2. The edges ofa cube incease ata raterof2 cm/s. How fast is the voiume changing when the length ofeach edge is 3O cm? Write an equation elating the volume ofa cube, V and an edge ofthe cube, a, Deentiate both sides of the equation with espect to t. (Type an expression using a as {he vaiable) The rate of change of the volume is(1) (Simpifty your answer.) C e S C m C m cm2 /sec. . C m .3/2 C m :) h cm3 /sec. . 3. A bug is moving along the rightside ofthe parabola y=X2 ata ate such that jts distance from the oigin is increasjng at 3 cm / min" At what rates are the x- and y-COOrdinates ofthe bug inceasing when the bug is at the point (1, 1)? Let D be the distance the bug is from the oigin Write an equation elating D, X, and y. Derentiate both sides of the equation with respect to t, =(( The x-COOrdinate ofthe bug is i=CreaSing at a rate of (Type an exact answer, uSing radicals as needed.) The y-COOdinate ofthe bug lS lnCeaSing at a ate of (Type an exact answer, uSing radicals as needed.) Cm / min.(2) Cm/min. C m n ( m n cm2 lmin. ( C m m C m 23 - - ( cm3 /min. 4"A surfece ship is moving in a straighne (horizonta!!y) at 16 km/hr. At the same time, an enemy Submaine maintains a position diect-y beIow the ship wh=e diving at an angle that is 30O beow the hoizontai, How fast is the submarine-s altitude decreasing? Let x be the distance taveIed by the sace ship and y be the aItitude ofthe submarine. Write an equation eiating x and y. Choose the corect answer below. A, Sin(3OO)=Y !B, Sin(3OO)=i '' C. tan(30O= , D, COS(30O)=r 'I E" COS(300 tan(300 Diffeentiate both sides of the equation with espect to t. Choose the coect answer below. "an(30O'i B. g=Sin(300) cos(30O)'D" i 1dx dy l dx dt _ tan(300) dt dy l dx dt sin(30O) dt The aititude ofthe submaine is decreasing at a rate of about (Do not round unt= theai answe. Then ound to two decimal places as needed.) m ( m ) - k k - m - m ) hh /h/ 2/.3 ( "K.K '