# Search results

1. ### EE Tutoring ~ 1st Lesson \$20 | Selective, OC, HSC Chemistry (97), MX1 (99), Med Interviews | HSC All-Rounder | Medical Student | Baulko Graduate

What med schools did you get offers for?
2. ### Differential Equations Question

Yep thanks. I think thats where the confusion was for OP since the textbook makes it look like P_y.
3. ### Differential Equations Question

Is it P \times y or P_y, why can you factor out a P like that?
4. ### 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}...
5. ### 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...
6. ### Differential Equations Question

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

cool
8. ### 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...
9. ### 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...
10. ### 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...
11. ### 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.
12. ### 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.
13. ### Maths-Ext 1/2 Marks Lost and Hardest Topics

This is extension 2 so don't worry haha.
14. ### 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}...
15. ### Maths-Ext 1/2 Marks Lost and Hardest Topics

My bad I remembered it wrong.
16. ### 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
17. ### 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
18. ### 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...
19. ### 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.
20. ### 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.