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Answer to #24:-
You're right, JaneFairfax!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#26. What is the value of
#27. What is the value of log tan1° + log tan2° + log tan3° + log tan4° + ....log tan 89°
#28. What is the value of
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#29. Decompose into partial fractions:-
.#30. If p and q are the roots of the equation x²+8x = -15, form the equation whose roots are (p+q) and 3pq.
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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Answer to #30:-
Excellent, JaneFairfax! You're right again!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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JaneFairfax,
Did you see the solution to Problem #17? (Post #49 on Page 2)
Do you agree with my answer?
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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When you worked out the area of the parallelogram, you use its slant height instead of its perpendicular height and so your answer is larger than the actual area.
I get the area of the trapezium to be the same as Jane's 3rd attempt.
Why did the vector cross the road?
It wanted to be normal.
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Oops!
That was a stupid mistake!
Thanks, mathsyperson, for correcting me!
I am sorry Jane, I said your last attempt was wrong too!
I shall be more careful while checking the answers!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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Answer to #27:-
Absolutely right, JaneFairfax!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#31. A person covers the distance from P to Q at the speed of 3 kilometers per hour. From Q to P, he covers the distance at 6 kilometers per hour. What is the average speed per hour?
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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Last edited by JaneFairfax (2009-01-09 08:52:38)
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Answer to #31:-
You are correct, JaneFairfax!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#32. Find the value of
#33. Find the value of x if
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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Answer to #33:-
You are correct, JaneFairfax!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#34. Which is the largest number each number of the sequence is divisible by?
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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Answer to #34:
(1) The question has been modified. I didn't notice what meaning the question conveyed while posting, sorry!
(2) I have a proof that every number of the form
It can be seen that the last digit of
is always 0 or 5, which means it is a multiple of 5.It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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For proving that
is always divisible by 5
Either
or .If
then clearly .If
, then by Fermats little theorem.In that case,
.Hence
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Thanks, JaneFairfax!
That has made things a lot more clearer to me!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#35. What is the value of xyz if
#36. What is the value of z if
andIt is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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Answer to #35:-
You are correct, JaneFairfax!
Your point is fully acceptable.
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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To JaneFairfax:
It occured to me that, as mentioned by you in post #70, if n is a multiple of of 5,
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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