(3 cos x-4 sin x)+(3sin x+4 cos x)=5
(3cos x+4cos x)+(-4sin x+3 sin x)=5
7 cos x-sin x=5
7cos x=5+sin x
(7 cos x)²=(5+sinx)²
49 cos²x=25+10 sinx+sin²x
49(1-sin²x)=25+10 sinx+sin²x
49-49sin²x=25+10sinx+sin²x
50 sin² x+10sinx-24=0
Sin x=[-10⁺₋√(100+4800)]/100=(-10⁺₋70)/100
We have two possible solutions:
sinx =(-10-70)/100=-0.8
x=sin⁻¹ (-0.8)=-53.13º (360º-53.13º=306.87)
sinx=(-10+70)/100=0.6
x=sin⁻¹ 0.6=36.87º
The solutions when 0≤x≤360º are: 36.87º and 306.87º.
Answer:
C. g(x) = x^2 + 3
Step-by-step explanation:
Answer:
y = (1/3)x
Step-by-step explanation:
If this is truly a line, then we can find its equation using any two of the three given points. If we go from (3, 1) to (27, 9), x increases by 24 and y increases by 8. Thus, the slope of this line is m = rise / run = 8 / 24, or m = 1/3.
Using the point (3, 1) and the slope m = 1/3, the slope-intercept form y = mx + b becomes 1 = (1/3)(3) + b. Thus, b = 0, and the line is y = (1/3)x.
Answer:
See attachments
Step-by-step explanation:
