(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:
Hey there!
I=PRT
I=3200(0.035)(1)
I=112
The interest is 112 dollars.
Hope this helps :)
Answer:
Each song costs $2 and each album costs $10.
Step-by-step explanation:
Since a website allows users to download individual songs or whole albums, and all songs cost the same price to download and all albums cost the same price to download, and Karim pays $ 30 to download 5 songs and 2 albums while Kimberlyn pays $ 26 for download 3 songs and 2 albums, to determine what is the cost to download 1 song and the cost to download 1 album, the following calculations must be made:
5X + 2Y = 30
3X + 2Y = 26
(30 - 26) / (5 - 3) = X
4/2 = X
2 = X
Therefore, each song has a cost of $ 2.
Thus, to know the cost of each album (knowing that both downloaded the same amount, that is, 2), the following calculation must be performed:
5x2 + 2Y = 30
10 + 2Y = 30
2Y = 30 - 10
2Y = 20
Y = 20/2
Y = 10
Therefore, each album has a cost of $ 10.
Let's begin by evaluating f(x) using the value of 3: f(x) = 2x2 - 4x - 4 (original function) f(3) = 2(3)2 - 4(3) - 4 (plugging in 3 for x) f(3) = 2 (computed result) Now let's evaluate g(x) using the value of 3: g(x) = 4x - 7 (original function) g(x) = 4(3) - 7 (plugging in 3 for x) g(x) = 5 (computed result) Finally, we'll sum our results: (f + g)(3) = 2 + 3 (add f(3) and g(3)) <span>(f + g)(3) = 5 (final answer)</span>
