At 1:00 pm one winter afternoon, there is a power failure at your house in Wisconsin, and your heat does not work without electricity. When the power goes out, it is $68^{\circ} \mathrm{F}$ in your house. At 10:00 pm, it is $57^{\circ} \mathrm{F}$ in the house, and you notice that it is $10^{\circ} \mathrm{F}$ outside. Assuming that the temperature, $T$, in your home obeys Newton's Law of Cooling, write the differential equation satisfied by $T$.

The tool in an orthogonal cutting operation is 0.250 in wide and has a rake angle $=5^{\circ}$. The machine tool is set for a chip thickness before the cut of 0.012 in, and cutting speed $=100 \mathrm{~ft} / \mathrm{min}$. After the cut, the deformed chip thickness $=0.031$ in. Calculate (a) the shear plane angle, (b) the shear strain for the operation, and (c) material removal rate.

You will need a piece of string or yam, a pair of scissors, and a tape measure. Measure oat any length of string at least 5 feet long. Double over the string and cut it in half. Take one of the resulting halves, doable it over, and cut it in half. Continue this process until you are no longer able to cut a length of string is half. How many cuts were you able to make? Construct a sequence of the resulting string lengths after each cut, starting with the original length of the string. Find a formula for the nth term of this sequence. How many cuts could you theoretically make? Write a short paragraph discussing why you were not able to make that many cuts.

At 1:00 pm one winter afternoon, there is a power failure at your house in Wisconsin, and your heat does not work without electricity. When the power goes out, it is $68^{\circ} \mathrm{F}$ in your house. At $10: 00 \mathrm{pm}$, it is $57^{\circ} \mathrm{F}$ in the house, and you notice that it is $10^{\circ} \mathrm{F}$ outside. Solve the differential equation to estimate the temperature in the house when you get up at 7:00 am the next morning. Should you worry about your water pipes freezing?

Consider the data presented in Exercise 14.14.

What is the value of the rate constant?

The philanthropic organization in the earlier exercise expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise l you looked at the histograms showing distributions of sample proportions from 1000 simulated mailings for samples of size 20, 50, 100, and 200. The sample statistics from each simulation were as follows:

$$\begin{array}{r|c|c} {\boldsymbol{n}} & \text { mean } & \text { st. dev. } \\ \hline 20 & 0.0497 & 0.0479 \\ 50 & 0.0516 & 0.0309 \\ 100 & 0.0497 & 0.0215 \\ 200 & 0.0501 & 0.0152 \end{array}$$

Looking at the histograms in the earlier exercise, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution? $\newline$ What does the Success/Failure Condition say about the choice you made above.

At 1:00 pm one winter afternoon, there is a power failure at your house in Wisconsin, and your heat does not work without electricity. When the power goes out, it is $68^{\circ} \mathrm{F}$ in your house. At 10:00 pm, it is $57^{\circ} \mathrm{F}$ in the house, and you notice that it is $10^{\circ} \mathrm{F}$ outside. Assuming that the temperature, $T$, in your home obeys Newton's Law of Cooling, write the differential equation satisfied by $T$.

What assumption did you make in above Problem about the temperature outside? Given this (probably incorrect) assumption, would you revise your estimate up or down? Why?

The following information relates to the intangible assets of Lettuce Express: a. On January 1, 2012, Lettuce Express completed the purchase of Farmers Produce, Inc., for $1,500,000 in cash. The fair value of the identifiable net assets of Farmers Produce was$1,350,000. b. Included in the assets purchased from Farmers Produce was a patent for a method of processing lettuce valued at $45,000. The original legal life of the patent was 20 years. There are still 17 years left on the patent, but Lettuce Express estimates the patent will be useful for only 10 more years. c. Lettuce Express acquired a franchise on July 1, 2012, by paying an initial franchise fee of$175,000. The contractual life of the franchise is seven years.

Required:

1. Record amortization expense for the intangible assets at December 31, 2012.
2. Prepare the intangible asset section of the December 31, 2012, balance sheet.

A rainbow is produced by the reflection of sunlight by spherical drops of water in the air. Figure shows a ray that refracts into a drop at point $A$, is reflected from the back surface of the drop at point $B$, and refracts back into the air at point $C$. The angles of incidence and refraction, $\theta_a$ and $\theta_b$, are shown at points $A$ and $C$, and the angles of incidence and reflection, $\theta_a$ and $\theta_r$, are shown at point $B$. A rainbow will form when the angular deflection $\Delta$ is stationary in the incident angle $\theta_a^A$ — that is, when $d \Delta / d \theta_a^A=0$. If this condition is satisfied, all the rays with incident angles close to $\theta_a^A$ will be sent back in the same direction, producing a bright zone in the sky. Let $\theta_1$ be the value of $\theta_a^A$ for which this occurs. Show that $\cos ^2 \theta_1=\frac{1}{3}\left(n^2-1\right)$.

True or False. Food enters the alimentary canal which runs from your mouth to your anus only the food that is absorbed enters the body.

A uniform spring with k=8600 N/ m is cut into pieces 1 and 2 of unstretched lengths L_1=7.0 cm and L_2=10 cm. What are piece 1?

There were 4 in the first group and their average quality was 6 . There were 10 in the second group and their average quality was 4 . What should be the average quality of the last 16 so that the overall average quality would be 8 ?

Suppose a cut is made through a solid object perpendicular to the $x$-axis at a particular point $x$. Explain the meaning of $A(x)$.

Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest tenth of a degree.)

$$\langle 4,1,8\rangle$$