Given the vector \( \vec{u}=(-5,4) \), find the magnitude and angle in which the vector points (measured counterclockwise from the positive \( x \)-axis, \( 0 \leq \theta<2 \pi \) )

\( 1 \leftarrow \) Graph the hyperbola \( x^{2}-y^{2}=36 \). Give the domain, range, center, vertices, foci, and equations o. asymptotes for the figure. (Type an ordered pair.) The vertices are \( \square \). (Type ordered pairs. Use a comma to separate answers as needed.) The foci are \( \square \). (Type ordered pairs. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) What are the equations of the asymptotes? Choose the correct answer below. A. \( y= \pm 6 x \) B. \( x= \pm 6 y \) C. \( x= \pm y \) D. \( y= \pm x \) Graph the hyperbola \( x^{2}-y^{2}=36 \). The domain is \( \square \). (Type your answer in interval notation.) The range is \( \square \). (Type your answer in interval notation.)

A laboratory designed a radio telescope that had a diameter of 300 ft and maximum depth of 46 ft . (a)Write an equation of a parabola that models the cross section of the dish if the vertex is placed at the origin and the parabola opens up. (b) The receiver must be placed at the focus of the parabola. How far from the vertex should the receiver be located? (a) The equation of the parabola is \( \square \). (Simplify your answer. Use integers or fractions for any numbers in the equation.) (b) The receiver should be located at approximately \( \square \mathrm{ft} \) above the vertex. (Type an integer or decimal rounded to the nearest tenth as needed.)

-ind the standard form of the equation of the hyperbola satisfying the given conditions. -intercepts \( \pm 12 \); foci at \( (-13,0) \) and \( (13,0) \) The equation in standard form of the hyperbola is \( \square \). (Simplify your answer. Use integers or fractions for any numbers in the equation.)

\( \begin{array}{l}\text { The retail flat rate in dollars for first-class mail weighing } \\ \text { up to } 5 \text { ounces could be computed by } \\ \text { the piecewise-constant function } f \text {, where } x \text { is the } \\ \text { number of ounces. } \\ \text { (a) Evaluate } f(0.5) \text { and } f(5) \text {. Interpret your results. } \\ \text { (b) Sketch a graph of } f \text {. What is the domain of } f \text { ? What } \\ \text { is the range of } f \text { ? }\end{array} \quad f(x)=\left\{\begin{array}{ll}0.60 \text { if } 0<x \leq 1 \\ 0.79 & \text { if } 1<x \leq 2 \\ 0.98 & \text { if } 2<x \leq 3 \\ 1.17 & \text { if } 3<x \leq 4 \\ 1.36 & \text { if } 4<x \leq 5\end{array}\right. \)

For the exponential function \( y=3(1.6)^{x} \), complete parts (a) through (g). (a) Does the function represent exponential growth or decay? A. The function represents exponential decay.