A ball is thrown straight upward. The function \( f(t)=-16 t^{2}+64 t \) describes the ball's height above the ground, \( f(t) \), in feet, \( t \) seconds after it is thrown. Complete parts a through \( c \). \( I(4)=0 \) Interpret \( f(4) \). The ball is 0 feet above the ground after 4 seconds. c. Factor the polynomial \( -16 t^{2}+64 t \) and write the function in factored form. \( f(t)=\square \) example Get more help \( ~ \)

Factor the trigonometric expression \[ (\csc x+\sin x)^{2}-(\csc x-\sin x)^{2} \]

How much money will you make if you invest \( \$ 3,200 \) with a simple interest rate of \( 4.25 \% \) over the course of 18 years? Round your answer to the nearest cent. (Just enter a value, do not include units in your answer)

Draw a box-and-whisker diagram of the following set of data: \( [1,25 ; 1,5 ; 2,5 ; 2,5 ; 3,1 ; 3,2 ; 4,1 ; 4,25 ; 4,75 ; 4,8 ; 4,95 ; 5,1] \) If 3 blue balls and 7 red balls are placed in a bag and 2 balls are randomly chosen without replacement, determine the probability of choosing: 3.2 .1 a blue ball and then a red ball. 3.2 .2 a red ball and then a blue ball. 3.2 .3 red ball and a blue ball in any order. 3.2.4 2 blue balls. Given the sample space \( s=\{6,7,8,9,10\} \), determine whether or not the following events are complementary: 3.3.1 selecting an even number and a multiple of 5 . 3.3.2 selecting a mutple of 3 and a prime number. 3.3.3 selecting an odd number and a multiple of 2 .

Let \( y=\tan (2 x+5) \). Find the differential \( d y \) when \( x=2 \) and \( d x=0.2 \) Find the differential \( d y \) when \( x=2 \) and \( d x=0.4 \)

Plot the intercepts to graph the equation. \[ x+y=-3 \]