(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:
It is a solution
Step-by-step explanation:
y = -4x - 8
Let x = -9 and y = 28
Substitute these values in
28 = -4(-9) -8
28 = 36 -8
28 =28
This is true so it is a solution
Answer:
7 miles
Step-by-step explanation:
Mr. Luna's travels east and west are irrelevant to the question. He drives 3 miles north, then he drives 4 more miles north. 3 + 4 = 7, so Mr. Luna ends up 7 miles north of his home.
Even numbers end with 2,4,6,8, or 0. Thus, 28 is the even number.
Answer:
Step-by-step explanation:
4
