hey all, I am doing my Bachelors/Masters in Teaching at the University of Sydney. I did my undergraduate degree in Mathematics in Ottawa, Canada. I have tutored mathematics to highschool students in Canada for 2 years. I have substituted for math teachers at an American School in the Middle East. If you need help with math call 0410923453 and ask for Aaron. I charge $30/hour. I am available Mondays, Tuesdays, Thursdays and Fridays after 3pm and all day Saturdays. Study well!
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Math Tutoring (1 Viewer)
- Thread starter mathtcha
- Start date
answer me this... this question was in my HSC paper which I was a bit unsure of...
a) Find all values of θ with 0≤θ≤2 pi such that sin θ-√(3) cosθ=1.
b)The difference between a real number r and the greatest integer less than or equal to r is called the fractional part of r, F(r). Thus F(3.45)=0.45.
Note that for all real numbers r, 0≤F(r)<1,
i) Let a =2136 log _(base 10)_ 2
Given that F(a)=7.0738... x 10^-5
observe that
F(2a)=14.1476... x 10^-5
F(3a)=21.2214... x 10^-5
(α) Use your calculator to show that
log_(base 10)_ 1.989 < F(4223a) < log_(base 10)_ 1.990.
(β) Hence calculate an integer M such that the ordinary decimal representation of 2^M begins with 1989. Thus 2^M=1989... .
ii) Let r be a real number and let m and n be non-zero integers with m ≪ n.
(α) Show that if F(mr)=0, then r is rational.
(β) Show that if F(mr)=F(nr), then r is rational.
iii) Suppose that b is an irrational number. Let N be a positive integer and consider the fractional parts F(b), F(2b), ..., F((N+1)b).
(α) Show that these N +1 numbers F(b), ..., F((N+1)b) are all distinct.
(β) Divide the interval 0≤x<1 into N subintervals each of length 1/N and show that there must be integers m and n with m ≪ n and 1 ≤ m, n ≤ N+1 such that F((m-n)b)<1/N.
iv) Given that log_(base 10)_2 is irrational, choose any integer N such that 1/N < log_(base 10)_ (1990/1989);
note that in (i), F(a) < log_(base 10)_ (1990/1989)
Use (iii) to decide whether there exists another integer M such that 2^M=1989....
a) Find all values of θ with 0≤θ≤2 pi such that sin θ-√(3) cosθ=1.
b)The difference between a real number r and the greatest integer less than or equal to r is called the fractional part of r, F(r). Thus F(3.45)=0.45.
Note that for all real numbers r, 0≤F(r)<1,
i) Let a =2136 log _(base 10)_ 2
Given that F(a)=7.0738... x 10^-5
observe that
F(2a)=14.1476... x 10^-5
F(3a)=21.2214... x 10^-5
(α) Use your calculator to show that
log_(base 10)_ 1.989 < F(4223a) < log_(base 10)_ 1.990.
(β) Hence calculate an integer M such that the ordinary decimal representation of 2^M begins with 1989. Thus 2^M=1989... .
ii) Let r be a real number and let m and n be non-zero integers with m ≪ n.
(α) Show that if F(mr)=0, then r is rational.
(β) Show that if F(mr)=F(nr), then r is rational.
iii) Suppose that b is an irrational number. Let N be a positive integer and consider the fractional parts F(b), F(2b), ..., F((N+1)b).
(α) Show that these N +1 numbers F(b), ..., F((N+1)b) are all distinct.
(β) Divide the interval 0≤x<1 into N subintervals each of length 1/N and show that there must be integers m and n with m ≪ n and 1 ≤ m, n ≤ N+1 such that F((m-n)b)<1/N.
iv) Given that log_(base 10)_2 is irrational, choose any integer N such that 1/N < log_(base 10)_ (1990/1989);
note that in (i), F(a) < log_(base 10)_ (1990/1989)
Use (iii) to decide whether there exists another integer M such that 2^M=1989....
velox
Retired
You couldnt be any ruder Pals.
Sounds like a reasonable rate mattcha. Good luck
Sounds like a reasonable rate mattcha. Good luck
math
well im glad I could give you guys a reason to procrastinate, well done!! well if the above posed question was a general math question, I would have to go through it with you step by step. Giving you the answer to it wouldnt do. And if you posted that question to check my math skills, you are just going to have to trust my competence with the subject. God Bless.
-Math is like a Woman, ignore her, and she'll put you in the dog house; but stick with her and she'll take you far!
well im glad I could give you guys a reason to procrastinate, well done!! well if the above posed question was a general math question, I would have to go through it with you step by step. Giving you the answer to it wouldnt do. And if you posted that question to check my math skills, you are just going to have to trust my competence with the subject. God Bless.
-Math is like a Woman, ignore her, and she'll put you in the dog house; but stick with her and she'll take you far!
Forbidden.
Banned
Trig ratios are learned in the General Maths HSC Course, but the logarithmic stuff ?PC said: