How to derive: f(w)=ln(cos(w-1))
1 answer:
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Start with the answer format we want, and work your way toward forming a single fraction like so
Compare that last expression to (2x+1)/(x+2). Notice how the ax and 2x match up, so a = 2 must be the case.
Then we have 2a+b as the remaining portion in the numerator. Plugging in a = 2 leads to 2a+b = 2*2+b = 4+b. Set this equal to the +1 found in (2x+1)/(x+2) to have the terms match.
So, 4+b = 1 leads to b = -3
Therefore, a = 2 and b = -3
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An alternative route:
I added and subtracted 4 in the third step so that I could form 2x+4, which then factors to 2(x+2). That way I could cancel out a pair of (x+2) terms toward the very end.
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Other alternative methods involve synthetic division or polynomial long division. They are slightly separate but related concepts.
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Answer:
1. B, E
2. A, E
16. B'(1, 5)
Step-by-step explanation:
Lines p and r are parallel, as are lines a and b. Either of the lines in one parallel pair is perpendicular to the lines in the other parallel pair. Line q has no necessary relation to anything, so can be ignored. (No answer containing q can be correct.)
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1. p ⊥ b
r ⊥ a
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2. r║p
a║b
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16. Point B(3, 2) translated (right, up) = (-2, 3) will be ...
B' = B + (-2, 3) = (3, 2) +(-2, 3) = (3 -2, 2 +3)
B' = (1, 5)
Note: (x, y) coordinates are (<em>right</em>, <em>up</em>). So, in translation problems it is important to <em>pay attention.</em> Often, the up/down translation is listed before the left/right translation. If you're not paying attention, you may inadvertently reverse the numbers that need to be added to the coordinates to do the translation.
