8. Consider the polar curve given by the equation \( r=2 \sin (\theta) \) a) \( (7 \mathrm{pts}) \) The point \( \left(\sqrt{2}, \frac{\pi}{4}\right) \) is a point on this polar curve. Determine the \( x y \)-coordinates of this point. b) (8pts) Represent this curve as a parametric curve (with parameter \( \theta \) ).

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) d) Determine the symmetry of the graph. Odd; origin symmetry Even; \( y \)-axis symmetry Neither

6) O domínio da função dada por \( \mathrm{f}(\mathrm{x})= \) é a) \( \{x \in R \mid-2 \leq x \leq 3\} \). b) \( \{x \in R \mid-2 \leq x<3\} \). c) \( \{x \in R \mid 2 \leq x<3\} \). d) \( \{x \in R \mid-2 \leq x \leq 3\} \). e) \( \{x \in R \mid x \neq 3\} \).

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.)

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

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 \( (-3,0) \)