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Chapter 6: Problem 52
Find the angle \(\theta\) (in radians and degrees) between the lines. $$\begin{aligned} &3 x-5 y=3\\\ &3 x+5 y=12 \end{aligned}$$
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The points represent the vertices of a triangle. (a) Draw triangle \(A B C\) in the coordinate plane, (b) find the altitude from vertex \(B\) of the triangle to side \(A C,\) and \((\mathrm{c})\) find the area of the triangle. $$A(-2,0), B(0,-3), C(5,1)$$
A projectile is launched at a height of \(h\) feet above the ground at an angle of \(\theta\) with the horizontal. The initial velocity is \(v_{0}\) feet per second, and the path of the projectile is modeled by the parametric equations $$x=\left(v_{0} \cos \theta\right) t$$ and $$y=h+\left(v_{0} \sin \theta\right) t-16 t^{2}.$$ Use a graphing utility to graph the paths of a projectile launched from ground level at each value of \(\boldsymbol{\theta}\) and \(v_{0} .\) For each case, use the graph to approximate the maximum height and the range of the projectile. (a) \(\theta=15^{\circ}, \quad v_{0}=50\) feet per second (b) \(\theta=15^{\circ}, \quad v_{0}=120\) feet per second (c) \(\theta=10^{\circ}, \quad v_{0}=50\) feet per second (d) \(\theta=10^{\circ}, \quad v_{0}=120\) feet per second
Find a polar equation of the conic with its focus at the pole. Conic Ellipse Eccentricity \(e=\frac{1}{2}\) Directrix \(y=1\)
Find the slope of the line with inclination \(\boldsymbol{\theta}\) $$\theta=2.88 \text { radians }$$
Finding the Standard Equation of a Hyperbola, Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: \((-2,1),(2,1)\) passes through the point \((5,4)\)
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