<![CDATA[Math Is Fun Forum / Exercises]]> 2021-12-02T02:43:07Z FluxBB http://www.mathisfunforum.com/index.php <![CDATA[Compute the solution:]]> Hi,

1113.

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http://www.mathisfunforum.com/profile.php?id=682 2021-12-02T02:43:07Z http://www.mathisfunforum.com/viewtopic.php?id=21675&action=new
<![CDATA[In an acute-angled]]> hi tony123

Thanks for another interesting puzzle.

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2021-11-16T10:17:09Z http://www.mathisfunforum.com/viewtopic.php?id=26761&action=new
<![CDATA[solve]]> hi tony123

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2021-11-07T08:46:42Z http://www.mathisfunforum.com/viewtopic.php?id=26741&action=new
<![CDATA[Mathematics]]> hi abbeycity

As far as I know there is no totally algebraic way to solve this.

What I would do is to sketch two graphs, y = 2^x and y = 2x to see where these cross.

You can try this at https://www.mathsisfun.com/data/function-grapher.php

In this case they look like they cross at (1,2) and at (2,4);  and it's easy to check by substitution that these are solutions **.  But are they the only ones?

y = 2x is an increasing function, negative when x<0.

y = 2^x is also increasing but never negative.  So we can rule out any negative solutions for x.

2x increases at a steady rate (constant gradient) whereas 2^x gets steeper as x goes up.  So they will never cross again after (2,4)  when the 2^x curve crosses y = 2x with an ever increasing gradient. So  x = 1 and x = 2 are the only solutions.

Does it matter that I spotted the answer without complicated algebraic work?  Well no actually.  If you have shown a solution works and found any others and can prove you've got them all, then that's ok as a way to answer the question.

Bob

** You shouldn't assume x= 1 is the answer just from the graph.  The 'correct' answer might be x = 0.9999997.  From a graph alone you only know the answer is roughly 1 as graphs are only as accurate as your ability to draw them (thickness of the pencil; degree of accuracy with the calculator etc)

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http://www.mathisfunforum.com/profile.php?id=67694 2021-09-10T12:38:27Z http://www.mathisfunforum.com/viewtopic.php?id=26611&action=new
<![CDATA[Geometry For You]]> ]]>
http://www.mathisfunforum.com/profile.php?id=237451 2021-08-31T06:22:36Z http://www.mathisfunforum.com/viewtopic.php?id=26261&action=new
<![CDATA[Calculating Quartiles]]> Any set of data can be described by its five-number summary. These five numbers, which give you the information you need to find patterns and outliers, consist of (in ascending order). The minimum or lowest value of the dataset The first quartile Q1, which represents a quarter of the way through the list of all data The median of the data set, which represents the midpoint of the whole list of data The third quartile Q3, which represents three-quarters of the way through the list of all data The maximum or highest value of the data set.

IQR = Q3 - Q1. The interquartile range [link removed by moderator] shows how the data is spread about the median. It is less susceptible than the range to outliers and can, therefore, be more helpful.

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http://www.mathisfunforum.com/profile.php?id=236959 2021-06-07T06:38:38Z http://www.mathisfunforum.com/viewtopic.php?id=24844&action=new
<![CDATA[Testing For Functions]]> In Exercises 9 and 10, which sets of ordered pairs represent
functions from A to B? Explain.

9. A = {0, 1, 2, 3} and B = {−2, −1, 0, 1, 2}

(a) {(0, 1), (1, −2), (2, 0), (3, 2)}
(b) {(0, −1), (2, 2), (1, −2), (3, 0), (1, 1)}
(c) {(0, 0), (1, 0), (2, 0), (3, 0)}
(d) {(0, 2), (3, 0), (1, 1)}

10. A = {a, b, c} and B = {0, 1, 2, 3}

(a) {(a, 1), (c, 2), (c, 3), (b, 3)}
(b) {(a, 1), (b, 2), (c, 3)}
(c) {(1, a), (0, a), (2, c), (3, b)}
(d) {(c, 0), (b, 0), (a, 3)}

NOTE: THIS IS EXTRA PRACTICE FOR MEMBERS. I AM NOT ASKING FOR HELP WITH 9 AND 10.

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http://www.mathisfunforum.com/profile.php?id=223890 2021-05-13T07:04:49Z http://www.mathisfunforum.com/viewtopic.php?id=26260&action=new
<![CDATA[Find Distance Between Points]]> Not Dav wrote:
mathland wrote:

Find the distance between the points.

17. (−2, 6), (3, −6)

18. (8, 5), (0, 20)

19. (1, 4), (−5, −1)

20. (1, 3), (3, −2)

21. (1/2, 4/3) (2, −1)

22. (9.5, −2.6), (−3.9, 8.2)

___________________
would the formula be √ (x1 - x2)² + (y1 -y2)²    ? edit: oop the link already said so

I posted the problems as extra practice for members.

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http://www.mathisfunforum.com/profile.php?id=223890 2021-05-13T07:00:40Z http://www.mathisfunforum.com/viewtopic.php?id=26124&action=new
in which (x, y) could be located.

9. x > 0 and y < 0

10. x < 0 and y < 0

11. x = −4 and y > 0

12. x < 0 and y = 7

13. x + y = 0, x ≠ 0, y ≠ 0

14. xy > 0

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http://www.mathisfunforum.com/profile.php?id=223890 2021-04-22T08:11:41Z http://www.mathisfunforum.com/viewtopic.php?id=26122&action=new
<![CDATA[find area]]> Now knowing the radius, here are 2 methods for finding the area of the shaded region:

In the formulas...
r = the radius of the circumscribed circle
i = the radius of the respective inscribed circle
s = the sagitta of the respective circular segment

Method A (Area of circular segments minus area of inscribed circles)
1. Total area of the 3 circular segments = 481.49203......respective segment areas = r²ArcCos((r - s)/r) - (r - s)√(2rs - s²)
2. Total area of the 3 inscribed circles R, M & L = 175.92919......respective circle areas = πi²

481.49203
- 175.92919
------------
=======

Method B (Area of circumscribed circle minus areas of inscribed objects)
1. Area of circumscribed circle = 756.47691......πr²
2. Total area of the 3 inscribed circles R, M & L = 175.92919......respective circle areas = πi²
3. Area of triangle ABC, using Heron's Formula on the 3 circular segment chord lengths AB, AC & BC = 274.98488......respective chord lengths = 2√(2sr - s²)

756.47691
- 175.92919
- 274.98488
------------
=======

Edit: I first had Method B as my only method (same as the one in my post #5), but then discovered Method A.

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http://www.mathisfunforum.com/profile.php?id=40741 2021-02-20T01:32:00Z http://www.mathisfunforum.com/viewtopic.php?id=26016&action=new
<![CDATA[puzzle by Xodus]]> I am not yet claiming that is the lowest 'n'.  Still working on it.
http://www.mathisfunforum.com/misc.php?action=rules

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http://www.mathisfunforum.com/profile.php?id=222445 2020-08-06T09:11:57Z http://www.mathisfunforum.com/viewtopic.php?id=25773&action=new
<![CDATA[Statistics]]> Could you(i.e Zeeshan 01) take a look at some statistical concepts and their definitions? This is NOT a "we solve your problems, no strings attached~~" kind of deal, this is a "do your work and we'll help ya out." subforum..

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http://www.mathisfunforum.com/profile.php?id=188456 2020-06-11T15:43:36Z http://www.mathisfunforum.com/viewtopic.php?id=25708&action=new
<![CDATA[Integration by Substitution]]> Zhylliolom wrote:

Hi,

I wasn't able to solve this using substitution, but here's a solution I came up with:

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http://www.mathisfunforum.com/profile.php?id=118786 2020-05-17T00:07:35Z http://www.mathisfunforum.com/viewtopic.php?id=4208&action=new
<![CDATA[..find X]]> Ahhh, I see it now! Thanks, Bob! ]]>
http://www.mathisfunforum.com/profile.php?id=118786 2020-05-16T19:27:38Z http://www.mathisfunforum.com/viewtopic.php?id=25644&action=new
<![CDATA[Measure Theory]]> zetafunc wrote:

#4

Hi,

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http://www.mathisfunforum.com/profile.php?id=118786 2020-05-15T20:34:26Z http://www.mathisfunforum.com/viewtopic.php?id=23094&action=new