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If ax^3 + cx + d = 0 has a double root, show that 27ad^2 + 4c^3 = 0

integrate sqrt(x)/(x*sqrt(x) +2) u = x*sqrt(x)

Hey guys, Can someone give me a good explanation on how the RBA affects the exchange rate by dirtying the float? Also, how does sterilisation work?

A few questions about this option module 1) Is this option any good? My teacher wants to do this option because he specialises in it (although he's not a very good teacher anyway so i don't see the point in picking such an obscure option module). 2) How hard is this topic relative to the...

A few questions about this option module 1) Is this option any good? My teacher wants to do this option because he specialises in it (although he's not a very good teacher anyway so i don't see the point in picking such an obscure option module). 2) How hard is this topic relative to the other...

Hey guys. I'm not sure if this is the right place to post this, but anyway. In 2009 i was accelerated and did 2unit and extension 1 maths for the HSC. For extension 1 maths, my mark was 47/50. However this year I'm also doing extension two maths, so my mark for extension one maths will become...

P(x) = 8x^3 -12x^2 + 6x + 13. For what values of x is P(x) increasing?

When looking at past HSC solutions the answer always derives how to transform asinx + bcosx into Rsin(x + $) I was wondering if we have to derive it as well, or can we simply use the formula for finding R and $ using: R = sqrt(a^2 + b^2) and tan $ = b/a ???

A particle, whose displacement is x, moves in simple harmonic motion. Find x as a function of t if: acceleration = −4x and if x = 3 and v = −6root3 when t = 0.

3.c) A particle moves in a straight line and its position at time t is given by: x=1+sin4t+ (root3)cos4t (i) Prove that the particle is undergoing simple harmonic motion about x = 1. When i was reading the exam report, they said it was incorrect to do the following: a = −16 sin 4t −...

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Haha please don't scorn me for my ignorance :(

This was only in question 3, but i had no idea how to do it. :( When the polynomial P(x) is divided by x^2-1 the remainder is 3x -1. What is the remainder when P(x) is divided by (x-1) (answer = 2)

3.a) An urn contains 3 white balls, 4 red balls and 5 black balls. Three balls are drawn at random. What is the probability that they are different colours? (answer = 3/11) 22. Urn A contains 6 white and 4 black balls. Urn B contains 2 white and 2 black balls. From urn A two balls are...

In how many ways can 8 girls be divided into 4 sets of 2? (answer = 105)

11. An eleven is to be chosen from 15 cricketers of whom 5 are bowlers only, 2 others are wicketkeepers only and the rest are batsman only. How many possible elevens can be chosen which contain at least 4 bowlers and at least 1 wicketkeeper? (answer = 742 18. In how many ways can n things be...

Hey guys... again.... I finished the permutations exercise thanks to all the help you guys provided. But now i'm doing combinations and i'm bad at this too. Anyway these are the questions i couldn't get correct so far.... :( 7. A committee of 6 is to be selected from 10 people of whom A and B...

Hey guys i fail at this topic. Need some help in figuring out how these questions are done. Much appreciated :cry: 23. Find the number of arrangements of the letters in the word pencils if: i) e precedes i (answer = 2520) ii) there are 3 letters between e and i (answer = 720) 28. A car can...

Hey guys i can't do these permutation questions :S Could someone please show me how they are solved. These questions are all from fitzpatrick 3unit text book exercise 28a) 4. How many five digit numbers can be formed from the digits 2,3,5,6,8,9 if no digit can be used more than once in a...

The period of a particle moving in SHM is 6 s and its amplitude is 8cm. Calculate its velocity and acceleration (correct to 1 decimal place) when the displacement is 5cm from the centre of motion. :) answer: v = -6.5cm/s a = -5.5cm/s/s