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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) =

Find the curvature of the space curve.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 ______

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

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