A) What are the particle's coordinates when t =0? B) What are the particle's coordinates whent =2 seconds? C) Find the velocity vector, v(t).

Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: A straight line has vector equation given by r=(1-A)i+(3+2A)j.How far is this line from the origin?

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Q: Find the velocity and acceleration vectors in terms of u, and u. r= a(9 + sin t) and 0 = 3 - e ',…

A: we derivative to find velocity and acceleration

Q: Find the acceleration vector for the position vector r(t) = (sin(5t), 6t", e "). x component = y…

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Q: At how many point(s) does the helix with vector equation r(t) : (cos t, sin t, t) intersect the…

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Q: Express the vector in terms of it's length and direction. Velocity vector v = (-2 sin t)i + (2…

A: It is known that, if their is any vector, let's say vector A, then length of the vector A is defined…

Q: Given the vector function: *(t) = (1+ sin (3t), tan (2t), t) Relate the vector functions to the…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. r= 6 sin 2t and 0 = 4t v=u, +Due…

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Q: Evaluate, don't forget the constant vector, (ri - 2tj + k) dt

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Q: Use cylindrical coordinates to evaluate d V when

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Q: Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ,…

A: Consider that: rθ=sin θ, cos θ, cos 3θ at θ=π3. Velocity vector denoted by vθ is vθ=r'θ.  Calculate…

Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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Q: Find the tangential and normal components of acceleration for the position vector denoted by 7 = (t…

A: We have given position vector  t+29,2t,t2 Then, Tangential component of acceleration aT=r't.r''tr't…

Q: What are the vector and parametric equations for ideal projectile motion?

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Q: Find the acceleration vector for the position vector 7 (t) = (sin(11t), 3t', e -*). x component = y…

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Q: Find the velocity vector for the position vector r(t) = (sin(12t), 8t°, e-6*). x component = y…

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Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

Q: A point, p, is moving with acceleration 6t j -k at time t. If at t 1, the coordinates of P are (1,…

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Q: The normal component of the acceleration vector for an object with position vector r(t) = (cos(t),…

A: To check the given statement for True/False.The normal component of the acceleration vector for an…

Q: Find a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make…

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Q: The acceleration vector points in the direction of motion. O True O False

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a sin 60 and 4t, where a is…

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Q: Determine the velocity vector of the given path. c(t) = 5ti + 3t?j + 6t³k

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t), sin(3t), cos(3t))…

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Q: Find the acceleration vector for the position vector r(t) = (sin(11t), 4tº, e -2t). x component = y…

A: We need to find acceleration vector.

Q: A plane flies at a speed of 420 mph with a bearing of S45°E. Write the velocity vector in terms of i…

A: A plane flies at a speed of 420 mph with a bearing of S45°E. To write the velocity vector in terms…

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(3t), cos(t), sin(t)) when…

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Q: For time >0, the position of a particle moving in the xy-plane is given by the parametric equations…

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Q: Find the velocity and acceleration vectors in terms of u, and ue. r=7 sin 3t and 0= 9t 3Du, +ue V =…

A: Given To determine  the velocity and acceleration vectors

Q: Find the acceleration vector for the position vector r(t): = (sin(11t), 2t", e-10t).

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(3t))…

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Q: Determine the moment of the force F = -40i + 30j + 20k kN about axis OA using vector method.

A: To determine: the moment of the force F → = - 40 i → + 30 j → + 20 k →  N about axis OA using vector…

Q: The position of point moving in space is given by R(t) = 3 tan t i+ cot t j + 2 lntk, find the…

A: We will find out the required velocity and acceleration vector functions.

Q: and ue. Find the velocity and acceleration vectors in terms of u, r= 5 sint and 0 = 8t

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Q: Suppose you are standing on the paraboloid directly above the positive y-axis. In the direction of…

A: REsult :

Q: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

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Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

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Q: Find the velocity, acceleration, and speed of an object with position vector r(t) = (Vi, 4 + Vi,…

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Q: An object is launched from ground level with an initial velocity of 50 m/s, at an angle of elevation…

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Q: Find the velocity and acceleration vectors for the motion described by x = 4 – 3t2, y = 4 – 5t, z= 9…

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Q: Sketch the curve with the vector equation 7(t) = (t,2 – t, 2t). Indicate with an arrow the direction…

A: Solution

Q: Sketch the curve with the vector equation ř(t) = (sin t, t). Indicate with an arrow the direction in…

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Q: The magnitude of the torque t developed by applying a force F at a point with position vector r at…

A: First we have to complete the required step by using the correct expression for torque.

Q: A rifle at A is fired at a target at B. If the speed of the bullet is 1800 ft/s, determine the…

A: Let θ be the angle with the x-axis Then the rectangular form will be  v=1800cosθi+1800sinθj  ft/s

Q: Find the velocity vector for the position vector r(t) = (sin(3t), 10t°, e -"). x component = y…

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.