Yeah, translating the axes by defining a new set of axes such as x' and y', then rotating it via trigonometric function but I was struggling big time about that. Any suggestions?
Homework Statement
Come up with a set of equations to draw the following picture:
http://img197.imageshack.us/img197/7428/equation.jpg [Broken]
Homework Equations
The Attempt at a Solution
The circle is easy.
1000 = sqrt(x^2+y^2)
I can just model the equation with sines. So
y_1 = 300...
Homework Statement
1. f(n) = log(n) ^ (log(n)). Simplify for Big-O notation.
The Attempt at a Solution
1.
I'm just trying to prove a big-O notation for one of my courses, and this was simplified to
f(n) = n^log(log(n))
And I'm having a hard time seeing why. Any guidance would be...
Homework Statement
Problem 1:
Two Arithmetic Sequences are given.
a_n = 200,196,192,188,184....
[ltaex]b_n = 100,103,106,109,112....[/itex]
For integers l,m, find the number of pairs consisting of (l,m) which satifies condition a_l = b_m
Problem 2:
Three terms, sin(x)...
U( r ) = r(r+1)(r+2)(r+3), show that U (r + 1) - U ( r ) = 4(r+1)(r+2)(r+3)
U(r+1) is = (r+1)(r+2)(r+3)(r+4)
so U(r+1) - U( r ) = (r+1)(r+2)(r+3)(r+4) - r(r+1)(r+2)(r+3)
let (r+1)(r+2)(r+3) = z
= z((r+4)-r)
= 4z
= 4(r+1)(r+2)(r+3)
Then if we say V(r) = U(r+1) - U( r )
V(r) + V(r + 1) =...
Homework Statement
U( r ) = r(r+1)(r+2)(r+3), show that U (r + 1) - U ( r ) = 4(r+1)(r+2)(r+3) Hence, find the sum to n terms of the series 2x3x4 + 3x4x5 + 4x5x6 +.....
Homework Equations
Sequence Knowledge..
The Attempt at a Solution
I can't even TOUCH on the problem. Can you...
Homework Statement
If P is proportional to q^2
and q is inversely proportional to r
Show that p is proportional to r^2
Homework Equations
p = kq^2
q = c/r
where k and c are proportional constants
The Attempt at a Solution
I'd say this is impossible. This is all the...
I thank you for your reply, but that is exactly what I was trying to avoid. This problem was shown on 6th grade exam paper, and should not require any trigonometry to solve this. Are you absolutely certain that is the only way to go about this problem?
Homework Statement
http://img16.imageshack.us/img16/9616/area.jpg [Broken]
The Attempt at a Solution
Area of square = 25cm^2 therefore
Area of the shaded area = 25 - (Area of A + Area of B + Area of C)
Area of A = Area of C
Therefore, Area of the shaded area = 25 - (2 * Area of...
Well, here's the whole problem:
The two exponential functions
f(x)=a^{bx-1}
g(x)=a^{1-bx}
Satisfy the following conditions
a)Functions y = f(x) and y=g(x) are symmetric to the line x = 2 when graphed
b)f(4) + g(4) = \frac {5}{2}
Find a and b.
Homework Statement
Suppose two exponential functions, f(x) and g(x) are symmetric with respect to x = 2.
f(x)=a^{bx-1}
g(x)=a^{1-bx}
Prove f(2) = g(2)
Homework Equations
The Attempt at a Solution
This isn't actually a problem. This is a property used to solve a different...
Unfortunately, it actually is an exam question (Supposedly solvable). This was a question from Korean National Standarized Test. From what I heard, there's a real simpler way of doing this, but I just cannot figure out what it is.
http://img385.imageshack.us/img385/5272/12qu6.jpg [Broken]
Homework Statement
For the following irrational equation
x^2 + 7x + 10 + \sqrt{x^2 + 7x + 12} = 0
Find all possible unknown of X.
Homework Equations
None. Just your ability to solve equations.
The Attempt at a Solution
First of all, I am not allowed to use a calculator to...
Homework Statement
K this is a question from GRE Testbook.
At Blinky Burgers restaurant, two hamburgers and five orders of French fries cost the same as four hamburgers and two orders of French fries. If the restaurant charges $1.50 for a single order of French fries, how much does it...