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- A cable hangs between two poles of equal height and 26 feet apart. Set up a coordinate system where the poles are 13, where x is measured in feet. The height (in feet) of the cable at position x is placed at x = -13 and x = h(x) = 18 cosh(x/18), where cosh(x) = (eª + e¯*)/2 is the hyperbolic cosine, which is an important function in physics and engineering. The cable is feet long.The following represents the graph of the function: OS(x) = cos x- cos x+- 2 2 X. TU2 3 T/ 2 (points) Based on the graph of this function do the following: a. Use your understanding of how to identify the parameters of the sinusoidal function y = asin(hx +c) + d or y = acos(hx +c)+d_to write the equation of a simpler function p(x) that describes the graph. Explain your choices. b. Check the answer you obtained in (a) by graphing the new function p(x). Obtain a printout of the graph. Explain how you used your graphing calculator to verify that your answer is сопеct. c. Verify algebraically that the two equations are equivalent.A storm is approaching and causing the depth of the water in the bay to fluctuate. The depth D(t), in meters, can be described by the function D(t) = 6 cos Which of the following graphs represents the depth of the water in the bay? TT 2T 3T 4m 5TT 6T 7T 8T 9T ^^/ +10, such that t represents the time in minutes.
- Differentiate cos(t^2 - 6)Graph y = 1 - (x²/6), y = (x sin x)/(2 - 2 cos x), and y = 1 together for-2 sxs 2. Comment on the behavior of the graphs as x -0. 3DPlot the graphs of f(x) = x(x - 3) (x + 3) and g(x) = cos 2 x together on the same set of axes and over the interval [-20, 20]. Use the PlotRange option to adjust the range of the viewing window so that their points of intersection are visible.
- Solve the Bernoulli's equation given below: dy -y cot2x = y' csc2x dx A. [(y )^(- 2)] sin 2x = - x + C B. [(y)^(- 2)] sin 2x = - 2x + C C. [(y )^(- 2)] cos 2x = - x + C O D. [(y )^(- 2)] cos 2x = - 2x + CQ4) Graph the following functions and determine (domain , range): (a) y=2sin (b) y=2+ cos (x+) (c) y= 2+ vx+2 (d) y=/x- 4/The function g(x) is obtained by shifting the graph of y=x2. (a) If g(3)=36, give a possible formula for g when g is the result of applying only a horizontal shift to y=x^2.
- (D'-00-60)2 = (2x +j) COS(1 point) Approximate cos(4.6) using a quadratic approximation: First note that cos(4.6) cos(3/2). Let f(x) = cos(x). Then, f'(x) = -sinx and f"(x) = -cosx Let a = 3x/2. Then f' (3/2) = -sin(3pi/2) and f" (3л/2) = -cos(3pi/2) Q(x), the quadratic approximation to cos(x) at a = 3/2 is: Q(x) = cos(3pi/2) Use Q(x) to approximate cos(4.6). cos(4.6) cos(3pi/2)Find tan(u2)tan(u2) if sinu=−0.723sinu=-0.723