Answer:
let x adult and y student attended
x+y= 94
x=94-y
again
4x+2y = 294 53 adults and 41 student attended
376-4y+2y =294 the event
2y =82
y=41
substituting the value of y in
x+y =94
x= 94-41 = 53
Step-by-step explanation:
(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.
1600<2570-125.5x<2000 subtract 2570 from all terms...
-970<-125.5x<-570 divide all terms by -125.5 (and reverse signs because of division by a negative!)
7.73>x>4.54 and x is months since January, and since months can only be integers...
x=[5,7]
So January + 5, 6, and 7 respectively are the three months that satisfy the equation...
June, July, and August.
The answer to -2(x-8) is 16-2x
