Find the length of the curve with the given vector equation.r(t) = 3ti + j + k; 2≤ t ≤ 7

Write the equation for the plane.The plane through the points P(-1, 7, -44) , Q(2, -3, 20) and R(1, -1, 4). 

Find the unit tangent vector of the given curve.r(t) = 3t2i – 12t2j + 4t2k

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the acceleration vector.r(t) = (7 ln(9t))i + (8t3)j

Solve the problem.A 150-lb sign is hanging from the end of a hinged boom, supported by a cable inclined at 36° with the horizontal. Find the tension in the cable and the compression in the boom rounded to the nearest pound.

Evaluate the line integral along the curve C.ds, C is the curve r(t) = (4 sin t)i + (4 cos t)j + 12tk, 2 ≤ t ≤ 4

During what age range is brain growth the fastest? At what age does the brain finish pruning the prefrontal cortex? 

Use the following set-up for Problems 5-8:Below is a list of exam scores for a class of 15 students:55, 62, 72, 77, 82, 83, 84, 85, 86, 87, 90, 91, 95, 95, 100How do you find the score at the 30th percentile?

Solve the problem. Unless stated otherwise, assume that the projectile flight is ideal, that the launch angle is measured from the horizontal, and that the projectile is launched from the origin over a horizontal surfaceA projectile is fired at a speed of 1160 m/sec at an angle of 36°. How long will it take to get 29 km downrange? Round your answer to the nearest whole number.

Match the following with their descriptions: