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#1 Re: Exercises » Mathematical Induction » 2018-07-15 20:35:17

What do you mean by why is n term not 2n−1?

Since the thread title is mathematical induction, I take it you want to prove the formula for the sum of the first n odd positive integers. To do this, you need to know what the formula is in the first place. If you’re not given the formula, you can make a guess and then proceed to prove it. So, trying the first few sums …

I think you can make a guess as to what the formula is going to be.

#2 Re: Exercises » Quadratic » 2018-07-15 00:12:13

I presume ɑ and β are the roots, which are complex. Since we are going to deal with their powers, best to convert them to cos–sin form:

So the roots are

one of them is ɑ, the other is β. Since the question doesn’t say which is which, you may as well take your pick. Now use De Moivre’s theorem.

#4 Re: Help Me ! » Division » 2018-07-04 21:59:22

Do the long division yourself!

#5 Re: Puzzles and Games » [ASK] Exact Measure Using 2 Bottles » 2018-07-04 20:35:26

By the way, this thread is better in the Puzzles and Games section.

#6 Re: Help Me ! » Division » 2018-07-04 20:28:34

Zeeshan 01 wrote:

Do that division, given in https://www.mathsisfun.com/long_division.html

Alg Num Theory wrote:

I’m not doing your homework for you. You do it yourself.

#7 Re: Help Me ! » Division » 2018-07-03 10:14:23

In problems like this, the first thing to is to reduce the fraction to its lowest terms:

so you’ll be doing the following long division:

If the denominator ends with one or more 0, you can shift the decimal point in the numerator to get rid of the 0:

giving

#8 Re: Help Me ! » Division » 2018-07-02 08:55:25

I’m not doing your homework for you. You do it yourself.

#9 Re: Help Me ! » Division » 2018-07-02 05:19:07

Go on, then. Use long division.

#13 Re: Jokes » Country jokes » 2018-06-17 17:30:58

Q: Why is the Northeast of England is so old and broken down?
A: Because it has aged with Tyne and is now the worse for Wear!

#14 Re: Help Me ! » Sequences » 2018-06-16 23:11:58

Bob, I think r=0 is also possible for (a).

For (b), I think the answer is all nonnegative integers. Clearly there are infinite geometric sequences with no integers, e.g.

If r = 1, add 1 as the first term to the above sequence.

If r > 1, then

is an infinite geometric sequence (common ratio 1/r) with exactly r integer terms (the first r of them).

#15 Re: Exercises » highest position » 2018-06-02 23:20:53

Let the insect’s speed along the minute hand be v. After time t, the insect has moved a distance vt from the base of the hand and so its height h above the horizontal through the centre of the clock face is given by

(note that the angular velocity of the minute hand is 2π/(60×60) radians per second). Differentiate:

Set to to 0:

This equation can’t be solved analytically; using Wolfram|Alpha, I get t ≈ 493 seconds = 8 minutes 13 seconds, i.e. the insect is at its highest position at 12:08:13.

Check that d²h/dt² < 0 so that this is indeed a maximum value.

#16 Re: Help Me ! » Conditional Statements and Venn Diagrams » 2018-06-01 08:09:20

3. The statement is: “If something is a dog, then it is a mammal.” This is of the form pq where p is the statement “something is a dog” and q is the statement “it is a mammal”. So what do you think the statement “if something is not a dog, then it is not a mammal” should be? (Hint: It is not A or D.)

7. Did you make a typo in the following?

riaaaa wrote:

"If x2>10, then x>0."

As it stands, that question doesn’t make sense.

13. Hint: What is the inverse of the given statement? Write it down and think about it.

#17 Re: Help Me ! » Number series » 2018-05-30 04:25:17

Sorry, I made some typos in my formula. I’ve edited my post and fixed it now.

#18 Re: Jokes » Bird Jokes : Questions and Answers » 2018-05-29 08:26:34

Q: What is the favourite sitcom of ducks?
A: You Rang, Mallard?!

#19 Re: Help Me ! » Number series » 2018-05-29 08:24:28

I actually used Wolfram to simplify the following expression (which I had to do in two stages as it was too long for the software to process in one go):

#20 Re: Help Me ! » Number series » 2018-05-28 12:13:56

phrontister wrote:

No doubt there's a solution much closer to the surface that is simply staring me in the face, but which I'm blind to! faint

#21 Re: Help Me ! » Long division on these polynomials? » 2018-05-27 00:13:19

That’s because the degree of the numerator polynomial is less than that of the denominator polynomial. Maybe you want to divide the latter by the former?

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