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apple2357
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apple2357
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03-09-2018
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12-16-2018,
03:58 PM
apple2357
replied to a thread
This one has me stumped - entrance exam for junior high school in Japan
in
Geometry and Trig
Nice problem! Actually, i started by printing it out and tried to rearrange the pieces into more familiar shapes ( just for fun). I just wondered...
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15 replies | 259 view(s)
12-14-2018,
03:41 AM
apple2357
replied to a thread
polar form of decagon by using r = cos( 1+sqrt(theta))
in
Intermediate/Advanced Algebra
Your suspicion is right He has made them look straight by fiddling with the step length when plotting. This can be done on Autograph too.
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2 replies | 156 view(s)
12-13-2018,
03:04 PM
apple2357
started a thread
polar form of decagon by using r = cos( 1+sqrt(theta))
in
Intermediate/Advanced Algebra
In this article ( http://www.foster77.co.uk/ATM-MT224-10-11.pdf) It states you can generate a decagon by using r = cos( 1+sqrt(theta)) as below....
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2 replies | 156 view(s)
12-09-2018,
02:00 PM
apple2357
replied to a thread
Help with understanding dividing fractions
in
Arithmetic
Really good blog! Exactly the issue i have been thinking about. By the way, the link below seems to be broken. I curious what this picture would...
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12 replies | 475 view(s)
12-09-2018,
01:51 PM
apple2357
replied to a thread
Help with understanding dividing fractions
in
Arithmetic
Thanks, we posted at the same time but i will look at your link. Always an interesting read!
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12 replies | 475 view(s)
12-09-2018,
01:50 PM
apple2357
replied to a thread
Help with understanding dividing fractions
in
Arithmetic
Many thanks for your thoughts! For my son's p.o.v he doesn't understand why it works as he only understands equivalent fractions and i don't wish...
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12 replies | 475 view(s)
12-09-2018,
12:13 PM
apple2357
started a thread
Help with understanding dividing fractions
in
Arithmetic
Working with my 9 year old son on multiplying and dividing fractions. Without any understanding but playing with a calculator he worked out that...
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12 replies | 475 view(s)
12-06-2018,
03:38 PM
apple2357
replied to a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
Good idea.
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20 replies | 867 view(s)
12-06-2018,
02:34 PM
apple2357
replied to a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
so would this lead to 8x = x+ 360n or 180-x +360n x = (360/7)n or x = 20 +40n Is that correct?
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20 replies | 867 view(s)
12-05-2018,
05:46 PM
apple2357
replied to a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
so multiply by sinx sinx cosx cos2x cos4x = 1/8 sinx 1/2 sin2x cos2x cos4x = 1/8 sinx (1/2)(1/2)sin4x cos4x = 1/8 sinx (1/8) sin8x =...
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20 replies | 867 view(s)
12-05-2018,
12:40 PM
apple2357
replied to a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
Yes! My mistake. So sorry! What a mess up. The original question is cosx cos2x cos4x = 1/8
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20 replies | 867 view(s)
12-05-2018,
09:48 AM
apple2357
replied to a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
yes i believe thats correct. I have just asked him to confirm!
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20 replies | 867 view(s)
12-05-2018,
07:50 AM
apple2357
replied to a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
I have been given a hint: Try multiplying by sinx!
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20 replies | 867 view(s)
12-04-2018,
03:47 PM
apple2357
replied to a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
Yes, a friend who teaches maths sent me this and asked if i can spot a nice trick? But after musing on it for a while, like you, i haven't made...
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20 replies | 867 view(s)
12-04-2018,
02:35 PM
apple2357
replied to a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
Yes, i was trying different possible products! and wondering if there is some kind of symmetry to exploit. I have tried sketching it for inspiration.
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20 replies | 867 view(s)
12-04-2018,
12:26 PM
apple2357
started a thread
cosxcos4xcos8x =1/8: efficient way of solving this?
in
Geometry and Trig
I am trying to find an efficient way of solving cosxcos4xcos8x=1/8, 0 to 2pi, i am thinking about the product of three trig expressions and what...
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20 replies | 867 view(s)
11-27-2018,
04:13 AM
apple2357
replied to a thread
Solving xy-3x+4y=12
in
Intermediate/Advanced Algebra
Also, something else i don't understand. I could approach the above problem in a different way and rearrange for x ( say) to get x(y-3) = 12-4y...
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5 replies | 242 view(s)
11-27-2018,
04:03 AM
apple2357
started a thread
Solving xy-3x+4y=12
in
Intermediate/Advanced Algebra
I am trying to get my head around how to express the solution to xy-3x+4y=12 I can see how to factorise this to get xy-3x+4y-12=0 ...
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5 replies | 242 view(s)
11-27-2018,
03:22 AM
apple2357
replied to a thread
Point of inflection, max and min?
in
Calculus
I can't see why a quartic can't have this property? When you differentiate it , it's possible to have three solutions? Or does the second derivative...
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7 replies | 301 view(s)
11-26-2018,
06:08 PM
apple2357
replied to a thread
Point of inflection, max and min?
in
Calculus
I experimented using graphical software and it appears there are plenty. Here is one, if anyone is interested: y= -x^5+3x^3 I guess a...
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7 replies | 301 view(s)
11-26-2018,
05:52 PM
apple2357
replied to a thread
Point of inflection, max and min?
in
Calculus
thanks, I will get to work on this!
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7 replies | 301 view(s)
11-26-2018,
07:14 AM
apple2357
started a thread
Point of inflection, max and min?
in
Calculus
I know that all cubics have a point of inflection and many can have Max and min stationary points. Is it possible for any polynomial to have a...
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7 replies | 301 view(s)
11-20-2018,
03:23 AM
apple2357
replied to a thread
semi circle turning point: why (0,1) rather than anywhere else on the semi-circle?
in
Calculus
That's exactly my question and you have given me good explanation! Thank you!
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5 replies | 350 view(s)
11-19-2018,
07:13 PM
apple2357
replied to a thread
semi circle turning point: why (0,1) rather than anywhere else on the semi-circle?
in
Calculus
A turning point is where the derivative changes sign? Or where the derivative is zero?
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5 replies | 350 view(s)
11-19-2018,
06:34 PM
apple2357
started a thread
semi circle turning point: why (0,1) rather than anywhere else on the semi-circle?
in
Calculus
If you take the equation of a semi circle y= root(1-x^2) and try to find its turning point you get (0,1). I don't understand why it is turning at...
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5 replies | 350 view(s)
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