Question [-12 Points] DETAILS SCALCET8 7.2.064. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = 5 sec(x), y = 5 cos(x), OS X ST/3; about y = -5 V=

Workshop 9 Problem 1: Using Derivative Information to Construct Functions Problem: Suppose f is a differentiable function whose first derivative is sketched below: y 15 y = f'(30) ; 3 -2 -1 1 2 3 Use this information to answer parts (a)-(f). (a) Find the critical points for f. (b) Find the interval(s) where f is increasing and the interval(s) where f is decreasing. (c) Does f have any local extrema? If so, give the location of each local extremum and determine the nature of the local extremum. (d) Does f have any absolute extrema? If so, give the location of each absolute extremum and the nature of the absolute extremum. If this can't be determined, explain your reasoning. (e) Draw 2 possible sketches of the graph of y = f(x). Explain how your sketches are different and why you know this is valid. (Hint: can a consequence of the MVT help here?)

MATLAB A water tank shaped as an ellipsoid (a = 1.5m, b = 4.0m, c= 3m) has a circular hole at the bottom as shown. According to Torricelli's law, the speed v of the water that is discharging from the hole is given by v = 2gy where y is the height of the water and g = 9.81m/s2. The rate at which the height, y, of the water in the tank changes as the water flows out through the hole is given by dy 2gyra dt ac 1+ 420)2] where r is the radius of the hole. r=0.025m V Solve the differential equation for y for 0 < t < 515s. The initial height of the water is h = 5.9m. Make a plot of y as a function of time. Add a title and axis labels.

A 29-g bullet is shot vertically into an 8-kg block. The block lifts upward 4.0 mm (see the figure). The bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s. Assume the force on the bullet is constant during penetration and that air resistance is negligible. The initial kinetic energy of the bullet is closest to A) 43 J B) 58

A 22-3 bullet is shot vertically into an 4-kg block. The block lifts upward 6.0 mm (see the figure). The bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s. Assume the force on the bullet is constant during penetration and that air resistance is negligible. The initial kinetic energy of the bullet is closest to O 21 J O 29 J O 0.24 J O 43 J 1.3x10-3 Submit Request Answer

Shown in the figure below is a long solenoid. Your solenoid has N loops, a length of L, and is carrying a current of I. We shall use the "long" approximation for which the field outside the solenoid is very very small compared to the field inside the solenoid. Use an Ampere path that extends the full length of the solenoid and closes outside the solenoid. N turns in the coil www00000000000) L A "Long" Solenoid (i.e. length >> diameter) What is the length of your Ampere path over which the field is not negligible? What is the current though this path? Use Ampere's Law to determine the FORMULA for the magnetic field inside the solenoid: What is the direction of the magnetic field inside the solenold? Toward the right Toward the left Clockwise as viewed from the left Counter-clockwise as viewed from the left Out of the screen Into the screen Toward the top of the screen Toward the bottom of the screen The solenoid in the picture looks like a "stretched out" spring because the loops of the coil are far apart. If you compressed the coil so that the loops are touching (same number of loops, same current), what would happen to the magnetic field? The field would increase The field would briefly increase then settle to the original value. The field would decrease Not enough information given. The field would stay the same. An EMP would be generated disabling nearby computer equipment. The field would briefly decrease then settle to the original value. length of L, and is carrying 3 current of J. We shail use the “long” Shown in the figure below is @ long solenoid. Your solenoid has N loops, a length of prying @ current of I. We shall spproximation for which the fl outside the solencd ls very very smal compared tothe field inside the solenokd. Use an Ampere path that extends the ful length ofthe solenoid and closes outside the Solenoi Nturns in the coil A “Long” Solenoid (ie. length >> diameter) nat is the length of your Ampere path over which the fll isnot negigible? Wats the current though tis path? Use Ampere Law to determine the FORMULA forthe magnetic nsde the solenoid What the ection ofthe magnetic field inside the Solencia? © Tomar the right Toward the left ‘locise a vewes from the let ‘Counter-clockwise 9 viewed from the et 9 Out ofthe seen > Toward the top of the screen Toward the bottom ofthe screen » ‘The solenoid nthe picture looks lke a “stretched out” spring because the loops ofthe col {ar touching (seme numberof oops, same current), what would happen tothe magnetic (©The fils would increase re far apart. you compressed the col 3 thatthe loops fi? (© Te fea mould riety increace then sete to the erigna vale. (© The Mets would decrease [© Niet enough ltormation sven. © The fea woul stay the same © An EMP would be generated aisabing nearby computer equipment BO) The fais wousd brietyy decrease then sette to the original valve, 

Please help me with the following Linear Algabra question. Please show work. Describe the additive inverse of a vector in the vector space. M2.3 In M2.3 the additive inverse of [a_11 a_12 a_13 a_21 a_22 a_23] is [-a_11 -a_12 -a_13 -a_21 -a_22 -a_23] In M2.3 the additive inverse of [a_11 a_12 a_13 a_21 a_22 a_23] is [-a_11 -a_12 -a_13 -a_21 -a_22 -a_23] In M2.3 the additive inverse of [a_11 a_12 a_13 a_21 a_22 a_23] is [a_21 a_22 a_23 a_11 a_12 a_13] In M2.3 the additive inverse of [a_11 a_12 a_13 a_21 a_22 a_23] is [-a_21 -a_22 -a_23 -a_11 -a_12 -a_13] In M2.3 the additive inverse of [a_11 a_12 a_13 a_21 a_22 a_23] is [a_11 a_12 a_13 a_21 a_22 a_23]