In the following sentence, underline each preposition and draw an arrow from the preposition to its object.

However, the new "penny post" made mail delivery affordable for most people

Normally the post office processed letters at a rate of 2500 per hour. During the holiday season the rate tripled. How many hours did it take to process 60,000 letters during the holiday season?

Place a check next to each sentence in which the subject and verb agree. _____ On the fence post hangs several pieces of twine.

In the sentences below, draw an arrow from each pronoun to its antecedent. Farmers expect to harvest less than they harvested last year.

The centric force P is applied to a short post as shown. Knowing that the stresses on plane $a-a$ are $\sigma=-15 \mathrm{ksi}$ and $\boldsymbol{\tau}=5 \mathrm{ksi}$, determine (a) the angle $\beta$ that plane $a-a$ forms with the horizontal, (b) the maximum compressive stress in the post.

Consider $f(x)=\dfrac{x^2}{x^2+3}$. Find the local maximum and minimum values of $f$.

A small-scale hydraulic power system is shown. The elevation difference between the reservoir water surface and the pond water surface downstream of the reservoir, $H$, is $15 \mathrm{~m}$. The velocity of the water exhausting into the pond is $5 \mathrm{~m} / \mathrm{s}$, and the discharge through the system is $1 \mathrm{~m}^3 / \mathrm{s}$. The head loss due to friction in the penstock is negligible. Determine the power produced by the turbine in kilowatts.

Find (by hand) all critical numbers and use the First Derivative Test to classify each as the location of a local maximum, local minimum or neither. $y=x^{4 / 3}+4 x^{1 / 3}$

The nuclide $_{15}^{32} \mathrm{P}$ decays by emitting an electron whose maximum kinetic energy can be 1.71 MeV. Calculate the daughter's atomic mass (in u).

Identify two reasons why insects sometimes must be controlled.

A rancher wants to build a fence for a square lot with dimensions of 50 yd by 50 yd. He wants to install a fence post every 5 yd with a post at each corner. How many fence posts will he need?

Write the name and symbol of the element with the following atomic number: (4.4) a. 22 b. 48 c. 26 d. 54 e. 78 f. 83

In the following sentences, underline the participle once and the word it modifies twice. The spruce trees, having been planted and nurtured, were ready to harvest.

Consider an NMOS transistor that has $g_m =1\ \text{mS}$ and $r_d = 10\ \text{k}\Omega$ for a Q point of $V_{GSQ} = 1\ \text{V}$, $I_{DQ} = 2\ \text{mA}$, and $V_{DSQ} = 5\ \text{V}$. Sketch the drain characteristics to scale for a small region around the Q point, say for $v_{GS} =0.8$, 1.0, and 1.2 V and for $4.0 < v_{DS} < 6.0\ \text{V}$.