We turn -5,12 into polar coordinates. It's a Pythagorean Triple so
r = 13 Ф=arctan(-12/5) + 180° ( in the second quadrant )
so -5 = 13 cos Ф, 12 = 13 sin Ф
12 sin x - 5 cos x = 6.5
13 sinФ sin x + 13 cos Ф cos x = 6.5
13 cos(x - Ф) = 6.5
cos(x - Ф) = 1/2
cos(x - Ф) = cos 60°
x - Ф = ± 60° + 360° k integer k
x = Ф ± 60° + 360° k
x = 180° + arctan(-12/5) ± 60° + 360° k
That's the exact answer;
x ≈ 180° - 67.38° ± 60° + 360° k
x ≈ 122.62° ± 60° + 360° k
x ≈ { 62.62°, 182.62°} + 360° k, integer k
Answer:
the integer is 5
Step-by-step explanation:
x^2+3(x+1)=43
x^2+3x+3=43
x^2+3x+(9/4)=43-3+(9/4)
(x+(3/2))^2=42 1/4
x+(3/2)=sqrt(42 1/4)
x+(3/2)=6 1/2
x=(6 1/2)-(3/2)
x=5
check:
5^2+3(6)=43
25+18=43
43=43
Answer:
x = 25
Step-by-step explanation:
.20x + .68(120 - x) = .54(120) (Distribute .68 to 120 and -x)
.20x + 81.6 - .68x = .54(120) (multiply .54 and 120)
.20x + 81.6 - .68x = 69.6 ( add .20x and -.68x)
-.48x + 81.6 = 69.6 ( subtract 81.6 on each side)
-.48x = -12 (divide -12 by -.48)
x = 25
Answer:
Number 21 is < number 23 is > number 22 is < and number 24 is >
Step-by-step explanation:
