1. \( 25 x^{2}+y^{2}-200 x+6 y+384=0 \), centro 2. \( (x+1)^{2}+(y+8)^{2}=100 \), intersecciones con el eje \( x \) 3. \( y^{2}-(x-2)^{2}=1 \), intersecciones con el eje \( y \) 4. \( y^{2}-y+3 x=3 \), pendiente de la recta tangente en \( (1,1) \) 5. \( x=t^{3}, y=4 t^{3} \), nombre de la gráfica rectangular 6. \( x=t^{2}-1, y=t^{3}+t+1 \), intersecciones con el eje \( y \) 7. \( r=-2 \cos \theta \), nombre de la gráfica polar 8. \( r=2+\operatorname{sen} \theta \), nombre de la gráfica polar 19. \( r=\operatorname{sen} 3 \theta, \operatorname{tangentes~a~la~gráfica~en~el~origen~} \) 20. \( r=\frac{1}{2+5 \operatorname{sen} \theta} \), excentricidad 21. \( r=\frac{10}{1-\operatorname{sen} \theta} \), foco yértice 22. \( r=\frac{12}{2+\cos \theta} \), centro

A farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What are the maximum dimensions that can be enclosed with 80 ft of fence? What is the maximum area of this garden? Select the correct choice below and fill in the answer box(s) to complete your choice. A. The area is maximized when both sides are \( \square \mathrm{nt} \). The area is maximized when the longer side is \( \square \mathrm{ft} \) and the shorter side is The maximum area that the farmer can enclose with 80 ft of fence is \( \square \mathrm{sq} \mathrm{ft} \)

What is the dot product of vector \( h \) with a magnitude of 5 and vector \( i \) with a magnitude of 8 if the angle between the vectors is \( \frac{\pi}{6} \) radians? (Round your answer to the nearest hundredth.)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (-7,0) \) and \( (7,0) \); vertices at \( (3,0) \) and \( (-3,0) \)

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-2} \) To graph the function, first determine the symmetry of the graph of f . Choose the correct answer below. y-axis symmetry origin symmetry neither \( y \)-axis symmetry nor origin symmetry What is the \( y \)-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( y \)-intercept is (Type an integer or a simplified fraction.)

Use transformations of the absolute value function, \( \mathrm{f}(\mathrm{x})=|\mathrm{x}| \), to graph the function \( g(x)=-|\mathrm{x}-3|-5 \). ... \( \square \) A. Horizontal shift \( \square \) B. Vertical stretch/shrink \( \square \) C. Horizontal stretch/shrink \( \square \) D. Vertical shift \( \square \) E. Reflection about the \( x \)-axis \( \square \) F. Reflection about the \( y \)-axis