Alan

9 Questions
9007 Answers

+16

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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.

+16

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4586

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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.

+6

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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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albina:
:roll:sa kilogram gelqeror te pashuar cao perfitohet me pjekjen 1500 kg te gurit gelqeror caco3

How many kg of CaO are formed from 1500kg of CaCO ₃?

CaCO ₃ -> CO ₂ + CaO

1 mole of CaCO ₃ produces 1mole of CaO
100g of CaCO ₃ produces 56g of CaO
1500kg of CaCO ₃ produces (56/100)*1500kg of CaO:

Alan25 мар. 2014 г.

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Here's my offering:

dfdx.PNG

Alan25 мар. 2014 г.

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Princess Sophie E:
The time base of a cathode ray oscilloscope (CRO) is set 1ms/cm. When an alternating current signal of 200Hz is applied to the y-plate of the CR0, what is the minimum number of cycles seen on the 30cm wide screen?

A 30cm screen can show 30ms worth of signal. That is 0.03s worth of signal. 1Hz is 1 cycle per second, so 200Hz is 200 cycles per second, so the screen will show 0.03x200 cycles, namely 6 cycles.

Alan25 мар. 2014 г.

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Princess Sophie E:
The electrostatic force between two charges Q1 and Q2 at a distance r apart is given by F=(Q1*Q2)/(4Pie*Eo*r^2). What is the unit of E?

If charge is in Coulombs (C), distance is in metres (m) and force is in Newtons (N) then Eo, the permitivity of free space is in C ²/(N.m ²)

Alan25 мар. 2014 г.

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Maufeat:
283-24/4*62+412-999/4*8532-5000/44-92/44-1000*4/99+23+50000*3/65-23*34+5/4*8532-5000/44-92/44-1000*4/99+23+50000*3/65-23*34+5/5-4000*77/99/9

= ? -2117438.(...) cant be right

Plug it into the calculator here to see:

283-24/4*62+412-999/4*8532-5000/44-92/44-1000*4/99+23+50000*3/65-23*34+5/4*8532-5000/44-92/44-1000*4/99+23+50000*3/65-23*34+5/5-4000*77/99/9

Why do you think it's not right? Possibly because you've made a typographical error in writing it?
Does it arise from something real, or is it just a silly test?

Alan24 мар. 2014 г.

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gearteen:
:shock: how do you i find the exact value of the six trigonometric functions of theta with two give numbers

I'm guessing that, by "six trigonometric functions" you mean sin, cos, tan, cosec, sec and cot, and that the "two given numbers" refer to two sides of a right-angled triangle. If so, then in order to answer the question you'd need to specify which two sides.

Alan24 мар. 2014 г.

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Balamurugan:
10^X=2912.35/10power X = 2912.35 then X= ?

X = ?

Looks to me as if it's the same question twice (written slightly differently); namely, given 10 ^X=2912.35 what is X?

The way to do this is to take logs (to the base 10) of both sides. log ₁₀10 ^X is just X, so X = log ₁₀2912.35

On the calculator here, just using the word log means log to the base 10 so

X = log(2912.35)

Alan23 мар. 2014 г.

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Guest:
918 in scientific notation?

Alan22 мар. 2014 г.

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katy:
225,314,672(280,270,378-30,799,600) i need it to be in decimal

225,314,672(280,270,378-30,799,600)

Not sure what you mean by "in decimal", these are just very large integers! Do you mean something like 5.6209426518654816*10 ¹⁶?

Alan22 мар. 2014 г.

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ladiilaced:
h(t)=4t+3
g(t)= 3t-5
find: h(g(-8))

g(-8) = 3*(-8) - 5 = -29

so (h(g(-8)) = h(-29) = 4*(-29) + 3 = -113

Alan21 мар. 2014 г.