Butterfly : r7(t) = (6 cos (; t),6 sin (Ft),t+1) %3D Wasp : r¿(t) = (t² – 9, –2t² + 12,3t² – 23) 5. Use the given formulas to determine the following : (a) Describe the paths of the butterfly and the wasp (you do not have to sketch). (b)Verify that the butterfly and wasp collide at t = 3 , and determine the angle at (c) Find the speeds of both the butterfly and the wasp when they collide.

Q: sin(x2 + y?)dA, where 34. Calculate D = +

A:

Q: (5.)Given that sec(x) = 4 and csc(y) = -3 and both x and y are in the fourth quadrant, find tan(x +…

A: Given, sec(x) = 4 and csc(y)=-3. Here, angles x and y are in the fourth quadrant, so cosine and sec…

Q: y = ay +b cos(wt) Scale and non-dimensionalize: C1 C2 Pick c1, c2 + change variable

A: We have to define this partial derivative in terms of x and t

Q: Evaluate 8 cos (2a² + 2y²) dy dæ Hint: You could take a cab to the pole.

A:

Q: Graph: y = 2 sin 27x, 0 s xs 2.

A: To graph: y=2sin2πx,     0≤x≤2 Solution: We know, for a sine curve of the form: y=asinbxAmplitude…

Q: (cos2y-3x²y-)dx + (cos2y-2xsin2y-2x°y)dy = 0

A:

Q: What is the particle's starting position (t = 0);

A: We have to find

Q: Find the value of each variable. 1. 2. (5x + 12) 50 75 60 (x+30)0 Find'x se that

A: Sum of interior angle of triangle is 180

Q: 74.(z-2y) -3z (12) |

A: To find the value of the given expression (z-2y)2-3z3(12) at x=3, y=-2, z=-1

Q: || (cos (a2 + y²) dA where D = {(x, y) | 16 < x² + y² < 49} Find SUBMIT A PHOTO OF YOUR HANDWRITTEN…

A:

Q: 2. The function y = 2 sin (x +) has an x-intercept at A. (,0) B. (,0) C. (π, 0) D. (2π,0)

A:

Q: (x+2) dx (x + 3)*(x +1)³

A: ∫-20x+2(x+1)3(x+3)3dxSubstitute u=(x+1)(x+3)→dudx=2x+4→dx=12x+4du=12∫1u3du

Q: The curves T1 (t) = (3t, t°, – 4t°) and r2(t) = (sin(5t), sin( – 2t), t) intersect at the origin.…

A: We have to find the direction vector first.

Q: Q1. If w = f(u, v), u = cosx and v = sinx, show that: d?w v2 fuu + u² fov – 2uv fuv - ufu - vf dx2

A:

Q: Differentiate: s(t) = sec √r A. tan² Vi C. sec √i-tan vi B. D. sec √t-tan √1 2√1 csc √t √r

A: Given,

Q: x²y(cos(Tz) +2) dæ dy dz

A:

Q: (b) 는(cosx)=-sinx (d) VI+ tan x 1+* Q1) Show that: (a) (1+x) =1+6x (e) (V): *- () %3D

A:

Q: sec2 z dz, any path from 7/4 to Ti/4

A:

Q: (r, 0) = (2, 110°) What is the sum of x and y?

A:

Q: Find Duf at P. NOTE: Enter the exact answer. Duf= f(x, y) = sin(3x – 4y); P(4,3); - = u 3 i

A:

Q: find dy dx ² +F y = 3 casch + Cosa 3 and x = Sin²³ o

A:

Q: Mathematics Exercise: Find y 10x nghi CHS, 210-sink Ⓒy=cscx - 4√x +7 cotx 55cx- cotx helt > y = dy…

A: