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The position vector of a particle is r(t). Find the requested vector.The acceleration at t = 0 for r(t) = t2i + (4t3 – 9)j + k

A small sculpture made of brass is believed to have a secret central cavity. The weight of the sculpture in air is 15.76 N. When it is submerged in water, the weight is 13.86 N. What is the volume of the secret cavity?

Find the domain and range and describe the level curves for the function f(x,y).f(x, y) =

Match the equation with the surface it defines.x2 + y2 = 1

Solve the problem.A force of magnitude 14 pounds pulling on a suitcase makes an angle of 60° with the ground. Express the force in terms of its i and j components.

Solve the problem. Unless stated otherwise, assume that the projectile is launched from the origin over a horizontal surfaceAn ideal projectile is launched from level ground at a launch angle of 26° and an initial speed of 48 m/sec. How far away from the launch point does the projectile hit the ground?

Solve the problem.Find the magnitude of the torque in foot-pounds at point P for the following lever: = 3 in. and = 10 lb

Use implicit differentiation to find the specified derivative at the given point.Find at the point (1, -1) for 5xy2 – 4x2y + 2x = 0.

Find the unit tangent vector of the given curve.r(t) = (6t cos t – 6 sin t)j + (6t sin t + 6 cos t)k

Find the domain and range and describe the level curves for the function f(x,y).f(x, y) =