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HOW DO YOU SEE? The graph shows several representative curves from the family of curves tangent to a force field F. Which is the equation of the force field? Explain your reasoning.
a)
c)
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Chapter 16 Solutions
Multivariable Calculus - With WebAssign
- The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 2 cos ti + 2 sin tj (VZ, V2) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. a(#) =arrow_forwardCan you please provide explanationsarrow_forwardI need a 3d sketch of the equation Z=x+xsiny+xyarrow_forward
- Sh1 Advanced matharrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3V2, 3V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. E) - =arrow_forwardQuestion The position of a drone at time t≥ 0 (in minutes) is given by the parametric function. x = a(t) cos(3nt) + b(t)cos 4πt y = a(t) sin(3πt) + b(t)sin (4) where a(t) and b(t) are functions of time. Both x and y are measured in metres. a) Show the squared distance from the origin, i.e. d² = x² + y²,can be written d² = (a(t))² + (b(t))² + 2a(t)b(t)cos ( b) If the functions a(t) and b(t) 5πt 5πt a(t) = 4+2cos 3 5πt b(t) = 1 -4cos (5) now show the squared distance from the origin, i.e. d² = x² + y², can be rewritten as d² = -16 cos³ -8 cos² 5nt '5πt' +16cos 5πt +17 c) Using (b) find algebraically all times, t≥0 (in exact form i.e. in terms of fractions) when the distance d is 3 mi.e. d = 3 or d² = 9. Hint. periodic solutions can be represented in the form t = a + nT where a is one solution, T is the period, and n is an integer n = 0,1 ....arrow_forward
- 2) Consider the vector function r(t) = (sin(t), −3t, cos (t)). Analyze the function, then sketch a graph.arrow_forwardRepresent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q corresponds to t = 1.) P(−7, −5, −1), Q(−1, −9, −6) (a) r(t) = (b) Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.)arrow_forwardExperiments show is that in temprature field, heat flows in the direction of maximum decrease of temprature T. T = x2 + y2 + 4z2 , P:(2,-1,2) 1. Find the direction of maximum decrease at P. 2. Find the maximum decrease of T at P. 3. Find the Unit vector of max decrease. 4. Sketch the direction at P as arrow.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,