Careful; (dy/dx)^2 = x^2 cos^2(x) + 2x sin x cos x + sin^2(x).
<span>So, the arc length equals </span>
<span>∫(x = 0 to 2π) √[1 + (x^2 cos^2(x) + 2x sin x cos x + sin^2(x))] dx </span>
<span>= ∫(x = 0 to 2π) √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)] dx, via double angle identity. </span>
<span>Let Δx = (2π - 0)/10 = π/5. </span>
<span>Using Simpson's Rule with n = 10, this integral approximately equals </span>
<span>((π/5)/3) * [f(0) + 4 f(π/5) + 2 f(2π/5) + 4 f(3π/5) + 2 f(4π/5) + 4 f(π) + 2 f(6π/5) + 4 f(7π/5) + 2 f(8π/5) + 4 f(9π/5) + f(2π)], </span>
<span>where f(x) = √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)]. </span>
<span>------- </span>
<span>I hope this helps!</span>
Answer:
Answer is explained in the photo
It would take you 26.1 minutes to clean all the showers. If it takes 5.22 minutes to clean the one and you have five to clean just multiply the time by five. Good luck!
Question 1
cos(C) = adj/hyp
cos(C) = BC/AC
cos(C) = 15/17
Answer: Choice C) 15/17
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Question 2
sin(E) = opp/hyp
sin(E) = FD/DE
sin(E) = 24/25
So angle E is the answer
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Question 3
AC is the adjacent side to the given angle A = 33 degrees
AB = 14 is the hypotenuse
cos(angle) = adjacent/hypotenuse
cos(33) = x/14
14*cos(33) = x
x = 14*cos(33)
x = 11.741
x = 11.7
Answer: 11.7
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Question 4
x = length of board
cos(angle) = adj/hyp
cos(55) = 6/x
x*cos(55) = 6
x = 6/cos(55)
x = 10.46068
x = 10.5
Answer: 10.5
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Question 5
112 is the adjacent side to the given angle 62 degrees
x = height of building, which is the opposite leg
tan(angle) = opp/adj
tan(62) = x/112
112*tan(62) = x
x = 112*tan(62)
x = 210.641364
x = 210.6
Answer: 210.6
