need help (2 Viewers)

[user18181818]

can someone please help with this

answer is min=3m/s and max=4m/s

 

[tywebb]

Sydney Grammar 2023 trial Q11g

 

[user18181818]

where did the sin^2t go?

 

[synthesisFR]

where did the sin^2t go?

sin^t and cost^t married each other and it was like two destined loves, two halfs becoming a whole. EXCEPT THEY DID IT NINE TIMES
because they kept cheating every time

 

[user18181818]

sin^t and 9cost^t married each other and it was like two destined loves, two halfs becoming a whole. EXCEPT THEY DID IT NINE TIMES
because they kept cheating every time

wow ur analogy actually makes complete sense

 

[user18181818]

wait also how did they know that 0<cos^2x<1

 

[tywebb]

where did the sin^2t go?

9(sin²t+cos²t)+7cos²t=9+7cos²t

 

[synthesisFR]

wait also how did they know that 0<cos^2x<1

one day cos was living happily ever after between the range of maccas and his home
his home was abusive and hence he felt negative there, it was not his one and only place
maccas was his happy place, it was his one and only place
so then one day cos evolved using a cos-emite mega stone
but cos^2 t wasn't powerful enough still and he got banished from his home by his mother into a pot hole which looked like a zero
therefore cos^2 t was forever confined within the bounds of maccas and the pothole

 

[tywebb]

wait also how did they know that 0<cos^2x<1

-1≤cos t≤1 ∴ 0≤cos²t≤1

 

[user18181818]

thanks yall

 

[user18181818]

also another funky question from sydney grammar please help with (ii)

 

[tywebb]

Sydney Grammar 2023 trial Q14c

 

[user18181818]

Sydney Grammar 2023 trial Q14c
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i saw but i don't understand what they're doing
why do they let f(x)-g(x)=-p(x)?

 

[tywebb]

i saw but i don't understand what they're doing
why do they let f(x)-g(x)=-p(x)?

To get 4 equations in m,n,a,b by equating coefficients or using Vieta's formulas. Then solve for a,b.

 

[Luukas.2]

i saw but i don't understand what they're doing
why do they let f(x)-g(x)=-p(x)?

The curves y = f(x) and y = g(x) meet only when f(x) = g(x), or f(x) - g(x) = 0.

We know this equation is a degree four polynomial as the degree of f(x) is 4 and the degree of g(x) is 2.

We also know that this equation has only two solutions (as two points of contact) and in each case the curves touch without crossing, meaning that the equation f(x) - g(x) = 0 must have two double roots.

Hence, it can be expressed in the form from part (i)
...except that P(x) in part (i) is monic whereas f(x) - g(x) has a leading coefficient of -1, and so we have f(x) - g(x) = -P(x) = 0.