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Chapter 5: Problem 34
Use Heron's Area Formula to find the area of the triangle. $$a=33, \quad b=36, \quad c=25$$
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A batted baseball leaves the bat at an angle of \(\theta\) with the horizontal and an initial velocity of \(v_{0}=100\) feet per second. The ball is caught by an outfielder 300 feet from home plate (see figure). Find \(\theta\) if the range \(r\) of a projectile is given by \(r=\frac{1}{32} v_{0}^{2} \sin 2 \theta\).
Consider the function given by \(f(x)=3 \sin (0.6 x-2)\). (a) Approximate the zero of the function in the interval [0,6] (b) A quadratic approximation agreeing with \(f\) at \(x=5\) is \(g(x)=-0.45 x^{2}+5.52 x-13.70 .\) Use a graphing utility to graph \(f\) and \(g\) in the same viewing window. Describe the result. (c) Use the Quadratic Formula to find the zeros of \(g\). Compare the zero in the interval [0,6] with the result of part (a).
Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the given interval. $$\cos ^{2} x-2 \cos x-1=0, \quad[0, \pi]$$
Write the expression as the sine, cosine, or tangent of an angle. $$\cos 3 x \cos 2 y+\sin 3 x \sin 2 y$$
Determine whether the statement is true or false. Justify your answer. The equation \(2 \sin 4 t-1=0\) has four times the number of solutions in the interval \([0,2 \pi)\) as the equation \(2 \sin t-1=0\).
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