Solve the problem.Consider a fluid with a flow field F = x2y5i + 3z2j + zk. A miniature paddlewheel (idealized) is to be inserted into the flow at the point 
Find a vector describing the orientation of the paddlewheel axis which produces the maximum rotational speed.
What will be an ideal response?
The paddlewheel axis points along the vector r = -6i - 5k.
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Use the total differential dz to approximate the change in z as (x, y) moves from P to Q. Then use a calculator to find the corresponding exact change ?z (to the accuracy of your calculator).4x3y2; P(1, 1), Q(1.01, 0.99)
A. dz = 0.04; ?z = 0.0381920404 B. dz = 0.04; ?z = 0.0391920404 C. dz = 0.03; ?z = 0.0391920404 D. dz = 0.04; ?z = 0.0416920404
Make a scatterplot of the relation after determining an appropriate viewing rectangle.{(0.5, 3.5), (0.2, 2.0), (0.3, 0.5), (0.7, 3.0)}
A. [0, 5, 1] by [0, 8, 1]
B. [0, 1, 0.2] by [0, 4, 0.5]
C. [0, 1, 0.2] by [0, 4, 0.5]
D. [0, 5, 1] by [0, 8, 1]
Complete the identity.tan ? + cot ? = ?
A. 
B. 
C. 
D. 
Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of ?, where 
.
?
A. 4 sin ? B. - 4 cos ? C. 4 cos ? D. 16 sin ? E. 16 cos ?