Breanna has been described as being chatty, having a lot of friends, and lighting up a room at social events. According to the Big Five theory of personality, she most likely would be rated high on the trait of  

Solve the problem.Write an iterated triple integral in the order for the volume of the tetrahedron cut from the first octant by the plane .

Find the triple scalar product (u x v) ∙ w of the given vectors.u = -5i – 3j + 4k; v = 5i – 3j + 6k; w = 10i – 6j – 5k

Solve the problem.A 450-lb sign is hanging from the end of a hinged boom, supported by a cable inclined at 48° 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) = (6 sin 2t)i + (6 cos 2t)j + 5tk, 2 ≤ t ≤ 4

Give a geometric description of the set of points whose coordinates satisfy the given conditions. x2 + y2 + z2 ≤ 64

Find the angle between the given vectors. Round to the nearest tenth of a degree.u = i – j, v = 3i + 5j

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 angle between the given vectors. Round to the nearest tenth of a degree.u = i – j, v = 5i + 6j

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