<![CDATA[Math Is Fun Forum / Exercises]]> 2022-01-20T12:02:14Z FluxBB https://www.mathisfunforum.com/index.php <![CDATA[Compute the solution:]]> Hi,

1174.

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https://www.mathisfunforum.com/profile.php?id=682 2022-01-20T12:02:14Z https://www.mathisfunforum.com/viewtopic.php?id=21675&action=new
<![CDATA[Find the real solutions]]> Now we can say great job
Thanks bob

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https://www.mathisfunforum.com/profile.php?id=8775 2022-01-20T09:18:25Z https://www.mathisfunforum.com/viewtopic.php?id=27003&action=new
<![CDATA[congruent]]> nice work
thanks Bob

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https://www.mathisfunforum.com/profile.php?id=8775 2022-01-10T19:40:09Z https://www.mathisfunforum.com/viewtopic.php?id=27000&action=new
<![CDATA[solve equation]]> hi zetafunc and tony123,

Thanks for providing me with ways to do this.

Bob

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https://www.mathisfunforum.com/profile.php?id=67694 2022-01-08T10:57:39Z https://www.mathisfunforum.com/viewtopic.php?id=26982&action=new
<![CDATA[X / 5 + (5x10-45)]]> Well done ganesh

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https://www.mathisfunforum.com/profile.php?id=238506 2022-01-03T11:33:57Z https://www.mathisfunforum.com/viewtopic.php?id=26969&action=new
<![CDATA[About the Exercises]]> I find arranging new things very fascinating. That is because back in my time, it was everything to be done by yourself. Thus, most of us did not consider doing all the hard work for a little pleasure. Having short math exercises is always fun. The best thing I remembered was solving different word problems from a dedicated book. And this was around ten years ago. Back then, technology was not as such as it is now. Technology has advanced so much that creating such exercises is easy and accessible.
Thus, I love the idea of generating creative and indulging short exercises regarding math concepts such as algebra, basic word problems, trigonometry, etc. However, there is one thing which we need to adapt, and that comes from the idea of websites. They have everything arranged in different sections for easy identification. Thus, having math problems, we must arrange them in specific sections only; thus, people easily begin an exercise knowing where their interest and strength lies.

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https://www.mathisfunforum.com/profile.php?id=238300 2021-12-16T14:04:37Z https://www.mathisfunforum.com/viewtopic.php?id=3941&action=new
<![CDATA[Integration by Substitution]]> gAr wrote:

Hi,

Next integral:

hi gar

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https://www.mathisfunforum.com/profile.php?id=118786 2021-12-11T14:11:06Z https://www.mathisfunforum.com/viewtopic.php?id=4208&action=new
<![CDATA[prove]]> Let
and
be acute angles such that
. Prove that
.

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https://www.mathisfunforum.com/profile.php?id=8775 2021-12-03T13:31:16Z https://www.mathisfunforum.com/viewtopic.php?id=26830&action=new
<![CDATA[In an acute-angled]]> hi tony123

Thanks for another interesting puzzle.

Bob

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

Bob

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https://www.mathisfunforum.com/profile.php?id=67694 2021-11-07T08:46:42Z https://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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https://www.mathisfunforum.com/profile.php?id=67694 2021-09-10T12:38:27Z https://www.mathisfunforum.com/viewtopic.php?id=26611&action=new
<![CDATA[Geometry For You]]> ]]>
https://www.mathisfunforum.com/profile.php?id=237451 2021-08-31T06:22:36Z https://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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https://www.mathisfunforum.com/profile.php?id=236959 2021-06-07T06:38:38Z https://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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https://www.mathisfunforum.com/profile.php?id=223890 2021-05-13T07:04:49Z https://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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https://www.mathisfunforum.com/profile.php?id=223890 2021-05-13T07:00:40Z https://www.mathisfunforum.com/viewtopic.php?id=26124&action=new