# Alex

### Solve the following complex equations....?

Solve

i) x^2 - 4i - 3 = 0

ii) x^2 + (2 - 2i)x - 1 - 2i = 0

How do I do this? Any help is much appreciated :D

3 AnswersMathematics9 years ago### Find the extension of the string....?

A box of mass m hangs from an elastic string, one end of which is attached to the ceiling. The string has natural length l and modulus of elasticity λ. Given that the box hangs in equilibrium find the extension in the string.

Can anyone explain how to do this please, showing all the working. Thanks :)

1 AnswerMathematics9 years ago### Help with degree Mechanics...?

Suppose that the trajectory of a particle moving in a plane is given by the polar equation r = ae^θ for some constant a > 0.

(i) Deduce that r' = rθ'.

(ii) Hence show that if there is no radial component of acceleration then the particle moves with a constant angular velocity ω

Can anyone show me how to answer these questions please

1 AnswerMathematics9 years ago### Using a calculator, please could you tell me the answer to these....?

I've lost my calculator and have looked everywhere for it but it hasn't showed up and so in a desperate attempt to do my work for tomorrow, i'm asking this. I have looked everywhere on the internet for a calculator that will express the answer in fraction or surd form but have not had any luck and it is the type of question that requires fractions/surds rather than decimals. Please could some plug cos(5), sin(5), cos(3) and sin(3) into their calculators (if they show fractions) and write the answers for me, PLEASE! Thank you!

2 AnswersHomework Help9 years ago### Best way of upgrading phone early....?

About a year ago I got tricked into having the worst contract in the world with the Samsung Galaxy Ace for £35 a month for 24 months. The phone is not malfunctioning and my fiance, who works for Carphone Warehouse, has said that the best thing for me to do is to try and get out of my contract and he'll get me a new one with Carphone for 40% off as he's an employee. However, my contract is with Orange itself and so I would somehow have to get out of my contract to open one with Carphone. Can anyone suggest the best way for me to go about doing this? He suggested reducing my contract down to as low as I can get it with Orange and then opening one with him but I was wondering if there was anything else I could do, thank you :)

2 AnswersCell Phones & Plans9 years ago### Finding the arc length of a curve...?

The question I have to answer is this....

Consider the curve given by the vector equation,

r(θ) = {aθ(3 - θ^2)i + 3aθ^2j + aθ(3 + θ^2)k}/√2

where a > 0 is some constant and i, j, k are vectors.

(i) Find the arc length of the curve as the parameter ranges from 0 to θ.

Where do I start and how can I work through it to get the right answer...?

1 AnswerMathematics9 years ago### Determining whether sets are countable...?

Determine which of the following sets are countable (giving reasons):

(i) The set 3N of all natural numbers divisible by 3.

(ii) {x × 2^y | x in Z, y in Q}

(iii) {x^3y | x in R; y in Q}

where Z is the set of integers, Q is the set of rational numbers and R is the set of real numbers.

Can anyone help me to answer this question please :D

2 AnswersMathematics9 years ago### Find the vector equation of the plane....?

Find the vector equation of the plane 7x - 2y + 3z = 5. What is the unit normal vector to the plane? How far is the plane from the origin?

How do I go about doing this?

If anyone can help could you please explain step by step so I understand how to do other examples too please.

Thank you :)

2 AnswersMathematics9 years ago### Prove 2n^n ≤ (n+1)^n...?

Using Bernoullis inequality

(1+a)^n ≥ 1+na for a>0

prove that 2n^n ≤ (n+1)^n.

Can anyone help please??

1 AnswerMathematics9 years ago### Help understanding what a tuple formulation is?? ?

''Consider an experiment that you throw a fair dice three times. Write down the sample space for this experiment. [Hint: Do not write down all elements of the sample space Ω explicitly, instead please use a tuple formulation.].''

This is one of the questiona in my probability and statistics homework however, I don't know what a tuple formulation is and can't find anything about it in my lecture notes. Could anyone help please :)

1 AnswerMathematics9 years ago### Vector help pleaseee..?

Suppose a,b and c are vectors. Simplify the following expressions explaining clearly every rule you use at each step; but be very careful...some of them are meaningless rubbish. For those that are meaningless explain what is wrong with them.

(i)(4a+2b)+6(3c+(a+b+(a−2b)))

(ii)(4a+2b)+6(3c+(a+b+(a−2a·b)))

(iii)(4a·a+2b·b)c+6(3c+(a+b+(a−2b)))

(iv)1 2(4a+2b)+6(3c+(a+b+(a−2b)))

(v)1 2c(4a+2b)+6(3c+(a+b+(a−2b)))

Could someone please help :)

1 AnswerMathematics9 years ago### Sketching the graph of a function...?

I have been asked to sketch the graph of

f(x)= 1/[(x-3)(x-2)]

making use of information about the first and second derivatives of f.

How do I do this?

I know that x is undefined at x = 3 and x = 1, but I don't know anything else.

Can anyone help??

Thank you :)

3 AnswersMathematics9 years ago### How to use the mean value theorem to deduce that |sin(x)| ≤ x...?

Suppose that sin'(x) = cos(x) for all x є R (the set of real numbers) and suppose that |cos(x)| ≤ 1. Use the mean value theorem to deduce |sin(x)| ≤ x by assuming that sin(0) = 0.

Please can someone explain this step by step to me. Thanks :)

2 AnswersMathematics9 years ago### How to find the area of an equilateral triangle...?

The following question is part of my homework... If anyone could help me answer it I would be extremely grateful.... Thank you :D

Let ABC be an equilateral triangle whose circumcircle has radius r. Find the area of ABC in terms of r.

1 AnswerMathematics9 years ago### How to find a non zero a in modulo4 [Z4] such that p(x)p(x) is equal to the polynomial 1 in Z4[x]?

p(x) = 1 + ax^3 over Z4. find a non zero a in modulo4 [Z4] such that p(x)p(x) is equal to the polynomial 1 in Z4[x]?

How do I do this? Step by step help please!! :)

1 AnswerMathematics9 years ago### Prove that sinx + cosx = {√(2)sin(x+π/4), √(2)cos(x-π/4)} and cosx - √(3)sinx = 2cos(x+π/3)?

By introducing additional multipliers prove that a) sinx + cosx = {√2sin(x+π/4), √2cos(x-π/4)}.

and b) cosx - √(3)sinx = 2cos(x+π/3)

Can someone please help me answer this, step by step so I understand how to do it. Thank you!

3 AnswersMathematics9 years ago### Deduce c^2 = a^2 + b^2 + 2abcosδ and hence prove the cosine rule.?

The triangle in my question resembles the one in the link below. However, in my question H = D, the line segment BD being labelled e, the angle BCD is δ amd the angle ACB is γ.

The first section of the question was to prove c^2 = a^2 + b^2 + 2bd which I have done. The next section of the question is to deduce c^2 = a^2 + b^2 + 2abcosδ and use this to prove the cosine rule: c^2 = a^2 + b^2 - 2abcosγ

2 AnswersMathematics9 years ago### Characteristic Function question help?

Show that the characteristic function χ[0,+∞)(x) = {1; x ≥ 0, 0; x < 0}

is not differentiable at x = 0 by showing that χ[0,+∞)(x) is not continuous at x = 0

This is one of the questions on my homework sheet for the MA101 module of my degree Maths course, however, i'm not really sure what the characteristic function is and i've looked over my lecture notes and can't make much sense of it. Can anyone explain what it is and how to answer this question (in detail so I understand how to do it). Thank you!

2 AnswersMathematics9 years ago