2u Mathematics Marathon v1.0 (1 Viewer)

[YBK]

Spoiler

5 (x^2 - 4x/5 - 2/5) = 0
x^2 - 4x/5 - 2/5 = 0

(x - 4/10) ^ 2 - 0.56 = 0
(x - 4/10) ^ 2 = 0.56
x - 4/10 = √0.56
x = +-√0.56 + 4/10

Edit: wait, no ... I'm right!! WOOOOOOO !

 

[Jono_2007]

Why do you divide by 5, aknowledge by post above and tell be what is wrong with it.

 

[SoulSearcher]

This is what i was told;
1)remove any constant to the RHS of the equation.
2)Note the coefficient of x, and follow the rule
"Half IT",
"Square IT",
and "add it to BOTH sides".
3)Rewrite the LHS as a perfect square and siplify the RHS.
4)Take the square root of both sides.
5)solve for x

what they forgot here was the step between 1 and 2

if the coefficient of x² is not 1, then make it 1

other than that, thats about how you are supposed to do these questions

 

[Riviet]

SoulSearcher, insert-username, and YBK's last answers are all correct. Nice use of decimal there YBK.

SoulSearcher, since you got the right answer first, you can post the next question.

 

[Jono_2007]

where did the 14 come from!

 

[insert-username]

Why do you divide by 5, aknowledge by post above and tell be what is wrong with it.

When you're completing the square, you're essentially using x² + 2xy + y² = (x+y)². Because of this, the coefficient of x² must be 1.

where did the 14 come from!

4/25 + 10/25 = 14/25.


I_F

 

[insert-username]

But still how did u guys get 14 and you 14/25

Not the /5 at the end of my answer. That's divided by 5.

2/5 + 4/25 = 14/25. Square root of 14/25 = √14/5

EDIT: Thanks for deleting your post and making me look silly.


I_F

 

[Jono_2007]

sorry to all of you, my mistake, i came home from work at 8:00pm and haven't recovered fully yet, very busy.

 

[SoulSearcher]

ahh ok then

lets see here .. ok then next question:

A radioactive substance is decaying at a rate proportional to its mass. Its mass initially is measured at 37.4 grams. Twelve hours later the mass is measured at 31.7 grams. Find:

(i) the decay constant
(ii) the half-life of the substance

 

[YBK]

How ahead are you guys!!!
we still havent done that stuff

 

[Jono_2007]

Is this direct variation.

 

[Riviet]

where did the 14 come from!

56/100 = 14/25, which comes from 2/5+(4/10)²

 

[Riviet]

Is this direct variation.

It's exponential decay. This topic is usually done around the second half of year 11. Even my school hasn't done it yet. XD

 

[insert-username]

Is this direct variation.

No. This is exponential growth and decay - half life is not a direct decay of particles. But jeez, this question's still way ahead for me...

EDIT: Riviet beat me... I'm really slow tonight.


I_F

 

[SoulSearcher]

How ahead are you guys!!!
we still havent done that stuff

i actually did the HSC course for 2 unit maths this year and sat the HSC exam as well

 

[Riviet]

i actually did the HSC course for 2 unit maths this year and sat the HSC exam as well

Wow, you accelerated... what mark did you get for it?

 

[Jono_2007]

This is dN/dt=k(N-P) and it is a extension 1 topic at my school.
the solution to this equation is N=Ce^k-P or something...

 

[SoulSearcher]

Wow, you accelerated... what mark did you get for it?

got 95 HSC exam mark, 96 assessment mark, 96 total HSC mark

 

[Jono_2007]

A=A₀e^kt is the solution to this question but i dont know how to use the formula

 

[Riviet]

got 95 HSC exam mark, 96 assessment mark, 96 total HSC mark

Congratulations! You must know your basics well then! Go for 4 unit!