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Answers by Roman C.

System: (1): x+y = -1 (2): x+2y = 0 Solution: (3)=(2)-(1): (x+2y) - (x+y) = 0 - (-1)                     x + 2y - x...

System:   (1): x+3y=7 (2): 6x+21y=51   Solution:   (3)=(2)-6(1): (6x+21y) - 6(x+3y) = 51 - 6·7                        ...

Let W be the width. Then the length is L=3W   So The equation is then 3W·W = 50 m2 or 3W2 = 50 m2.

integration help (answer)

I will set up the integrals for each.   Problem 1: x-axis and f(x)=2x-x2   Take g(x) = 0, whose graph is the x-axis.   Now let's solve the equation f(x) = g(x)   2x-x2 = 0 x(2-x) = 0   x = 0 or x = 2   So the...

complex analysis (answer)

The sum simplifies to ∑ zn for n=1,...,∞.   Use the ratio test   an = zn so |an+1/an| = |zn+1/zn| = |z|   Recall that if limn→∞|an+1/an| < 1, the series converges. If it's >1 the series diverges. Inconclusive if it's =1   Thus...

First of all, plugging in x=0 gives you that f(y)=f(0)+f(y) or f(0)=0.   Secondly, say that f(1) = s. Using induction it follows that f(n)=ns.   Say also that f(a) = t for some rational a ∉ {-1,0,1}. Then f(na) = nt by induction.   It also follows that...

probability (answer)

Since marbles are not replaced after being drawn, once a red one is drawn, it can't be drawn again. So the other of the two marbles drawn is one of the other three colors. There are three possible pairs of colors (Red,Blue), (Red, White), and (Red, Yellow).   If order in which the two...

Let's represent Bob's current account balance X. The clue says that if he added $150, making the balance or X+150, that balance will be 5X. This gives us an equation to solve.   5X = X + 150   4X = 150   X = 150/4 = 37.5   He currently has...

You don't need the perpendicular distance to L.   Tables of moments of inertia usually mention the circular disk plate about the axis of rotation, which is mr2/2 Placing it on the x-y plane, this is Iz and by the perpendicular axis theorem for flat plates, Ix+Iy = Iz so Ix =...

If a sequence {an} is generated by a polynomial of degree n, then the differences of consecutive terms {bn = an+1 - an} (called the first differences) form a sequence generated by a polynomial of degree n-1. The n-th differences sequence is constant   -1   2   ...

Let C be the number of chairs per row and R be the number of rows. The first clue gives CR = 54. In it plug in the equation of the second clue which is C = 2R - 3.   (2R - 3)R = 54   2R2 - 3R - 54 = 0   Factor by looking for two numbers with sum -3...