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.

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boo09:
Rewrite as a simplified fraction.

1.5¯=?

If the 5 recurs forever then:
Recurring.PNG

Alan17 мар. 2014 г.

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I think the reasoning may be as follows:

CriticalPoints.PNG

I've just noticed that the exponents of e in the image look like c's. They are meant to be x's!!

Alan17 мар. 2014 г.

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joeybob27:
graph y= |x-2| -4

You can do this in the scientific calculator on this site (choose the graphing option at the bottom).
graph.PNG

Alan17 мар. 2014 г.

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Anyone:
the price of fish in 1997 increased by 8% in 1998 to 9% in the three-year period 1999-2001 by 17%. What percent price increased throughout the period 1997-2001?

Let the price at the beginning of 1997 be x
Price at end of 1997 = 1.08*x
Price at end of 1998 = 1.09*1.08*x
Price at end of 2001 = 1.17*1.09*1.08*x

overall increase in price = 1.17*1.09*1.08*x - x

As a percent of the original price this is ((1.17*1.09*1.08*x - x)/x)*100 or

(1.17*1.09*1.08-1)*100

Or approximately 37.73%

Alan17 мар. 2014 г.

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spartian78:
At noon sarah headed from elk city to Idabel at 60 mph. Two hours later, Joan headed from Idabel to elk city at 46 mph. If it is 332 miles from Elk city to Idabel, what time did they meet?

Suppose Sarah has been travelling for x hours when they meet. This means Joan has been travelling for x-2 hours.

Distance travelled by Sarah in x hours is 60x miles.
Distance travelled by Joan in x-2 hours is 46(x-2) miles.
The sum of these two distances must be 332 miles, so

60x + 46(x-2) = 332

From this you can find x, the number of hours past noon.

Alan14 мар. 2014 г.

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Alan14 мар. 2014 г.

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HELLO:
What is the fundamental frequency for an organ pipe that is 4 m long? The pipe has one end that is open and another end that is closed. Use a wave speed of 340 m/sec.

There are two things you need to know for this:

1. speed = frequency x wavelength

2. For a pipe that is open at one end and closed at the other the fundamental will occur when one quarter of the wavelength fills the pipe (the closed end is a node, the open end an anti-node).

So, first calculate the wavelength of the fundamental (four times the pipe length), then use the formula above to find its frequency.

Alan14 мар. 2014 г.

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fracrem:
(3^(1/2))sinx-cosx = 2sin(x-30)
Find all values of x in the range 0<=x<=360 which satisfy the equation 4sinxcosx = (3^(1/2))sinx-cosx

One simple way to do this would be to run through the values of x from 0 to 360 (do it in steps of 10 degrees at a time) and see which make both sides equal (it works ok here because the solutions are whole numbers of degrees!).

Or look at the graph below:
angles.PNG

Alan13 мар. 2014 г.

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Melody:
Hi Reinout

I am not very familiar with set notation.

{(x,y) E R2: x+y = 12}

What does the E R2 stand for?

Thanks.

Alan13 мар. 2014 г.

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jkjkjk:
3a(n-1)+8, a(1)=-10

If this is meant to be a(n) = 3a(n-1) + 8 with a(1) = -10, and you are looking for an explicit expression for a(n) then you can do it by writing down the first few terms and looking for the pattern, as below:

a(n).PNG

Alan13 мар. 2014 г.