The blades of the portable fan generate a 1.2-lb thrust T as shown. Compute the moment $M_O$ of this force about the rear support point O. For comparison, determine the moment about O due to the weight of the motor-fan unit AB, whose weight of 9 lb acts at G.

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A commercial airliner with four jet engines, each producing 90 kN of forward thrust, is in a steady, level cruise when engine number 3 suddenly fails. Determine and locate the resultant of the three remaining engine thrust vectors. Treat this as a two dimensional problem.

The commercial airliner is redrawn here with three-dimensional information supplied. If engine 3 suddenly fails, determine the resultant of the three remaining engine thrust vectors, each of which has a magnitude of 90 kN. Specify the y- and z-coordinates of the point through which the line of action of the resultant passes. This information would be critical to the design criteria of performance with engine failure.

Express and identify the resultant of the two forces and one couple shown acting on the shaft angled in the x-z plane.

The control lever is subjected to a clockwise couple of 80 $\mathbf{N} \cdot \mathbf{m}$ exerted by its shaft at A and is designed to operate with a 200-N pull as shown. If the resultant of the couple and the force passes through A, determine the proper dimension x of the lever.

Using the principles of equilibrium to be developed in the chapter, you will soon be able to verify that the tension in cable AB is 85.8% of the weight of the cylinder of mass m, while the tension in cable AC is 55.5% of the suspended weight. Write each tension force acting on point A as a vector if the mass m is 60 kg.

Replace the three forces acting on the plate by a wrench. Specify the magnitude of the force and couple moment for the wrench and the point P(x, y) where its line of action intersects the plate.

Air at $98 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$ flows in a horizontal duct of variable cross-section. The water column in the manometer that measures the difference between the two sections has a vertical displacement of $5 \mathrm{~cm}$. If the velocity in the first section is low and the friction is negligible, find the velocity in the second section. Also, if the manometer reading has a possible error of $\pm 2 \mathrm{~mm}$, conduct an error analysis to estimate the range of validity for the velocity found.

The force F is directed from A toward D and D is allowed to move from B to C as measured by the variable s. Consider the projection of F onto line EF as a function of s. In particular, determine and plot the fraction n of the magnitude F which is projected as a function of s/d. Note that s/d varies from 0 to $2 \sqrt{2}$.

Find the zeros of the polynomials. $P(z)=z^{2}-2 i z-1$

Suppose C(r) is the total cost of paying off a car loan borrowed at an annual interest rate of r%. What are the units of C'(r)? What is the practical meaning of C'(r)? What is its sign?

Prepare a poster for the CEO detailing your findings from your quadratic function investigation. Include any insights you and your teammates found. Explain your conclusions and justify your statements. Remember to include both a table and a complete graph of your parabola with all special points carefully labeled. Be thorough and complete.

Find the general solution on the interval $(0, \infty)$ of the given DE using variation of parameters. $y^{\prime \prime}+4 y^{\prime}+4 y=\frac{e^{-2 x}}{x^{2}}$