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Chapter 4: Problem 77
Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) $$\cos \left(-110^{\circ}\right)$$
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A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 3.5 feet from its low point to its high point (see figure), and it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy where the high point corresponds to the time \(t=0\) (figure cannot copy)
A carousel with a 50 -foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel in radians per minute. (b) Find the linear speed (in feet per minute) of the platform rim of the carousel.
Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$g(x)=e^{-x^{2} / 2} \sin x$$
Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$y=\frac{6}{x}+\cos x, \quad x>0$$
Find a model for simple harmonic motion satisfying the specified conditions. Displacement \((t=0)\) 2 feet Amplitude 2 feet Period 10 seconds
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