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Q: In what direction from the point (1,-1) is the instantaneous rate of change of f(x.y) = 8x* - 10x°y?…
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- The position vector r describes the path of an object moving in space. Position Vector Time r(t) = 3ti + tj + k 8. t = 4 (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) : %3D s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. v(4) = a(4) =The position vector r describes the path of an object moving in space. Position Vector Time r(t) = t²i + tj + 2t³/2k t = 4 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) s(t) a(t) = a(4) = (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. v(4) =The position vector r describes the path of an object moving in space. Position Vector Time r(t) = 5ti + tj + 4 t = 2 (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 value of t. v(2) = a(2) =
- The position vector r describes the path of an object moving in space. Position Vector Time r(t) = Vti + 5tj + 3t²k t = 9 (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 value of t. v(9) a(9)The position vector r describes the path of an object moving in space. Position Vector Time r(t) - 3ti + + k t-2 (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 value of t. v(2) - a(2)The position vector r describes the path of an object moving in space. Position Vector Time r(t) = 76 + tj +k t = 2 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = s(t) %3D a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. v(2) = a(2) =
- How do you find the velocity and acceleration vectors at t=-1?Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) =8xy2, (5,-7) maximum rate of change direction vectorThe position vector r(t) =⟨ln t, 1/ t2, t4⟩ describes the path of an object moving in space. (a) Find the velocity vector, speed, and acceleration vector of the object. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t = √3
- Find the maximum rate of change of f at the given point and the direction in which it occurs. 3x + 9y f(x, у, 2) : (6, 7, –1) maximum rate of change direction vectorThe position vector r describes the path of an object moving in space. Position Vector Time r(t) 3ti + tj + 1 t²k t = 4 8 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. =A4) The position of a hummingbird flying along a straight line in t seconds is given by S(t) = 6t - 28t meters. (a) Determine the velocity of the bird at t = 7 sec. [L (b) Determine the acceleration of the bird at t =7 sec. (c) Determine the acceleration of the bird when the velocity equals 0. [0.