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Hi Βεν,
Welcome to the forum! Thanks for your contribution. That looks like a nice list. Some comments:
a^n=a multiplied by itself n times
If n is even then (-a^n)=a^n
a^n÷a^m=a^(m-n) (Makes sense right?)
If n>0 then (a^m)na=a^(m+n)
What did you mean here?
Hi zahlenspieler,
I have fixed your LaTeX.
Hi math9maniac,
Can I just check that the equation you wrote down is correct?
Hi vipin_sharma,
Welcome to the forum. Here's a hint:
Hi niravashah,
Thanks for posting this. Have you considered creating an account with us?
For reference, the sequence is:
4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6,
and we're asked to find the next two terms. Perhaps this will give you a hint:
4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6,
Good to hear -- welcome to the forum!
Draw a Venn diagram with 3 overlapping circles, labelling the four bits that overlap as A, B, C, D.
The information given in the question then allows you to form some equations for A, B, C and D. Can you see how?
Ok, but I wasn't looking for a proof with the answers in the beginning. I've gotten pretty far, but I need to find all the answers to
EDIT: With a rigorous demonstration that this is the answer.
Hi Stuti55,
Welcome to the forum.
Hi Zeeshan,
I've moved your thread to the Help Me ! forum.
Have you checked out Maths Is Fun's page on long division?
Hi Anduin,
Welcome to the forum. What features does the graph y = sin(x) have? How do they compare to the graphs y = 2sin(x) and y = 3sin(x)?
Hello,
I noticed that you've posted several times here as a guest. Why not register an account with us?
What have you tried? What sorts of restrictions do you think you can place on x and y?
Hi Zetafunc, if there are duplicate roots of a polymolial you should counts them as distinct roots.
Why? Precisely the opposite is true: if a root is repeated, then we cannot call those repeated roots 'distinct', and whether or not we count them in the same way we would distinct roots depends on the context.
For example, if you say that a give polynomial has “exactly” the roots -3, 4 and 8 that means there is no duplicate roots.
I am not convinced that the word 'exactly' necessarily implies distinctness -- I would have thought that the multiplicities were worth consideration, otherwise the problem appears to be a little simplistic.
The answer for part 1 is, by all means, yes. This is so because the condition that f(x) has the zeros -3,4 and 8 entails that:
f(x)=(x+3)×(x-4)×(x-8)
And since the zeros of g(x) are -5,-3, 2, 4 and 8 we also have:
g(x)=(x+5)×(x+3)×(x-2)×(x-4)×(x-8)
and hence:
g(x)/f(x)=[(x+5)×(x+3)×(x-2)×(x-4)×(x-8)]/[(x+3)×(x-4)×(x-8)]=(x+5)×(x-2)
and since the result of the division (x+5)×(x-2) is a polynomial without a remainer, therefore g(x) is divisible by f(x). The answer of part 2 is very clear from the answer of part 1. For a polynomial g(x) to be divisible by a polynomial f(x) at least all the roots (zeros) of f(x) should be also roots (zeros) of g(x). And the final statement completes the answer.
The denominator will not be 36. Remember: you want to restrict the number of possible outcomes to include only those that have a '5' in them.
The question as it stands has no answer (the area would be infinite). There is probably a typo in the question.
In particular, the second pair of brackets in the second line and the first pair of brackets in the third line are not correct.
However, the question appears to be badly worded. The area 'bounded' by the curve, the axes and the line x = 2 is not bounded at all -- it is infinite.
Yes, that is correct.
Yes -- do you know how to calculate this?
One way is to use the binomial distribution.
Suppose that represents the number of times that the goalkeeper saves a penalty. Then, has a binomial distribution: You want to calculate . Do you see why?Hi MellyBigD,
Welcome to the forum. You have posted 4 threads asking for help, but you have not shown any attempts at the problems or given any pointers about where you are stuck. We will endeavour to help you as best you can, and we happily volunteer our time to do so, but we will not do your homework for you. Can you please show some attempts at these problems, or be specific about what exactly you are stuck on?