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Q: What does flowery Leo call himself?

A: A dandy lion!

I think it’s called a stereoscopic Klein bottle.

I got two values of *m*:

– neither of which is among your multiple choices. Are you sure you haven’t made a typo copying the question?

*x* = 1 − *my* into the quadratic expression. If the line is tangent to the circle, this should be a perfect square. Complete the square (or otherwise) and solve for *m*.

Monox D. I-Fly wrote:

A.

B.

C.

D.

E.

The only one of these that has the point (6,0) lying on it is B – so that must be the answer. No need for any working.

See? If you use your brain a little bit more, you can save yourself a whole lot of time and hard work for nothing.

Also try

**Mathologer**– https://www.youtube.com/channel/UC1_uAI … JjXWvastJg.

The creator is a mathematics professor at Monash University, Melbourne; the channel is full of fun facts about various interesting everyday mathematical objects. I like the way he explains things step by step leading you from simple, easy-to-understand ideas to more complicated themes. In one video, he tries to explain why the infinite sum

as derived by some string-theory physicists (who have absolutely no clue what they’re doing) is wrong. It turns out that what they are doing is evaluating the Riemann zeta function at the point −1 – this function being the complex analytic continuation of the Dirichlet series. Now, most people, including the proverbial man in the street, know what sums are, even infinite sums. But what is analytic continuation? Dirichlet series? Riemann zeta function? Follow the explanation given by the creator of this channel to find out.

The area between two curves is always the integral of the top curve minus the bottom curve. It doesn’t matter if part or all of this area is below the *x*-axis: as long as you take the top curve minus the bottom curve and integrate, the result is always positive.

Take these examples:

They are plotted here. Find the area bounded by them and their points of interesection. Notice that this area is wholly below the *x*-axis. However the definite integral

is positive; this is the area required.

A: Hung(a)ry.

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Q: Which country do birds love?

A: Turkey.

***

Q: Which is the most musical country in the world?

A: Sing-apore.

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Q: Which country can hurt you the most?

A: S-pain.

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Q: Which is the dirtiest country in the world?

A: Germ-any.

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Q: Which two countries are the laziest in the world?

A: Slo(w)vakia and Slo(w)venia.

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Q: Which country has the most oil?

A: Greece. (=“Grease”.)

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Q: In which countries do pirates live?

A: Arrr-gentina and Arrr-menia.

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Q: Which country is home to one of the Teletubbies?

A: Poland.

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Q: What do you call a stupid person from Rio de Janeiro?

A: A Brazil nut!

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Q: What do people in one Central American country say to each other at Christmas?

A: Belize Navidad! (≈“Feliz Navidad¨.)

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**Alg Num Theory**- Replies: 1

Q: What is the coldest country in the world?

A: Chile. (=“Chilly”.)

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Q: What is the hottest country in the world?

A: Chile. (=“Chilli”.)

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7. The actress Charlotte Lucas shares her name with a character in the novel *Pride and Prejudice* by Jane Austen.

8. George Osborne, Chancellor of the Exchequer of Britain from 2010 to 2016, shares his name with a character in the novel *Vanity Fair* by William Makepeace Thackeray.

9. The actress Anne Hathaway shares her name with the wife of William Shakespeare (and may even have been named after her).

*y*-axis shouldn’t come into the question: it should just be area bounded by the two curves and the line *x*=3. I agree with Bob: the question is not very well stated.

IMHO the area required is just A. To calculate this, we need to know area C so we can subtract it from A+C.

Let’s calculate A+C. It’s

Area C is

Hence area A is

Hmm, I get a different answer myself.

Any time.

zetafunc wrote:

The question as it stands has no answer (the area would be infinite). There is probably a typo in the question.

The question makes perfect sense and there is a perfectly good answer.

So, noting that the function is negative between 0 and 1 and positive between 1 and 2, the area should be

The dot product of two vectors depends (as far as angles are concerned) only on the cosine of the angle in between. Since

it doesn’t matter whether we take the larger or smaller angle between them. Also, as

it doesn’t matter whether we measure the angle clockwise or counterclockwise – only the angular magnitude is important. Hence, whether **w** lies between **u** and **v** (i.e. passes through the smaller angle between them) or not is not really important: we can always take theta to be the smaller angle between **u** and **w**, and phi the smaller angle between **v** and **w**.

Does it matter?

Alg Num Theory wrote:

If the coefficients were

rational, then the statement would be true.

In general, if the coefficients are rational and one root is an irrational surd, then the other root must be the conjugate surd. This is not true if the coefficients can be irrational as well as rational.

Why do you want to consider the angle between two vectors to be reflex?

Mathegocart wrote:

If the coefficients of a quadratic equation are real, and if one of the roots is (1-sqrt(3)), the other root

mustbe (1+sqrt(3)).

TRUE?

FALSE?

If the coefficients were *rational*, then the statement would be true. It’s false if you allow the coefficients to be irrational, as the replies below your post show.

If the coefficients are real and one of the roots is complex (and non-real), then the other root must be the complex conjugate. This statement also fails if you allow the coefficients to be complex.

Take two.

Sorry, I made a mistake. See my revised post below.

If you can’t imagine, then don’t – just try the calculations and see for yourself!

*can* do it this way, but it could involve too many calculations and therefore might not be useful in practice. In this example, you would have to calculate the probability of exactly 2 people sharing a birthday, of exactly 3 sharing a birthday, 4 sharing a birthday, and so on, and add them all up – too much work, wouldn’t you agree? Much simpler to just calculate the probability for no shared birthday and subtract from 1.