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Find the curvature of the space curve.r(t) = (6t cos t – 6 sin t)j + (6t sin t + 6 cos t)k

Find the unit binormal vector B for the curve r(t)  r(t) = (6t cos t – 6 sin t)j + (6t sin t + 6 cos t)k

An ice skater is spinning on frictionless ice with her arms extended outward. She then pulls her arms in toward her body, reducing her moment of inertia. Her angular momentum is conserved, so as she reduces her moment of inertia, her angular velocity increases and she spins faster. Compared to her initial rotational kinetic energy, her final rotational kinetic energy is ______

A woman is enjoying a tropical drink while lying on a beach.  The acceleration due to gravity at her location is 9.78 m/s2. What gauge pressure must exist in the woman’s mouth if she is drinking through a straw extending 0.075 m above the surface of the drink? Assume the drink has a density of 1020 kg/m3.

Solve the initial value problem.Differential Equation: = i + (3t3 – 6t)j + kInitial Condition: r(0) = 2j + (ln 2)k

Write the equation for the plane.The plane through the points P(5, -8, 28) , Q(-3, -6, 60) and R(-1, -8, 64).

Find the limit if it exists

A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5 rad/s2.  What is its angular speed after it has turned through an angle of 628 radians?

How long does it take for a rotating wheel to speed up from 15 to 33.3 rad/s if it has an angular acceleration of 3.45 rad/s2?

A bicycle wheel of radius 0.7 m is rotating at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. What is the linear speed of the wheel?