Evaluate the surface integral

F · dS

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = x i − z j + y k

S is the part of the sphere

x² + y² + z² = 9

in the first octant, with orientation toward the origin

Evaluate the surface integral

F · dS  for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = xze^y i − xze^y j + z k
S is the part of the plane x + y + z = 3 in the first octant and has downward orientation

The Quest For Perpetual Motion It has been a tenet of physics that it is not possible to build a perpetual motion machine in a closed or isolated system. This fact has not stopped people from claiming to build such a machine. Explain why a perpetual motion machine violates the principles of thermodynamics. Do some research and provide an example of a supposed perpetual motion machine. Explain the machine in detail and why it does not exhibit perpetual motion.

1. Discuss the functional anatomy of the hip.
   

2. Discuss the normal Angle of Inclination of the adult hip and potential compensation patterns seen with excessive varus or valgus angles.
   

3. Discuss the normal Femoral Torsion Angle of the adult hip and potential compensation patterns seen with excessive anterior or posterior angulation.
   

4. Discuss 3 planes of closed chain hip osteokinematics.
   

5. Discuss the osteokinematics of contra-directional lumbopelvic movements in the sagittal and frontal planes.
   

Suppose the investment is very sensitive to the interest rate.That is, the function I(r), used to derive the IS curve, is very steep (that is, when we graph it with r on the vertical axis, it is very flat, almost horizontal). Graphically derive the IS curve in the closed economy. What can you say about the steepness IS curve? In this context, which policy do you think is likely to be more effective? Fiscal policy or monetary policy?

22.

A project will not produce any cash flows for two years. Starting in the third year, it will produce annual cash flows of $11,900 a year for two years. The project initially costs $43,600. In Year 6, the project will be closed and as a result should produce a final cash inflow of $50,500. What is the net present value of this project if the required rate of return is 8.7 percent?

$5,474.76

$3,935.56

$5,447.76

$7,465.95

$4,802.57

Ex. 840. A proportional controller, Kp, is desired for the plant
1/( (s) (s+ 8) (s+11) ).  Design the unity feedback system so that the
dominant poles indicate a closed loop step response with a 36% overshoot.
What is Kp, zeta, wn, wd, Ts, Tp, the velocity constant (Kv) and the resulting
SS error for a ramp input, and the gain, Kp, for marginal stability. ans:9

Evaluate the surface integral

F · dS

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = x i + y j + z⁴ k

S is the part of the cone z =

beneath the plane

z = 1

with downward orientation