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Here, cosh^2(x) = 1/2(1 + cosh(2x) L.H.S. = cosh^2(x) = (coshx)^2 = [(e^x+e^-x)/2]^2 = = (e^2x+e^-2x +2)/4 = [(e^2x + e^-2x)/2] / 2 + 1/2 = = 1/2(1 + cosh(2x) = R.H.S. >=========================< Q . E . D. ALSO, cosh^2 (2x) = 1/2(1 + cosh(4x) .... you are correct. Hence, cos^2x =...

y = 1/2 -1/2cos(2x -pie/3) Multiply both sides by 2, we get, 2y = 1 - cos(2x -pie/3) cos(2x -pie/3) = 2y +1 cos(2x -pie/3) = (2y +1)/1 A . N . S . W . E . R ........

y = 1/2 -1/2cos(2x -pie/3) Multiply both sides by 2, we get, 2y = 1 - cos(2x -pie/3) cos(2x -pie/3) = 2y +1 cos(2x -pie/3) = (2y +1)/1 A . N . S . W . E . R ........

Here slope m = -3/4 Thus y = -3x/4 + c .............. [1] To find c [1] is pases point (2, 2) So==> 2 = -3*2/4 + c OR c = 2 + 1.5 = 3.5 Hence the line is : y = -3x/4 + 3.5 A N S W E R

If the survey was based on 1,000 people, give the 95% confidence interval? Interpret this confidence interval in the context of the problem. Total = 1000 Confidence = 95% Thus = 1000*95/100 = 950 ..................... Answer

If the survey was based on 1,000 people, give the 95% confidence interval? Interpret this confidence interval in the context of the problem. Total = 1000 Confidence = 95% Thus = 1000*95/100 = 950 ..................... Answer

a) x^2 - 2 = (x + sqrt(2))(x - sqrt(2)) are the factors. b) x^2 + 1 = (x + i)(x - i), where i = sqrt(-1)

a) x^2 - 2 = (x + sqrt(2))(x - sqrt(2)) are the factors. b) x^2 + 1 = (x + i)(x - i), where i = sqrt(-1)