(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.
I'm thinking this is what the problem looks like:
. The first thing to do is to move the
over to the other side because it has a common denominator with the other side. Doing that and at the same time combining them over their common denominator looks like this:
. The best way to solve for x now is to cross-multiply to get 3(4-x)=-4(x-4). Distributing through the parenthesis is 12 - 3x = -4x + 16. Solving for x gives us x = 4. Of course when we sub a 4 back in for x we get real problems, don't we? Dividing by zero breaks every rule in math that there ever was! So, yes, the solution is extraneous.
Answer:
6 votes!
Step-by-step explanation:
Albert: 60% of 30= 18
Anthony: 40% of 30= 12
18 - 12= 6
2(c+7)=2c+14
Use distributive property
2*c +2*7
2c+14=2c+14
Hope it helps!
The number of students that will need to buy the tickets is 419.
<h3>How many students will need to buy tickets?</h3>
The equation that can be formed from the information provided in the question is:
$20s < $1250 + $625 + $1470 + $12s
Where s represents the number of students
$20s < $3345 + $12s
$20 - $12s < $3345
$8s < $3345
s < $3345 / $8
s < 419
To learn more about inequality, please check: brainly.com/question/5031619
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