# Official BMGf Homework Tutor/Help Thread

#### Krzysztof

##### Team Poland
Best subject: Mathematics (which is kinda vague, really, because what kind of math can I really do?)

"Clearly", mathematics is my best subject since the Ph.D. I'm currently working on is in mathematics. XD

I for some darn reason can't understand geometry enough to tutor it. I get chills down my spine each time I'm confronted with those two column proofs. As a result, I'm more of an algebra person. XD

The courses I can tutor include (but are not limited to):

High School:
- Algebra
- Trigonometry
- Precalculus
- AP Calculus AB/BC
- AP Stats (kind of)

University Level:
- Calculus (1,2,3, Vector Calc)
- Abstract/Linear Algebra
- Topology (kind of)
- Statistics (kind of)
- Number Theory
- Differential Equations (both Ordinary and Partial)
- Differential Geometry (kind of)
- Analysis (Real or Complex...for the most part)
- Discrete Math

#### Pseudonym

##### Now with capital letter
Just wondering...
Could someone help me with a little calculus exercise?

lim(x->0) (log(1+10x))/x

#### Krzysztof

##### Team Poland
Just wondering...
Could someone help me with a little calculus exercise?

lim(x->0) (log(1+10x))/x
Quick question: are you using
$image=http://latex.codecogs.com/png.latex?\log+(x)+=+\log_{10}(x)&hash=32e4f988cd297c6c74c8882c7d3c06bf$
or
$image=http://latex.codecogs.com/png.latex?\log(x)+=+\log_e(x)&hash=ddc9e70f7776c10bab1661acabbeda7e$
(i.e. the natural log)? I ask this because different parts of the world use one of those two definitions.

I'll proceed as follows. The answer will differ by a constant based on how you define your log. So, we observe that

$image=http://latex.codecogs.com/png.latex?\lim_{x\to&space;0}\frac{\log(1+10x)}{x}&space;\longrightarrow&space;\frac{\log(1)}{0}\rightarrow\frac{0}{0}&hash=d106a02f50bdc4a1ce72429cc87e5acf$
.

Now, we can apply L'Hôpital's rule (i.e. differentiate both the numerator and denominator).

You will get

$image=http://latex.codecogs.com/png.latex?\lim_{x\to+0}\dfrac{\dfrac{10}{1+10x}}{1}=\lim_{x\to+0}\frac{10}{1+10x}=10&hash=68643cd026af0e524036064413c25b08$

if
$image=http://latex.codecogs.com/png.latex?\log(x)+=+\log_e(x)&hash=ddc9e70f7776c10bab1661acabbeda7e$
and you will get

$image=http://latex.codecogs.com/png.latex?\lim_{x\to+0}\dfrac{\dfrac{10}{\ln(10)(1+10x)}}{1}=\lim_{x\to+0}\frac{10}{\ln(10)(1+10x)}=\frac{10}{\ln(10)}&hash=fe9ada0d173fdd5b14f4d8d8f7051368$

if
$image=http://latex.codecogs.com/png.latex?\log(x)+=+\log_{10}(x)&hash=b66cbfcc640f2b1fd4b3b1b369c9f09a$
.

Thus, it follows that

$image=http://latex.codecogs.com/png.latex?\lim_{x\to+0}\frac{\log(1+10x)}{x}+=+10&hash=63989328fee05f9ec19cc4ae93887715$

if
$image=http://latex.codecogs.com/png.latex?\log(x)=\log_e(x)&hash=8a475dfce83b1712e5622ebc1767e832$

or

$image=http://latex.codecogs.com/png.latex?\lim_{x\to+0}\frac{\log(1+10x)}{x}+=+\frac{10}{\log(10)}&hash=96da1c165fc60d43af61af2469fd923d$

if
$image=http://latex.codecogs.com/png.latex?\log(x)=\log_{10}(x)&hash=6aff60a56908dfbae32ec9c456984264$

I hope you're able to make sense out of this!!

#### Du Sundavar Freohr

##### New Member
Im only in 8th grade, but I have read and understood history books for 12th graders and passed a 12th grade history test so....
Du Sundavar Freohr. History (any kind you need)

#### hurristat

##### the future is not written
Im only in 8th grade, but I have read and understood history books for 12th graders and passed a 12th grade history test so....
Du Sundavar Freohr. History (any kind you need)
was it an essay test?

No

#### Sushi-X

##### Born at a Yung Age
I'm still learning but hey who isn't ya know.
I am willing to help anybody having trouble playing their guitar.

Subject:Guitar and Trombone
Teacher:King Maggot

#### Casual Cnidarian

##### New Member
What would be a good ~10-minute activity to help teach a class about aphorisms?

#### Pman

##### Insane Particle Collider
Re: For EE or Physics students

This question is for an EE or physics student.

Do you know how much power a return signal has to have in order for radar to be useful?

Here is why I need to know this. I'm designing a satellite that must detect a piece of space debris (Delta II second stage, about 6 meter tall 2.4 meter diameter radius) at a distance of up to 1 km. The satellite size is one cubic meter, so we don't have much room to work with antenna size. Also, we don't have very much power to spare. Ideally I would like to use no more than 30 Watts, and an antenna more than 0.5 m^2 would probably not be practical.
without doing any maths, you could probably do it with only a couple of watts. electrical engineering isn't my specialty but I doubt you'll get much help on here...

Also, do you mean diameter or radius? there is no such thing as a diameter radius...

give me the exact details and I migth be able to work it out.

#### GengarEatBanana

##### Banana eating Gengar
I see you don't have a World History Tutor, I'll step in

(Don't worry I'm very good at History; it's my best subject. If you need me for any other history I can help.)

Name: GengarEatBanana
Subject: World History

#### Zenax

##### Keep moving forward
How can I factorize an equation like 3xy-1-3x+y?

Also, if someone could do (x²-x-2)/(x-2) and leave their traces. Thanks.

#### edeneh

##### My boobies are big
I need someone to explain this simply.

Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (durationless) instant of time, the arrow is neither moving to where it is, nor to where it is not.[11] It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

#### UnownGoldHeart

##### 追放されたバカ
Sign me up for 3.

Pyschical Science, History and Japanise.

Name: unowngoldheart (cba finding the letters again)
Best Subject: Modern Studies.

#### Rocky505

##### Member
Best subject:English.

What would the answers to these be?

Find the slope and y-intercept of each equation

y=2/3x +1

y= -x - 7
The red one is subtract

y= -3/4x - 5
The red one means subtract
Please help me with these I need to complete this to pass algebra.

#### Fawkes.

##### qq
generally Gradient equations are set out in this manner

Y = (Gradient)X +/- (Y intercept)

so numbers in front of the x are the gradients(slopes) and the integers are the y intercept;

1. y=2/3x +1 so gradient is 2/3 and y intercept is 1

2. y= -(1)x - 7 so gradient is -1 and y intercept is -7

you can try the last one yourself so you learn instead of me giving you the answers

##### Guess Who's Watching...
Anyone here any good with Pascal?

#### Xolw

##### The Calm of the Storm
I need help with my Pre-Cal homework.

The problem I'm working on is:

Perform the indicated operation and use the fundamental identities to simplify.

(24/sec(X)+1)- 24/sec(x)-1

I know that I have to multiply by the other denominator and I'm pretty sure the denominator of the next step is (sec(x) +1)(sec(x)1)

I'm not sure if I should distribute or keep 24(secx-1) or 24(secx+1). If your interested, I could really use the help.

#### Leggo

##### bonsoir je m'appelle lafayette
I need help with my Pre-Cal homework.

The problem I'm working on is:

Perform the indicated operation and use the fundamental identities to simplify.

(24/sec(X)+1)- 24/sec(x)-1

I know that I have to multiply by the other denominator and I'm pretty sure the denominator of the next step is (sec(x) +1)(sec(x)1)

I'm not sure if I should distribute or keep 24(secx-1) or 24(secx+1). If your interested, I could really use the help.
Sorry, if it's late, but people can still learn and the problem is: ((24)/(sec(x)+1))-((24)/(sec(x)-1))
Right? This is how I would insert it into my calculator. My mind thought part of it said "((24)/(sec(x)))-1". I use too much paratheses; maybe I should use some brackets.
I would, after multiplying the numerator by the other denominator, try taking out 24. It would eventually become (-48)/(sec(x)+1)(sec(x)-1) because you would multiply secant x plus one by the negative one that was left behind when you took out 24. Negative secant plus positive equals zero and negative one minus one equals negative two. Then, multiply -2 by 24.
Distributing and then solving takes longer than just taking out the common factor. I like cancelling before-hand.

Ah, thanks.

#### Ludwig

##### New Member
Is this project still ongoing? If it is, I'll sign up as a tutor.