Answer: c = -5
Step-by-step explanation:
Combine like terms
Subtract 4c from both sides.
Subtract 14 from both sides.
Divide by 2 to isolate c
Check:
For 14, 15, and 16 you would move the decimal the number in the exponent to the left because the exponent is negative. For example 14 would be .00000030
<span>From Today (Monday 21 November 2016) it will be Tuesday 19th October 4754</span>
<h3>
Answer: A. 21</h3>
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C(n, r) = (n!)/(r!*(n-r)!) is the combination formula
C(7, 5) = (7!)/(5!*(7-5)!)
C(7, 5) = (7!)/(5!*2!)
C(7, 5) = (7*6*5!)/(5!*2!)
C(7, 5) = (7*6)/(2!) ..... note the "5!" terms divided and canceled
C(7, 5) = (7*6)/(2*1)
C(7, 5) = 42/2
C(7, 5) = 21
Assuming that arcs are given in degrees, call S the following sum:
S = sin 1° + sin 2° + sin 3° + ... + sin 359° + sin 360°
Rearranging the terms, you can rewrite S as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] + ... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] + ...+ [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
But for any real k,
sin(360° – k) = – sin k
then,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] + ... + [sin 179° – sin 179°] + sin 180° + sin 360°
S = 0 + 0 + ... + 0 + 0 + 0 (... as sin 180° = sin 360° = 0)
S = 0
Each pair of terms in brackets cancel out themselves, so the sum equals zero.
∴ sin 1° + sin 2° + sin 3° + ... + sin 359° + sin 360° = 0 ✔
I hope this helps. =)
Tags: <em>sum summatory trigonometric trig function sine sin trigonometry</em>
