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  1. Q

    Differential Equations Question

    Yep thanks. I think thats where the confusion was for OP since the textbook makes it look like P_y.
  2. Q

    Differential Equations Question

    Is it P \times y or P_y, why can you factor out a P like that?
  3. Q

    Inverse trig question

    Its always a good idea to state the domain for x before solving so: -1 \leq x \leq 1 and \frac{-2}{3}\leq x \leq 0. Now take the sin of both sides to obtain: \sin(\sin^{-1} (x) - \cos^{-1} (x))=\sin{(\sin^{-1} (3x+1)) \sin(\sin^{-1} (x))\cos(\cos^{-1} (x)) - \sin(\cos^{-1} (x))\cos(\sin^{-1}...
  4. Q

    3D Vectors.

    Let X=(2,1,3) Pick two random point on the line say t=0 and t=1 (can be anything really) So let A=(1,-1,2) and B=(3,-1,-1) Then \overrightarrow{AB}=(2,0,-3) and \overrightarrow{AX}=(1,2,1) The vector projection of v onto u is defined as proj_{u}v=\frac{u\cdot v}{|u|^2}u In our case the u is...
  5. Q

    Differential Equations Question

    Could you show what Q12 is so we actually know what the variables and constants mean?
  6. Q

    Math assessment example (math adv)

    cool
  7. Q

    Dot product

    Theres a bit of a problem with the question (this is why you don't use MIF lol).The dot product can only be negative if the angle between the two vectors is obtuse. Ignoring this: u\cdot v=|u||v|\cos\theta so -6=\sqrt{10}|b|\cos150 \implies |b|=\frac{12}{\sqrt{30}} (I'm assuming they meant...
  8. Q

    Paradoxes, anomalies and inconsistencies in Animal farm?

    Im not good at english so take everything I say with a grain of salt. -The main paradox I feel is the use of language to distort meaning in animal farm. The infamous "All animals are equal but some are more equal than others,' is pretty clearly a paradox (how can you be equal but still have...
  9. Q

    Dot product

    The dot product is defined as u\cdot v=|u||v|\cos\theta where theta is the angle between the vectors. So a-15=\sqrt{10}\sqrt{a^2+25}\cos120 Since there's square roots its a good idea to square both sides (a-15)^2=10(a^2+25)\left(\frac{1}{4}\right) At this point its just a quadratic. Which...
  10. Q

    HSC Biology

    https://en.wikipedia.org/wiki/Mathematical_and_theoretical_biology#:~:text=Mathematical%20and%20theoretical%20biology%20is,biology%20which%20deals%20with%20the Calculus is actually used to model some systems it's pretty cool.
  11. Q

    Maths-Ext 1/2 Marks Lost and Hardest Topics

    Yes you can also do IBP on the first integral from the third line: I=\int\sin^{99}(x) \sin(100x) \cos{x}dx+\int\sin^{100}(x)\cos(100x) dx to get I=\frac{1}{100}\sin^{100}(x)\sin(100x)-\int\sin^{100}(x)\cos(100x) dx+\int\sin^{100}(x)\cos(100x) dx Which is the same thing.
  12. Q

    Maths-Ext 1/2 Marks Lost and Hardest Topics

    This is extension 2 so don't worry haha.
  13. Q

    Maths-Ext 1/2 Marks Lost and Hardest Topics

    Yep I wanted to showcase the 'reverse product rule,' \int\sin^{99}(x)\sin(101x)dx =\int\sin^{99}(x)\sin(100x+x)dx \int\sin^{99}(x) \sin(100x) \cos{x}+\sin^{100}(x)\cos(100x) dx \text{Now notice how:}\quad\frac{d}{dx}\sin^{100}(x)=100\sin^{99}(x)\cos{x}...
  14. Q

    Maths-Ext 1/2 Marks Lost and Hardest Topics

    My bad I remembered it wrong.
  15. Q

    Maths-Ext 1/2 Marks Lost and Hardest Topics

    Also try this integral from the MIT integration bee: \int\sin^{99}(x)\sin(101x)dx
  16. Q

    Maths-Ext 1/2 Marks Lost and Hardest Topics

    Yup thats where I got that technique from. For anyone interested, the integral is: \int\frac{\ln x}{(1+\ln x)^2} dx
  17. Q

    Maths-Ext 1/2 Marks Lost and Hardest Topics

    It didn't load for me as well but looking at what @idkkdi said it seems like we convert it to sec and tan, but then wouldn't x=\cos{\theta} be better heres my working: dx=-\sin\theta d\theta \therefore I=-\int{\frac{\cos^6{\theta}\sin\theta}{(1+\cos{\theta})^8} dx...
  18. Q

    Announcement from BOSTES/NESA - 2019 Syllabus Changes for Calculus courses

    Nice that covers everything, except sum to product ironically wasn't part of the old syllabus but is part of the new syllabus.
  19. Q

    Announcement from BOSTES/NESA - 2019 Syllabus Changes for Calculus courses

    Ah right forgot abt locus of parabola. Poly is still a thing for 4u I think, just indirectly.
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