A$3-\mathrm{ft}$-long steel pipe is subjected to a torque of $1200\ \mathrm{lb} \cdot \mathrm{ft}$ at each end. The pipe is made of $0.2 \% \mathrm{C}$ hardened steel, failure is by yielding, and the factor of safety is $1.5$. Find the nominal diameter of the lightest standard-weight steel pipe that can be used for the shaft.

Described the relationship of the two graphed lines.

At the start of 2000, the U.S. money supply (M1) was $1,148 billion, distributed as follows: Currency totaling$523 billion, traveler's checks totaling $8 billion, and checking deposits totaling$616 billion. Let's say the Fed made the decision to raise the reserve requirement from 10% to 11% in order to decrease the amount of money in circulation. How much of a change in the money supply would the change in the reserve requirement have caused, assuming that all banks were initially lent up (had no extra reserves) and currency held outside of banks remained constant?

Two crosses were made in Neurospora involving the mating type locus and either the ad or p genes. In both cases, the mating type locus (A or a) was one of the loci whose segregation was scored. One cross was ad $A \times a d^{+}$ a (cross a), and the other was $p A \times p^{+}$ a (cross b). From cross a, 10 parental ditype, 9 nonparental ditype, and 27 tetratype asci. a. What are the linkage relationships between the mating type locus and the other two loci? b. Although these two crosses were performed in Neurospora, you cannot use the data given to calculate centromere-to-gene distances for any of these genes. Why not?

Two particles of charge $q$ and $-2 q$ are located as shown in the given figure. A third charge $Q$ is placed on the $x$ axis and it is found that the total electric force on $Q$ is zero. In which region in the given figure is $Q$ located?

(a) region A

(b) region B

(c) region C

In the given exercise below, find the centroid of the region.

Region between y=x(a-x) and the x-axis for a>0

How many straight lines that pass through the origin are tangent to y = cos x? Find (to 6 decimal places) the slopes of the two such lines that have the largest positive slopes.

A $4.00 \times 10^{2} \mathrm{N} \cdot \mathrm{m}$ torque is produced applying a force 1.60 m from the fulcrum and at an angle of $80.0^{\circ}$ to the lever. How large is the force?

Explaining the clues you use, make inferences about the speaker's character in (a) lines $31$-$43$ of "My Last Duchess" and (b) lines $18$- $20$ of "Life in a Love."

You have a fixed length $L$ of wire and wish to make a single loop that will experience the maximum torque in a magnetic field. Is it better to make the coil circular or square, or doesn't it matter?

Mendel studied a tall variety of pea plants with stems that are 20 cm long and a dwarf variety with stems that are only 12 cm long. A. Under blending theory, how long would you expect the stems of first and second hybrids to be? B. Under Mendelian rules and assuming stem length is controlled by a single gene, what would you expect to observe in the second-generation hybrids if all the first-generation hybrids were tall?

Vocabulary: Sex ratio

Sketch the given region R and then find its area. R is the region bounded by the curve $y = x^2 - 2x$ and the x axis. [Hint: Note that the region is below the x axis.

Find the volume of the given solid. The solid tetrahedron with vertices (0, 0, 0), (0, 0, 1), (0, 2, 0), and (2, 2, 0)