tutoring thread

[GMJ]

Well the first one is the same as (sin x)^3(tan4x)</p>

So start off with a product rule, and then once you get to the derivative of the first use a chain rule. Remember to put a '4' in front of everything, as that comes from the derivative of 4x once you do the chain rule on the tan term.</p>
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</p>

Same as the second one. Start off with a quotient rule, and then chain the denominator once you get there. Remember that the square root is the same as raising something to the (1/2) power. So then when you do the power rule, you'll bring the (1/2) down, subtract 1, and the power will be (-1/2)</p>
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The third one just looks like a pain in the ass chain rule. Just keep plugging along</p>

</p>

 

[lukewarmplay]

<div class='quotetop'>QUOTE (GMJigga)</div><div class='quotemain'></p>

Well the first one is the same as (sin x)^3(tan4x)</p>

So start off with a product rule, and then once you get to the derivative of the first use a chain rule. Remember to put a '4' in front of everything, as that comes from the derivative of 4x once you do the chain rule on the tan term.</p>
<hr width="100%" size="2" />

</p>

Same as the second one. Start off with a quotient rule, and then chain the denominator once you get there. Remember that the square root is the same as raising something to the (1/2) power. So then when you do the power rule, you'll bring the (1/2) down, subtract 1, and the power will be (-1/2)</p>
<hr width="100%" size="2" />

The third one just looks like a pain in the ass chain rule. Just keep plugging along</p>

</p>

</div></p>

The 2nd one doesn't need the quotient rule. Just think of it as 1/3 times (whatever)^(-1/2)</p>

</p>

 

[JCB]

Yea, I avoid the quotient rule whenever possible.</p>

 

[lukewarmplay]

<div class='quotetop'>QUOTE (chingy0007)</div><div class='quotemain'></p>

Here's a few for you to try, from my practice British Mathematical Olympiad papers (non-calculator):</p>

1. Let n be an integer greater than 6. Prove that if n-1 and n+1 are both prime, then n^2(n^2+16) is divisible by 720. Is the converse true?</p>

2. Adrian teaches a class of six pairs of twins. He wishes to set up teams for a quiz, but wants to avoid putting any pair of twins into the same team. Subject to this condition:
i) In how many ways can he split them into two teams of six?
ii) In how many ways can he split them into three teams of four?</p>

3. In the cyclic quadrilateral ABCD, the diagonal AC bisects the angle DAB. The side AD is extended beyond D to a point E. Show that CE=CA if and only if DE=AB.</p>

4. The equilateral triangle ABC has sides of integer length N. The triangle is completely divided (by drawing lines parallel to the sides on the triangle) into equilateral triangular cells of side length 1.
A continuous route is chosen, starting inside the cell with vertex A and always crossing from one cell to another through an edge shared by the two cells. No cell is visited more than once. Find, with proof, the greatest number of cells which can be visited.</p>

5. Let G be a convex quadrilateral. Show that there is a point X in the plane of G with the property that every straight line through X divides G into two regions if and only if G is a parallelogram.</p>

6. Let T be a set of 2005 coplanar points with no three collinear. Show that, for any of the 2005 points, the number of triangles it lies strictly within, whose vertices are points in T, is even.</p>

That is one full paper, that you get 3 1/2 hours to do. We were told that we would be doing very well if we manage to answer 2.</p>

Two more from another paper:</p>

1. Find four prime numbers less than 100 which are factors of 3^32 - 2^32.</p>

3. The number 916238457 is an example of a nine-digit number which contains each of the digits 1 to 9 exactly once. It also has the property that the digits 1 to 5 occur in their natural order, while the digits 1 to 6 do not. How many such numbers are there?</p>

</div></p>

I feel like I could do 1 from the first one, and the last 2. But that's just a hunch.</p>

Anybody seen the Joy of Mathematics DVD's?</p>

</p>

 

[GMJ]

cowards! haha but yeah, that would be easier.</p>

 

[GMJ]

Actually, no its not. if you separate the 3 out you're still left with 1 over the denominator. You could do the quotient rule, or use a chain rule if you convert 1/ denom to denom^-1</p>

 

[bbwMax]

doing a 4000 word Essay on how the Communist Governments maintained control over the Eastern states. Not really Stuck on it just thought i'd mention it. I've decided that instead of Cramming it for 2-3 hours i'd rather take 4-5 hours and put the odd post on here to Cool my brain down</p>

 

[pegs]

I'd rather do essays than math problems, at this point. Always felt that way, too. Why did I go into computer science again?</p>

 

[Денг Гордон]

A circle of radius 2 and center (0,0) can be parametrized by the equations x = 2 cost t and y = 2 sin t. Show that for any value t, the line tangent to the circle at (2 cos t, 2 sin t) is perpendicular to the radius.</p>

How the hell do you prove that?</p>

 

[GMJ]

not sure what parametrized means (perhaps that those equations form part of the circle?)</p>

The line perp. to the radius is the derivative, so I would try finding the deriviative to each equation and seeing where you go from there</p>

 

[Денг Гордон]

<div class='quotetop'>QUOTE (GMJigga)</div><div class='quotemain'></p>

not sure what parametrized means (perhaps that those equations form part of the circle?)</p>

The line perp. to the radius is the derivative, so I would try finding the deriviative to each equation and seeing where you go from there</p>

</div></p>

Parametrized means that the function has a parameter, which is time. (t).</p>

I'll try that, that assignment is like a week and a half late now.</p>

</p>

 

[GMJ]

Oh, as in 0<t<=x?</p>

Reading it again, I think the key is the point they give you the point (2 cos t, 2 sin t).</p>

The derivative will be perpendicular to the radius, if it lies on the circle (definition of circle, and derivative)</p>

So you have to prove that the point is on the circle within 0<t<=x</p>

So take the derivative of the cos and sin functions. They should equal each other. Boom; proved</p>

edit: to prove equality use x=2</p>

 

[lukewarmplay]

Parametrization is another way of defining a graph- especially one that can't be defined as a function (the way that a circle isn't really a function, since you have two y's for each x). It's kind of weird to go from the chain rule to parametrization- what class is this?</p>

The slope of the tangent line is dy/dt over dx/dt which I assume you already know. Once you get the slope, all you have to do is show that this is the negative reciprocal of the slope of the radius, right?</p>

 

[GMJ]

<div class='quotetop'>QUOTE (lukewarmplay)</div><div class='quotemain'></p>

Once you get the slope, all you have to do is show that this is the negative reciprocal of the slope of the radius, right?</p>

</div></p>

Good call. You can find the slope by using (2, 2cos(s)), and (0,0) as the other point</p>

</p>

 

[Master Shake]

I'll start helping in this thread when you guys have questions about sex ed.</p>

 

[Kid Chocolate]

<div class='quotetop'>QUOTE (Master Shake)</div><div class='quotemain'></p>

I'll start helping in this thread when you guys have questions about sex ed.</p>

</div></p>

</p>

Which hole?</p>

Why am I even asking, I KNOW the answer is the butthole.</p>

</p>

 

[Master Shake]

<div class='quotetop'>QUOTE (Kid Chocolate)</div><div class='quotemain'></p>

<div class='quotetop'>QUOTE (Master Shake)</div><div class='quotemain'></p>

I'll start helping in this thread when you guys have questions about sex ed.</p>

</div></p>

</p>

Which hole?</p>

Why am I even asking, I KNOW the answer is the butthole.</p>

</p>

</div></p>

</p>

If you're Greek, then yes. If you aren't, then maybe not.</p>

 

[GMJ]

<div class='quotetop'>QUOTE (Kid Chocolate)</div><div class='quotemain'></p>

Why am I even asking, I KNOW the answer is the butthole.</p>

</p>

</div></p>

That's the safe guess, like picking 'C' on a multiple choice exam</p>

</p>

 

[Денг Гордон]

I have this problem....</p>

</p>

Let f(x)= cos x + 3x</p>

Show that f has a differentiable inverse</p>

Find f(0) and f ' (0)</p>

Find f^-1 (1) and (f^-1)'(1)</p>

For part c, what is that? Is that just making the cos, into cos^-1 x ???</p>

 

[o.iatlhawksfan]

It's 5^2.5</p>

=)</p>

 

[lukewarmplay]

<div class='quotetop'>QUOTE (BG7 Lavigne)</div><div class='quotemain'></p>

I have this problem....</p>

</p>

Let f(x)= cos x + 3x</p>

Show that f has a differentiable inverse</p>

Find f(0) and f ' (0)</p>

Find f^-1 (1) and (f^-1)'(1)</p>

For part c, what is that? Is that just making the cos, into cos^-1 x ???</p>

</div></p>

no, it's asking you to find the inverse at 1 and the derivative of the inverse at 1. what is the inverse, if you don't mind sharing?</p>

</p>

 

[lukewarmplay]

might as well post this here as anywhere:puzzle.arpatubes.net/</p>

 

[Kid Chocolate]

<div class='quotetop'>QUOTE (lukewarmplay)</div><div class='quotemain'></p>

might as well post this here as anywhere:puzzle.arpatubes.net/</p>

</div></p>

</p>

Got it on the second attempt. My first wrong attempt was due to me being careless.</p>

</p>

Edit: I see lukewarm and his 5 attempts. I own you.</p>

</p>

 

[GMJ]

Got it on the first attempt. Get some.</p>

 

[lukewarmplay]

yep, i kept missing something.</p>

 

[o.iatlhawksfan]

I have a test tomorrow need help on similarities among polygons, and solving properties like these,</p>

</p>

2x+5/5 = 4/9</p>

</p>

3/10=3x-4/7x+1</p>

5/2x-4= 9/3x+1</p>

7/x+1= 2/3</p>

</p>

 

[cpawfan]

<div class='quotetop'>QUOTE (lukewarmplay)</div><div class='quotemain'></p>

might as well post this here as anywhere:puzzle.arpatubes.net/</p>

</div></p>

I did the one that is up there today about the Spruce Goose, Gin and Tonic and got it on the first attempt</p>

</p>

 

[Денг Гордон]

Anyone know how to do this garbage?

1. A marthoner ran the 26.2-mi New York City Marathon in 2.2 h. Show that at least twice, the marathoner was running at exactly 11 mph.

and then

2. x^4 + 3x+ 1 = 0, -2 (less then/equal to) x (less then/equal to) -1

For the first one, I don't get it. It doesn't make any sense. The only time that the runner has to go exactly 11 mph is when accelerating, because the runner could finish the marathon at a speed above 11 mph, ujnless it is including the deceleration, which in that case, I still have no idea how I would show that.

No idea what the hell they're looking for in the 2nd one.

 

[bbwchingy0007]

<div class='quotetop'>QUOTE (BG7 Lavigne @ Jan 14 2008, 12:18 AM) <{POST_SNAPBACK}></div><div class='quotemain'>Anyone know how to do this garbage?

1. A marthoner ran the 26.2-mi New York City Marathon in 2.2 h. Show that at least twice, the marathoner was running at exactly 11 mph.

and then

2. x^4 + 3x+ 1 = 0, -2 (less then/equal to) x (less then/equal to) -1

For the first one, I don't get it. It doesn't make any sense. The only time that the runner has to go exactly 11 mph is when accelerating, because the runner could finish the marathon at a speed above 11 mph, ujnless it is including the deceleration, which in that case, I still have no idea how I would show that.

No idea what the hell they're looking for in the 2nd one.</div>

1. You know that the runner has to reach 11 mph when accelerating. Perhaps the other is just when they slow down at the other end, lol.

2. I think they just want you to give them the values possible for x in that range. You could use fixed-point iteration, decimal search or the Newton-Raphson method for this.

 

[lukewarmplay]

The first one's a pretty straightforward application of the intermediate value theorem.