<![CDATA[Math Is Fun Forum / Exercises]]> 2020-06-05T10:49:36Z FluxBB http://www.mathisfunforum.com/index.php <![CDATA[Compute the solution:]]> Hi 666 bro,

Excellent!

676. Find two consecutive positive integers, sum of whose squares is 365.

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http://www.mathisfunforum.com/profile.php?id=682 2020-06-05T10:49:36Z http://www.mathisfunforum.com/viewtopic.php?id=21675&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
<![CDATA[log equation]]> Hi,

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http://www.mathisfunforum.com/profile.php?id=118786 2020-05-15T19:47:27Z http://www.mathisfunforum.com/viewtopic.php?id=24702&action=new
<![CDATA[find area]]> hi Tony,

Eek! That's an evil looking question.  I'm assuming that the outer shape must be a quadrilateral otherwise the midpoint information is meaningless.  I am not assuming the shape is either a square or a rectangle.

Thanks for the puzzles.  Still working on the other one.

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2020-04-30T14:10:28Z http://www.mathisfunforum.com/viewtopic.php?id=25643&action=new
<![CDATA[find AB]]> Hi Bob;

Thanks, that works perfectly well...and nice proof! The formula solves AB for a range of BMs (can be non-integer) without using the 3:4:5 triangle rule. LK is always 3. ]]>
http://www.mathisfunforum.com/profile.php?id=40741 2020-04-23T15:51:26Z http://www.mathisfunforum.com/viewtopic.php?id=25581&action=new
<![CDATA[Find all pairs (x,y)]]> Thanks,

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2020-03-30T09:08:54Z http://www.mathisfunforum.com/viewtopic.php?id=25567&action=new
<![CDATA[ordered pair]]> hi

I'm getting

Thanks for the puzzles.

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2020-03-30T09:05:39Z http://www.mathisfunforum.com/viewtopic.php?id=25569&action=new
<![CDATA[the areas]]> hi tony123

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2020-03-30T08:24:15Z http://www.mathisfunforum.com/viewtopic.php?id=25568&action=new
<![CDATA[Complex Numbers 1]]> Solution #k is 0+i

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http://www.mathisfunforum.com/profile.php?id=220123 2020-01-15T14:38:38Z http://www.mathisfunforum.com/viewtopic.php?id=4268&action=new
<![CDATA[Calculus MCQS IMPORTANT]]> hi Zeeshan 01

Haven't heard from you for a while.  You seem to have made good progress if you are on to topics like these.  Well done!

There's no need to put the word IMPORTANT into your titles.  I treat all requests for help as equally important and try to help if I can.

Question 5 : if the two vectors are A=3i+4j+k   and B=i-j+k then

a)They are orthogonal   b) orthonormal   c) antiparallel   d) none

Question 9 :   The angle between Vectors   -2i+3j+k  and i+2j-4k is
a) 0 degree           b)  90 degree    c) 180 degree

Two vectors, A and B are parallel if there is a constant, k,  such that A = kB.  If k is positive then the vectors go in the same direction so the angle between them is 0.  If k is negative then they go in opposite directions, so I suppose you could say the angle between them is 180, although I've never met this in a question before.

If the dot (or scalar) product is 0, then they are at right angles, so the angle between them is 90.  Orthogonal is just another way to say this.  If the vectors are orthogonal and unit vectors then they are orthonormal.  Use Pythagoras to determine whether they are unit vectors.

Question1 : if the function fxx(x0,y0)>0 then f has a ------ at (x0,y0)
a) Relative minima     b) relative maxima  c) saddle point    d) none

I don't understand the notation here 'fxx'.  Did you mean f(x,y) ?  If so then none of the answers can be chosen since any could be true.  If 'fxx' means the double differentiated functions then, as with the 2D case, this would be a local minimum.

Question 8 :    If function fxx(x0,y0)=0 then f has a -----  at (X0,y0)
a) relative minima        b ) relative maxima   c) saddle point

This seems to be the same question again.

Question2 : if phi=2xz^4-  (x^2y) , the |delta phi | at point (2,2,-1) is
a) 2sqrt93     b) sqrt 372  c) 2sqrt91    d) both a and b

Sorry, what does ' the |delta phi | ' mean?

Question 3 : if y=f(x) has continuous derivatives on [a,b] and s denotes the length of arc between the lines x a and x  b then

Question incomplete.

Question 4 :  arc length s=integral a to b   sqrt(r^2+(dr/d thetha)^2 ) d thetha is called

a) Rectangular Coordinates   b)  polar coordinates   c ) spherical coordinates   d) none

Is thetha meant to be θ ?  That looks like polar coordinates r and θ to me.  I don't think spherical as another angle would be required.

Question 6:  If phi =1/(r^2)   then (delta)^2  phi is

What does '(delta)^2 ' mean?
a) 1                         b) -1                c) 0          d)1/(r^2)

Question 7:   If f(x,y)=1 throughout the region D then I=integral integral dx dy represents

a) Volume   b) Arc        C)  bounded below          d) bounded above

Imagine a 3D graph with x,y in the horizontal plane and z values above.  If f is constant then the graph of f is a plane parallel to the x,y plane, one unit higher in the xz direction.  If you integrated in 2 directions you would get the volume below the graph.

Please post back clarifying questions 2,3 and 6.

Bob

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http://www.mathisfunforum.com/profile.php?id=67694 2019-12-30T10:34:46Z http://www.mathisfunforum.com/viewtopic.php?id=25429&action=new
<![CDATA[Calculus MCQS IMPORTANT [Part 2]]]> Answer

Question 6:  If phi =1/(r^2)   then (delta)^2  phi is

a) 1                         b) -1                c) 0          d)1/(r^2)

Question 7:   If f(x,y)=1 throughout the region D then I=integral integral dx dy represents

a) Volume   b) Arc        C)  bounded below          d) bounded above

Question 8 :    If function fxx(x0,y0)=0 then f has a -----  at (X0,y0)

a) relative minima        b ) relative maxima   c) saddle point

Question 9 :   The angle between Vectors   -2i+3j+k  and i+2j-4k is

a) 0 degree           b)  90 degree    c) 180 degree

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http://www.mathisfunforum.com/profile.php?id=212808 2019-12-29T19:24:45Z http://www.mathisfunforum.com/viewtopic.php?id=25430&action=new
<![CDATA[Probability and Statistics]]> There are 9*10=90 possible combinations. There are 3*4=12 possible prime number combinations: (2,3), (2,5), (2,7), (3,2), (3,5), (3,7), (5,2), (5,3), (5,7), (7,2), (7,3), (7,5). The probability is 12/90=2/15.

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http://www.mathisfunforum.com/profile.php?id=212090 2019-10-18T11:42:32Z http://www.mathisfunforum.com/viewtopic.php?id=25273&action=new