Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

Pages: 1

#1 Re: Help Me ! » Help with Mean Value Theorem Problem » 2016-11-30 11:56:13

mathattack

Thanks zetafunc!

One question: in order to use MVT again on f' to get an expression for f", what value do I use for f'(1/2)?  Do I use the f'(c) value that I found? [setting up MVT using f'(0) and f'(1/2)?]

Thanks!

#2 Help Me ! » Help with Mean Value Theorem Problem » 2016-11-30 08:09:28

mathattack
Replies: 2

Hello!

I've been trying to solve this proof, but only can provide examples, (e.g. y=2x^2).  Could someone help me with the proof?  Thanks!


Suppose f is a twice-differentiable function with f(0) = 0, f(1/2) = 1/2 and f ' (0) = 0. Prove that |f '' (x)| > or = 4 for some x in the interval [0,1/2].

#3 Re: Help Me ! » Functions and Continuity » 2016-10-19 07:14:35

mathattack

Thanks Thickhead!

#4 Help Me ! » Functions and Continuity » 2016-10-18 18:00:43

mathattack
Replies: 2

I'm having a little bit of difficulty with this question.  Could someone give some advice?

Consider the function:

f(x) = 1/b if x is rational and x = a/b in lowest terms and b>0
and f(x) = 0 if x is irrational.

Show that f(x) is continuous exactly at irrational points.



My thoughts so far: If a/b is in lowest terms, I'm guessing it means that and a and b are relatively prime?  So b would equal a/x, when x is a rational number?  I'm then getting that f(x) = x/a, when x is a rational number, but why would this not be continuous for any intervals?  Shouldn't the interval of a from (0,1] work at least? 

Any help would be much appreciated!

#5 Re: Help Me ! » Vector Geometry Proof » 2016-10-18 17:48:20

mathattack

Hi Thickhead,

Sorry for the slow response.  Your response was awesome and super helpful!  Thank you so much smile

#6 Help Me ! » Vector Geometry Proof » 2016-09-28 08:08:31

mathattack
Replies: 3

Hello! 

I've been working out the following question with vectors, but am having a little bit of problems with two things:

1. deriving the position vector of the various centroids
2. deriving the line through the centroid perpendicular to the other side.

Any help would be great!


Pentagon ABCDE is inscribed in a circle. For any edge of ABCDE, we can draw the line perpendicular to that edge that contains the centroid of the remaining three vertices. Show that these 5 lines are concurrent.

#7 Re: Help Me ! » Vector Geometry » 2016-09-28 07:53:01

mathattack

Thank you both!  I was able to work out both solutions.  I hadn't realized before that once I got my equations for both vectors, after setting them equal to each other I could separate each variable and solve for when they equaled zero!  I didn't expect that to work but it did.  Thank you both for your insight and help.

#8 Re: Help Me ! » Vector Geometry » 2016-09-21 07:13:41

mathattack

One more, with similar issues.  Any help would be great, thanks!


Let G denote the centroid of triangle ABC. Let M and N be points on sides AB and AC, respectively, so that M, G, and N are collinear, and AM/MB = 5/2. Find AN/NC.

#9 Help Me ! » Vector Geometry » 2016-09-21 07:12:11

mathattack
Replies: 5

I've been working on this problem using vectors, but can't quite finish it.  I wrote out two equations, one from A to S, the other from B to T, and set them equal to each other.  I just can't figure out what the two parameters would be.  Can someone help?  Thanks!


In triangle ABC, S is a point on side BC such that BS:SC = 1:2, and T is a point on side AC such that AT:TC = 4:3. Let U be the intersection of AS and BT. Find AU:US.

#10 Re: Help Me ! » Geometry, Polygon, Unit Circle, Roots of Unity proof » 2016-07-14 18:28:21

mathattack

Thanks thickhead!

#11 Help Me ! » Geometry, Polygon, Unit Circle, Roots of Unity proof » 2016-07-13 11:36:44

mathattack
Replies: 2

Hello!

I'm having some trouble with the following question, could anyone help please?

1.  A regular polygon P is inscribed in a circle ΓΓ. Let A, B, and C, be three consecutive vertices on the polygon P, and let M be a point on the arc AC of ΓΓ that does not contain B. Prove that

MA⋅MC=MB2−AB2

- I tried using law of cosines and substituting, but I got stuck here:

(MB)^2 - (AB)^2 = (MA)^2 + 2(AB)(MA)Cos(<BCM) = (MC)^2 - 2(BC)(MC)Cos(<BCM)

Any help would be great, thanks!

#12 Help Me ! » Trig and Sequences » 2016-05-26 08:35:03

mathattack
Replies: 8

Hi!  I'm having quite a bit of trouble with this problem, could someone help?  I really want to know how to solve it.  I set up the triangle, but can't figure how to use the tan and cot to form geometric or arithmetic progressions.  Thanks!


In triangle ABC, AB = BC, and BD is an altitude. Point E is on the extension of AC such that BE = 10. The values of tan CBE, tan DBE, and tan ABE form a geometric progression, and the values of cot DBE, cot CBE, and cot DBC form an arithmetic progression. What is the area of triangle ABC?

#13 Re: Help Me ! » Cool geometry » 2016-03-23 04:29:06

mathattack

Thanks for your help Bobbym and Bob! 

Both suggestions got me going and helped me to confirm my answer too.  I was able to get it with similar triangles in the end, a la power of a point:

If you label the point where CP crosses AB and call it D, then

6x5⍻2 = CDxDP = BD(10-BD), also 5⍻2xCD = 8xBD

I ended up with BD=30/7, CD = 24⍻2/7 & DP = 25⍻2/7, which matched Bobbym's 7⍻2 for CP.

You both are great by the way.  I've been following the forum for a while now, but only recently thought to add some posts of my own.  Till next time.

#14 Help Me ! » Cool geometry » 2016-03-22 08:17:05

mathattack
Replies: 4

Hi! This problem looks cool but it's giving me a little trouble.  Could someone help?

Thanks!!


In triangle ABC, AB = 10, AC = 8, and BC = 6. Let P be the point on the circumcircle of triangle ABC so that angle PCA = 45. Find CP.

#15 Re: Help Me ! » Square & Triangle question » 2016-03-22 08:14:31

mathattack

Thanks, this was great!

#16 Re: Help Me ! » Square & Triangle question » 2016-03-08 09:28:40

mathattack

Thanks for the answer!  How did you get it?

#17 Help Me ! » Square & Triangle question » 2016-03-07 15:25:37

mathattack
Replies: 11

In rectangle ABCD, we have AD = 3 and AB = 4. Let M be the midpoint of AB, and let X be the point such that MD = MX, angle MDX = 77, and A and X lie on opposite sides of DM. Find angle XCD, in degrees.

I'm trying to find out how to solve this question without using trig.  Could someone help?

Pages: 1

Board footer

Powered by FluxBB