HSC 2012 Maths Marathon (archive) (1 Viewer)

SpiralFlex · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Go Go Go Mathletes!

Timske · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

a^3+b^3+a+b
= (a^3+b^3) + (a+b)
= (a + b)(a^2 -ab + b^2)+(a+b) - factor (a + b) out

= (a+b)(a^2 -ab + b^2 + 1)

skillstriker · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Examine said:
Factor as fully as possible
a^3+b^3+a+b

(a+b)(a^2-ab+b^2) + (a+b)
= (a+b)(a^2-ab+b^2+1)

Examine · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Timske said:
Consider the equation x^2 + (k - 4)x + 9 = 0

For what values of k does the equation have:
i) equal roots;
ii) distinct real roots?

ii

2 distinct real roots means discriminant>0
(k-4)^2-4(1)(9)>0
k^2-8k+16-36>0
k^2-8k-20>0
(k-10)(k+2)>0
k=10,k=-2

Testing stuff, 1st and 3rd interval are valid.

K<-2, K>10

right/wrong?

Timske · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Examine said:
ii

2 distinct real roots means discriminant>0
(k-4)^2-4(1)(9)>0
k^2-8k+16-36>0
k^2-8k-20>0
(k-10)(k+2)>0
k=10,k=-2

Testing stuff, 1st and 3rd interval are valid.

K<-2, K>10

right/wrong?

right

SpiralFlex · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Of course the general rule of the 2U thread is that 4U students cannot answer any of the questions. Only provide them.

$Spiral's girlfriend is trapped inside a burning house and wants to rescue her! He is currently situated at his place of living. At the lighthouse directly north of A. The path he wants to take runs diagonally downwards and across. This mystical path is highlighted in blue as he waves his wand to find the shortest distance. To get there as quick as possible, Spiral must row across the destructive ocean from his lighthouse to point B,$\; x \;\textup{km} \;$ from A and then use his tiny feet to run towards the burning building. If Spiral's rowing speed is$\; 6 \textup{km/h}\;$ and his jogging speed is$\; 10 \textup{km/h}. $[Assume burning building is 10 km east from A.]$

$i. Find an expression in hours for Spiral to row from the lighthouse to B.$

$ii. Hence find the total time taken for Spiral to travel across the glowing path to rescue his girlfriend.$

$iii. Hence show that when$\; x= 4.5 \textup{km/h},$\; the time it takes for Spiral to travel from the lighthouse to rescue his girlfriend is a minmum.$

$iv. Hence find the quickest time it takes Spiral to go to the rescue his girlfriend from the lighthouse and live happily ever after. Give your answer correct to the nearest minute.$

Aysce · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Pretty diagram <3

SpiralFlex · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Aysce said:
Pretty diagram <3

Always. <3

Carrotsticks · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Solution: Acquire new girlfriend. This one's a goner.

SpiralFlex · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Carrotsticks said:
Solution: Acquire new girlfriend. This one's a goner.

Spiral is a loyal puppy.

Timske · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Spiral can be my gf

SpiralFlex · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Timske said:
Spiral can be my gf

Okay!

Timske · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

let lighthouse be point c so distance bc = sqrt(36+x^2)

d = s/t
d = 6/60

on right track spiral??

Aysce · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Carrotsticks said:
Solution: Acquire new girlfriend. This one's a goner.

Strong love right here.

SpiralFlex · Mar 4, 2012

Re: 2012 HSC Mathematics Marathon!

Timske said:
let lighthouse be point c so distance bc = sqrt(36+x^2)

d = s/t
d = 6/60

on right track spiral??

Maybe...Keep going and see!

Examine · Mar 5, 2012

Re: 2012 HSC Mathematics Marathon!

Jamflex I'm sorry for your loss. -gives flowers-

SpiralFlex · Mar 5, 2012

Re: 2012 HSC Mathematics Marathon!

Examine said:
Jamflex I'm sorry for your loss. -gives flowers-

Within a few more weeks at Harrys you be able to answer that question.

SpiralFlex · Mar 5, 2012

Re: 2012 HSC Mathematics Marathon!

SpiralFlex said:
Of course the general rule of the 2U thread is that 4U students cannot answer any of the questions. Only provide them.

$Spiral's girlfriend is trapped inside a burning house and wants to rescue her! He is currently situated at his place of living. At the lighthouse directly north of A. The path he wants to take runs diagonally downwards and across. This mystical path is highlighted in blue as he waves his wand to find the shortest distance. To get there as quick as possible, Spiral must row across the destructive ocean from his lighthouse to point B,$\; x \;\textup{km} \;$ from A and then use his tiny feet to run towards the burning building. If Spiral's rowing speed is$\; 6 \textup{km/h}\;$ and his jogging speed is$\; 10 \textup{km/h}. $[Assume burning building is 10 km east from A.]$

$i. Find an expression in hours for Spiral to row from the lighthouse to B.$

$ii. Hence find the total time taken for Spiral to travel across the glowing path to rescue his girlfriend.$

$iii. Hence show that when$\; x= 4.5 \textup{km/h},$\; the time it takes for Spiral to travel from the lighthouse to rescue his girlfriend is a minmum.$

$iv. Hence find the quickest time it takes Spiral to go to the rescue his girlfriend from the lighthouse and live happily ever after. Give your answer correct to the nearest minute.$

Quick! Help me find a way to minimise the time to save my girlfriend!

Examine · Mar 5, 2012

Re: 2012 HSC Mathematics Marathon!

SpiralFlex said:
Quick! Help me find a way to minimise the time to save my girlfriend!

1. Call 000
2. Hope for the best

feelsbadman.jpg

kingkong123 · Mar 5, 2012

Re: 2012 HSC Mathematics Marathon!

SpiralFlex said:
Quick! Help me find a way to minimise the time to save my girlfriend!

dont you need to give a distance from A to the house?

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