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?

A winch puller $A B$ is used to straighten a fence post. Knowing that the tension in cable $B C$ is $1040 \mathrm{~N}$ and length $d$ is $1.90 \mathrm{~m}$, determine the moment about $D$ of the force exerted by the cable at $C$ by resolving that force into horizontal and vertical components applied $(a)$ at point $C,(b)$ at point $E$.

Two same-size metal posts, one aluminum and one copper, are subjected to equal shear stresses. (a) Which post will show the larger deformation angle, (1) the copper post or (2) the aluminum post? Or (3) Is the angle the same for both? Why? (b) By what factor is the deformation angle of one post greater than the other?

Show that y=x$^3$-3x$^2$+3x-1 has no local extrema.

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 number of sales per month, $S$ is a function of the amount , $a$ (in dollars), spent on advertising that month , so $S=f(a)$. Interpret the statement $f(1000)=3500$.

Why did Martin Luther post his 95 Theses?

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

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).

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.

For a certain species of whale, the relationship between the length of the whale and the weight of the whale can be modeled by the function $W(l)=0.03 l^{27}$, where $l$ is the length of the whale in meters and $W$ is the weight of the whale in metric tons ( 1 metric ton $\approx 2205$ pounds). (a) Find the weight of a newborn calf that is $6 \mathrm{~m}$ long. (b) At 81 metric tons, how long is an average adult?

A weight on a spring has initial position s(0) and period P.

(a) To model displacement of the weight, determine a function s given by

$$s(t)=a \cos \omega t .$$

(b) Determine s(1). Determine whether the weight is moving upward, downward, or neither when t=1 . Support the results graphically or numerically. s(0)=-3 in.; P=0.8 $\mathrm{sec}$

Companies use many kinds of promotions to attract customers besides advertising. Which types of promotions work best at persuading you to buy?