didn't quite understand the question though. =P
Thats my excuse if I got it wrong. Lol
A complex pully could look like anything.
Haha

 

[Riviet]

Hint:

Spoiler

Differentiate and hence find the minimum value of x.

 

[Affinity]

A simple (doesn't work) population model assume that the change of population has four components, reproduction, death, emigrating abroad, and people coming from other places. Births and deaths and the number of people moving abroad is assume to be proportional to the population at any instant, but immigrants come in at a constant rate.

This model can be represented by the equation:

dP/dt = (B - D - E)*P + I

where B, D, E are certain constants to be determined.

a) Verify dP/dt = d/dt (P + I/(B-D-E))
b) let Q = P + I/(B-D-E), what is dQ/dt
c) solve for P as a function of t. leave your answer in terms of I,B,D,E and P(0) the initial population

hint: if you work through it step by step, it's easy.

 

[Affinity]

Stephen has a loan of 100,000.00 to pay. each month, interest of 0.8% is charged on the outstanding amount
a) If stephen pays 5,000 each month starting one month from now how long will it take him to repay the loan?
b) Now suppose stephen pays different amounts every months, but according to the rule that for every dollar of the balance, he'll pay eight cents, so he'll pay more initially, but less later. Find the outstanding amount after the n-th payment

 

[Affinity]

With a fair coin, what is the probability of having a run of Head,Head,Tails (in that order) with 5 tosses? assuming tosses are independent.

(out of scope can you generalise this to n tosses?

 

[fishy89sg]

find x.

 

[SoulSearcher]

Ok, there are 4 questions there for people to solve

 

[Riviet]

If no one gets my pulley question, I'll post up the solution in a few days.

 

[PC]

Differentiate L with respect to x:

dL/dx = [(x-10)√(x²+64) + x√(x²-20x+136)] / [√(x²-20x+136)√(x²+64)]

Make dL/dx = 0:
So numerator = 0, left addend to RHS, then square both sides.
x = 40 or 40/7.

Now verify solutions:
When x = 40, L = 71.386
When x = 40/7, L = 17.204

Therefore values of L is minimum when x = 40/7 = 5 5/7 = 5.714ish.

 

[snowbunny]

Stephen has a loan of 100,000.00 to pay. each month, interest of 0.8% is charged on the outstanding amount
a) If stephen pays 5,000 each month starting one month from now how long will it take him to repay the loan?
b) Now suppose stephen pays different amounts every months, but according to the rule that for every dollar of the balance, he'll pay eight cents, so he'll pay more initially, but less later. Find the outstanding amount after the n-th payment

i dont really know how i would write the answer/cant be bothered coz of all the working but my answers are:

a) takes him 22months to pay back?

b) i dont really understand this part...