(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:
The picture that represent her drawing is uploaded below. The height is 8 ft and the base is 6 ft.
Step-by-step explanation:
Renee garden is triangular in shape . The area of the triangular garden is given as 24 ft² . The area of a triangle can be represented below.
Area of a triangle = 1/2bh
where
b = base
h = height
The drawing that represent Renee drawing is given below. The height is 8 ft and the base is 6 ft .
Using the formula
Area of a triangle = 1/2bh
Area of a triangle = 1/2 × 6 × 8
Area of a triangle = 48/2
Area of a triangle = 24 ft²
40% of 65.00=0.40×65=26
65-26=39(your price)
sales tax(5%)=0.05×39=1.95 tax
39+1.95
=40.95(total)
It’s rational because the square root of 0.49 is 0.7