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 unit tangent vector of the given curve.r(t) = 3t8i – 12t8j + 4t8k

Write the equation for the plane.The plane through the points P(-1, 7, -36) , Q(2, 6, -17) and R(1, -7, 30). 

Test the vector field F to determine if it is conservative.F = i + j – k

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) = (4 ln(2t))i + (3t3)j

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

Match the following with their descriptions: 

A shallow groove on the surface of the cortex is called a _________________. 

Match the terms with their description. 

Bonus: What is the halo effect? In what circumstances is it used? What does it tell healthcare professionals?