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Okay so third and hopefully last dumb integration question: ∫ √(x/(1-x) dx {with limits between 1/2 and 0}, letting x = cos²@ Undoubtedly I'm doing something stupid again. Please and thanks! :)

Could someone please show me why the answer to this: ∫ (sinx)/(√(1 + 2cosx)) dx {with limits pi/2 and 0} using the substitution y = 1 + 2cosx is √3 - 1? I keep getting a quarter of this answer?? Thanks! (Sorry I don't know how to make my limits pretty)

I'm stuck on this integration question: Find ∫ dx / (25 + x²)^3/2 by letting x = 5tan@ I keep getting 1/25 sin(tan^-1(x/5)) + C but the answers give 1/25 x/√(25 + x²) + C. Are these answers equivalent (if so could someone please show me why) or am I...

Okie so when I simplify (tan2x)/(1-tan22x) I get (1/2)tan4x. The answers tell me I should get (1/4)tan4x. Am i doing something wrong? Please and thankyou! :)

Sorry this is probably a silly question. How do I prove that there are always two square roots of a non-zero complex number? I get four square roots! How do you know when to only take the positive number when you have +/- a square root? If that makes sense...? Thank you! :)

Hiii. Okay can someone please help me with this question? Keeping in mind you're speaking to someone who is mathematically challenged. I have a worked answer for it but I don't understand it. Factorise fully: (m+2n)3 + (m-2n)3 The answer is: 2m(m2+12n2) The first line of working...

... which I can't do. 1) Find the maximum and minimum values of y = (x + 5)1/2 for -4 ≤ x ≤ 4. Answer: max: 3, min: 1 2) A surfboard is made in the shape of a rectangle and semicircle, as shown. The perimeter is to be 4 m. Find the maximum area of the surfboard, correct to 2 decimal...

"A cross country runner runs at 3.2 ms^-1 for 5 minutes north, then runs at 4 ms^-1 for 10 minutes north. He then returns to the start at a steady pace, taking 20 minutes. Find: b) his diplacement after 10 minutes. e) his average speed for the whole journey." According to the answers: b) 3360...

Okie just to clarify... You can't use a prescribed text as your additional material, even if it's not your prescribed text. Right?? Because I wanted to do the book Romulus, My Father but I just realised it's prescribed. So I might just have to cry now. Yep. :mad1: I'm right right?

Okie another stupid (probably) question: "The curve y = ax^3 + bx^2 - x +5 has a point of inflexion at (1, - 2). Find the values of a and b." I suppose you have get two equations and solve them simultaneously or something but I can only get one and I don't know what else to do. Thanks. :)

Okie, this question's annoying me 'cause i know it's really easy but I can't get the same answer as is in the back of the textbook: "Find any turning points on the curve y = (4x^2 - 1)^4 and determine their nature." I worked out that the stationary points are (0, 1), (0.5, 0) and (-0.5, 0)...

Ok I'm just starting Preliminary Economics and I was wondering what textbook is the most effective to use? I assume the other threads refer to HSC textbooks. Thanks! :)

Okie dokie, question. Do you get given separate bands for history and geography? I was under the impression (no idea why) that they were combined, which would mean that my history would make up for geography. Thankyou!

Okay, I have a stupid question, sorry. How do you find the equation of a line passing through the point of intersection of two other lines and with a given gradient? I'm in year 10 and i don't think we've done this. I know how to find a line passing through the intersection and another point...

Well it's not long til a lot of people have to choose subjects for year 11 and i for one am having a hell of a lot of trouble. There's so much i want to do but it adds up so quickly. I've narrowed it down to 14 units. Is that too much? How many has everyone else done/going to do? How many...