Alan

9 Questions
9009 Answers

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web2.0calc solve function working again

Those who have complained about the fact that the web2.0calc calculator has been throwing an error when solving an equation recently will be pleased to know it seems to be working properly again now (1st May 2020).

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Alan 1 мая 2020 г.

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Area of intersecting circles

Here's a puzzle for when the site activity is low!

In the diagram below there are two quarter circles of radius 1 and 2 intersecting as shown. What is the area of their intersection (i.e. the shaded region)?
прочитайте больше ..

heureka ●●●●●●●●●●

Alan 28 окт. 2015 г.

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A puzzle (for those who are bored!)

An equilateral triangle of side length 2 is inscribed in a circle. A rectangle, with side lengths x and y, is inscribed in another circle of the same size as the first one. прочитайте больше ..

Brodudedoodebrodude ●●●●●●●●●●●●●

Alan 11 мая 2015 г.

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IOM 8th year sample questions for Kes1968

Note Kes, that I won't upload any more on this site though. прочитайте больше ..

Alan 9 мая 2015 г.

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Extract from sample paper of the International Olympiad of Mathematics for kes198 (and anyone else who ,might be interested.

прочитайте больше ..

HeatherF ●●●●●●●●●

Alan 8 мая 2015 г.

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cis for Melody

Melody, the question about cis(60)^1991 + cis(-60)^1991 + 1 = 1 seems to have disappeared, so I'll answer it here for you.

cis means cos + i*sin, so using De Moivre's theorem cis(60)^1991 is the same as cis(60*1991).
If we прочитайте больше ..

Alan 26 окт. 2014 г.

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Obtain the first derivative of the following functions from first principles, without using a series expansion:

Obtain the first derivative of the following functions from first principles, without using a series expansion:
(i) y(x) = 3/√(2x+1)
(ii) y(x) = 4√x
Recently, I provided solutions to these first principles derivatives, but made use прочитайте больше ..

Alan 24 июл. 2014 г.

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the roots of 3x^2 -2x-5=0 are alpha and beta find the equation whose roots are alpha^2 and beta^2 (Posted for sacha)

So alpha = 5/3 and beta = -1
To get the (quadratic) equation whose roots are alpha2 and beta2 we construct:
(x - alpha2)*(x-beta2) = 0 or:
x2 -(alpha2+beta2)*x + alpha2*beta2 = 0 прочитайте больше ..

Alan 22 апр. 2014 г.

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Site Graphing Calculator

I've been playing with the site calculator in its graphing mode, and I'm puzzled by the fact that I sometimes seem to get a spurious straight line through the origin on part of the graph - see example below, where I just want the e^(-x). Also, why is it highlighting прочитайте больше ..

Alan 2 мар. 2014 г.

+33667

+3

xo_princesolo:
what is log radical 2 x = 6

log(sqrt(2)*x)=6

noting that 15625*2 ^11/2 = 10 ⁶/sqrt(2)

Alan28 февр. 2014 г.

+33667

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xo_princesolo:
what is log radical 2 x = 6

log to the base 2 of x = 6 means that x = 2 ⁶, or x = 64

In general, log to the base n of x = b means that x = n ^b

Alan28 февр. 2014 г.

+33667

+3

Melody:
lila7339:
In an alternating-current circuit, the voltage E is given by E=IZ, where I is the cirrent (in A) and Z is the impedance.

If I=0.729-0.139j amperes and Z=260+110j ohms, find the complex-number representation.
E=

E = (0.729 - 0.139j) (260+110j)

= 189.54 - 15.29*-1 + 30.69j - 36.14j

= 204.83 - 5.45j

I think that is alright but I could have made a stupid mistake - you had best check it.

The method is right but I think you've made a small slip in the imaginary part.
Complex.PNG

Alan28 февр. 2014 г.

+33667

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Stu:
I will be asking Matlab questions, as new posts to this thread if they arise.

My first is, can I scroll lock the command window to a point I want to view?

A better place to ask Matlab questions is at www.mathworks.com
When there go to User Community and then Answers.

Alan28 февр. 2014 г.

+33667

+3

I should have added that only one of the two solutions found from the quadratic equations satisfies the original equation.

Alan27 февр. 2014 г.

+33667

+3

qwweqewrewqr:
what is t in
t^(1/2)+t =30

Another approach is to let x = t ^1/2, so the equation becomes x+x ²=30. This is also a quadratic that factors nicely to give two values for x. Having found the values for x you then need to square them to get back the corresponding values for t.

Alan27 февр. 2014 г.

+33667

+3

qwweqewrewqr:
what is t in
t^(1/2)+t =30

Rearrange to get t ^1/2=30-t then square both sides, expand the right-hand side and collect terms. You will have a quadratic equation in t from which you can find two values for t (the quadratic factorises nicely).

Alan27 февр. 2014 г.

+33667

+2

Russell:
What is maximum area from a perimeter of 246.549 metres?

The shape with a maximum area for a given perimeter is a circle.

Alan27 февр. 2014 г.

+33667

+2

Abdulwahab:
what is the cosine inverse of -2.5?

There is no angle whose cosine is -2.5. The values of cosine vary between +1 and -1.

Alan27 февр. 2014 г.

+33667

+15

This is known as the Monty Hall problem. There is an interesting Youtube video at http://www.youtube.com/watch?v=o_djTy3G0pg where mathematics professor Marcus Du Sautoy takes comedian Alan Davies through the problem.

Alan27 февр. 2014 г.