A Ferris wheel ride can be represented by a sinusoidal function. A Ferris wheel at Armencity Theme Park has a diameter of \( 30 m \) and travels at a rate of \( 6 \) revolutions per minute in a clockwise rotation. You get on the ride from a platform \( 1 m \) above the ground at \( t = 0 \) 

a) Determine the equation of the graph in the form \( H ( t ) = a \cos [ k ( t - d ) ] + c \) by finding the exact values of a. \( k \) , \( d \) , and \( c \) values. 

b) If the Ferris wheel does not stop, determine the height above the ground after \( 28 s \) 

 A rocket was launched and its height, \( h \) , in metres, above the ground after time, \( t \) , in seconds, is represented by \( h = 11 + 10 t - 2 t ^ { 2 } \) . For how many seconds was the rocket in the air? 

a.about \( 5.93 s \)   c. about \( 6.64 s\) 

b. about \(6.27 s\)  d. about \( 7.35 s\) 

Which of the following best describes the graph of \( w ( x ) = - ( x + 4 ) ^ { 2 } \) ? The image of \( f ( x ) = \) 

(a)\(\square \) \( x ^ { 2 } \)\(\square \)  \( x \) \(\square \) \(\sqrt { x} \)\(\square \) \(| x | \)\(\square \) \(x ^ { 3 } \)

after a (select all that apply)

(b)

\(\square \) reflection across the \(x\) -axis 

\(\square \)  translation \( 4 \) units up 

\(\square \) vertical compression by a factor of \( \frac { 1 } { 4 } \) units 

\(\square \) vertical stretch by a factor of \(4\) units 

\(\square \) translation \(4\) units to the right 

\(\square \) translation \(4\) units to the left 

\( \square \) translation \( 4 \) units down 

\(\square \) reflection across the \(y\) -axis 

Find all numbers for which the rational expression is undefined. If the rational expression is defined for all real numbers, state this. 

\( \frac { y - 2 } { y ^ { 2 } - 4 } \) 

A. \( \square \)(Use a comma to separate answers as needed.) 

B. The rational expression is defined for all real numbers. 

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. 

Passing through \( ( 8 , - 6 ) \) and perpendicular to the line whose equation is \( y = \frac { 1 } { 2 } x + 3 \) 

Write an equation for the line in point-slope form. 

\( \square \)(Simplify your answer. Use integers or fractions for any numbers in the equation.) 

Write an equation for the line in slope-intercept form. 

\( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)