A dart is thrown upward with an initial velocity of 58 ft/sec from an initial height of 4.5 feet and at an angle of elevation of 41. Consider the position of the dart at any time t, where t = 0 when the dart is thrown. Neglect air resistance. - - = - 58sin 41 58 cos41 4.5 ft X a) Write parametric equations to represent the 2-Dimensional Path of the *0/5 Dart. 1. x(t) = 58cos(41)t, y(t) = 1612 - 58sin(41)t + 4.5 2. x(t) = -1612 + 58sin(41)t + 4.5, y(t) = 58cos(41)t X 3. x(t) = 58cos(41)t, y(t) = -1612 + 58sin(41)t + 4.5 4. x(t) = 58cos(41)t + 4.5, y(t) = -16t2 + 58sin(41)t 5. X(t) = 58cos(41)t, y(t) = -16t2 + 58sin(41)t - 4.5 Given the Vectors shown below perform the following vector operation graphically. CH X Perform the Geometric Vector Operation indicated below: * 0/5 NIH V u OI O I X uX Find the given term in the binomial expansion below. * 0/4 x4 term, (x2 + 4)6 1. 232x4y2 2. 256x4 3. 3840x4 4. 15x4 X 5. 560x4 6. 280x4 X Find the given term in the binomial expansion below. * 0/4 x6 term, (x2 - 3)9 1. C3(X2)3(-3)3 = -2,268x6 X 2. ,C6(X2)3(-3)3 = 2,268x6 3. 9C3(X2)4(-3)2 = 756x6 4. C6(x2)3(-3)6 = 61,236x6\fThe Binomial Theorem The Binomial Theorem [Binomial Expansion] ( at b ) " = () anbo + () an- 161 + (3)an-2b2 + ...+ ()ab kth Term: 1 st 2nd 3rd ... (n+1 ) th r = k- 1 The kth term: ( ) ( a) n -r ( b ) " X Find the 5th term of the binomial expansion below. * (X + 2)8 1. &Cs(x)3(2)5 = 1792x5 X 2. &C4(X)4(2) 4 = 1120x4 3. 8C3(X) 5(2)3 = 448x5 4. X8 + 256 5. sCs(X)5(2)3 = 448x3X Find the 2nd term of the binomial expansion below. * 0/5 (a - 262)4 1. 4C3(a)1(-262)3 = -32ab6 2. 4C4(a)(-262)4 = 1668 3. 4C2(a)2(-262)2 = 24a2b4 X 4. 4Co(a)4(-262)0 = 24 5. 4C1(a)3(-262)1 = -8a362 X Find the 3rd term of the binomial expansion below. * 0/5 (a - 262)4 1. 4C3(a)(-262)3 = -32ab6 X 2. 4C4(a)(-262)4 = 1668 3. 4C1(a)3(-262)1 = -8a362 4. 4Co(a)4(-262)0 = 24 5. 4C2(a)2(-262)2 = 24a2b4X Find the 6th term of the binomial expansion below. * 0/5 (3x - 7)7 1. 7Cs(3x)2(-7)5 = -3176523x2 2. 7Cs(3x)4(-7) = -2,835x4 3. 7C6(3x)1(-7)6 = 2470629x6 X 4. 7C7(3x)(-7)7 = -823543 5. 7C6(3x)4(-7)3 = 16,384xX Find the given term in the binomial expansion below. * x8y?term, (x? + 4y) 1. 16x%y4 2. 20x8y 3.~ 192y 4. 256x%y* 5. 240x%? 6. 1oy 0/5 Given the vector u equal to 6 {cos 135, sin 135) and vector v equal to 4 {cos 225, sin 225) , find the sum u + v and write your answer in magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree, 0