Alan

9 Questions
9007 Answers

+17

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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.

+15

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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.

+10

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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.

+5

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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.

+33661

+3

hamza:
23q+3b=-9
21q-4b=3

One way is as follows:

Multiply the first equation through by 4 and the second equation through by 3 to get

92q + 12b = -36
63q - 12b = 9

Now add these two equations together to get

155q = -27

This allows you to find q. Then substitute the value you find back into one of the original equations and rearrange to find b.

Alan3 мар. 2014 г.

+33661

+3

carol:
How do you make a grey code matrix with 7 variables to determain gates to be used?

Then what do I need to know to illustrate it on matlab?

The following link: http://www.gaussianwaves.com/2012/10/natural-binary-codes-and-gray-codes/ has useful information on gray codes and implementing them in Matlab.

Alan3 мар. 2014 г.

+33661

+3

Melody:
1234smile:
y=-1^2+2(1)+3

-(1^2)+2(1)+3 = 4 This is the most acceptable interpretation is brackets are not used.

It is unfortunate that the scientific calculator on this site gives -1^2 as +1 (though it does show as (-1) ²=4 after you press the equals). Proper scientific calculators should obey the rule that raising to a power takes precedence over a minus. Without this we have the potentially confusing situation that -1^2 gives 1 and that 0-1^2 gives -1.

Alan3 мар. 2014 г.

+33661

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With 5x+10 equal to angle in degrees then with cos(angle)=1/2 we must have 5x+10 in the form 360n+60 or 360n-60, where n is an integer. That is, x must be in the form 72n+10 or 72n-14. With n = 0 only the first form gives x in the range 0 to 360; with n = 5 only the second form gives x in the right range; with n = 1, 2, 3, and 4, both forms give x in the right range. The values I get for x this way are: 10, 58, 82, 130, 154, 202, 226, 274, 298, 346, which match those in Melody's picture. Now I'm happy too, Melody!

Alan2 мар. 2014 г.

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+3

My calculation above assumed that 5x+10 was equal to theta measured in radians. However, it could also be that it should be equal to theta measured in degrees, in which case the results would look different (but there would still be several values of x in the range 0 to 360).

Alan1 мар. 2014 г.

+33661

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George MacDonald was a Scottish author, poet, and Christian minister. He was a pioneering figure in the field of fantasy literature and the mentor of fellow writer Lewis Carroll.(whose real name was C.L.Dodgson).

Alan1 мар. 2014 г.

+33661

+3

DavisDude:
In rectangle ABCD, diagonal AC is drawn. If CD=8 and AC=13, find m < ACD

if you sketch the rectangle you will see that cos(ACD) = 8/13, so you should be able to determine angle ACD from this.

Alan1 мар. 2014 г.

+33661

+3

Der:
could you please solve 2 cos (5x + 10) = 1 For 0< x < 360

You can see from below that there are several solutions that lie within the range 0<x<360

angles.PNG

Alan1 мар. 2014 г.

+33661

+3

judie:
/x/-2

The absolute value of -2 is just 2. In general, if you want to enter the absolute value of a number in a calculator on which there is no absolute value button, you could square it and then take the square root again!

Alan1 мар. 2014 г.

+33661

+3

Melody:
mmann:
Nakisa spent $ 328 on a total of 22 CD's and a DVDs if CD's cost $16 each, how many CD's did Nakisa
buy?

Hi mmann,

I don't think that the question makes sense.

It says in the question that Nakisa bought 22CDs

22*$16 = $352 which is more than Nakisa spent.

See, it does not make sense.

I think this might mean
n _CD + n _DVD = 22
16n _CD + c _DVDn _DVD = 328

where n is number and c is cost. However, we still need to know the cost of a DVD to answer the qustion.

Alan1 мар. 2014 г.