As a prank, someone has balanced a pumpkin at the highest point of a grain silo. The silo is topped with a hemispherical cap that is frictionless when wet. The line from the center of curvature of the cap to the pumpkin makes an angle $\theta_{i}=0^{\circ}$ with the vertical. While you happen to be standing nearby in the middle of a rainy night, a breath of wind makes the pumpkin start sliding downward from rest. It loses contact with the cap when the line from the center of the hemisphere to the pumpkin makes a certain angle with the vertical. What is this angle?

For each of the quantities listed below, explain which of the following properties (mass of the molecule, density of the gas sample, temperature of the gas sample, size of the molecule, and number of moles of gas) must be known to calculate the quantity. average number of collisions per second with other gas molecules

Graph each function in over the indicated interval. $N=\frac{200}{1+3 e^{-t}} ;[0,5]$

For saving energy, bicycling and walking are far more efficient means of transportation than is travel by automobile. For example, when riding at 10.0 mi/h, a cyclist uses food energy at a rate of about 400 kcal/h above what he would use if merely sitting still. (In exercise physiology, power is often measured in kcal/h rather than in watts. Here 1 kcal = 1 nutritionist’s Calorie = 4 186 J.) Walking at 3.00 mi/h requires about 220 kcal/h. It is interesting to compare these values with the energy consumption required for travel by car. Gasoline yields about $1.30 \times 108$ J/gal. Find the fuel economy in equivalent miles per gallon for a person (a) walking and (b) bicycling.

In terms of saving energy, bicycling and walking are far more efficient means of transportation than is travel by automobile. For example, when riding at 10.0 mi/h, a cyclist uses food energy at a rate of about 400 kcal/h above what he would use if he were merely sitting still. (In exercise physiology, power is often measured in kcal/h rather than in watts. Here, 1 kcal = 1 nutritionist’s Calorie = 4 186 J.) Walking at 3.00 mi/h requires about 220 kcal/h. It is interesting to compare these values with the energy consumption required for travel by car. Gasoline yields about $1.30 \times 10^8$ J/gal. Find the fuel economy in equivalent miles per gallon for a person bicycling.

A 650-kg elevator starts from rest and moves upward for 3.00 s with constant acceleration until it reaches its cruising speed, 1.75 m/s. What is the average power of the elevator motor during this period?

A block of mass $m=2.00 \mathrm{~kg}$ $I$ is attached to a spring of force constant $k=500 \mathrm{~N} / \mathrm{m}$. The block is pulled to a position $x_i=5.00 \mathrm{~cm}$ to the right of equilibrium and released from rest. Find the speed the block has as it passes through equilibrium if
(a) the horizontal surface is frictionless

Evaluate to five decimal places using a calculator. (A) $\log 72.604$ (B) $\log 0.033041$ (C) $\ln 40,257$ (D) $\ln 0.0059263$

A horizontal spring attached to a wall has a force constant of $k=850 \mathrm{~N} / \mathrm{m}$. A block of mass $m=1.00 \mathrm{~kg}$ is attached to the spring and rests on a frictionless, horizontal surface as.
(b) Find the speed of the block as it passes through the equilibrium point.

A sled of mass m is given a kick on a frozen pond. The kick imparts to the sled an initial speed of v. The coefficient of kinetic friction between sled and ice is $\mu_{k}.$ Use energy considerations to find the distance the sled moves before it stops.

In December 2016, Shire Computer’s management establishes the 2017 predetermined overhead rate based on direct labor cost. The information used in setting this rate includes estimates that the company will incur $747,500 of overhead costs and$575,000 of direct labor cost in year 2017. During March 2017, Shire began and completed Job 13-56. 1. What is the predetermined overhead rate for 2017? 2. Use the information on the following job cost sheet to determine the total cost of the job.

$$\begin{matrix} \quad & \text{JOB COST SHEET}\\ \text{Customer’s Name} & \text{Keiser Co.} & \text{Job No.} & \text{13-56}\\ \text{Job Description} & \text{5 plasma monitors—61 inch}\\ \quad & \text{Direct Materials} & \quad & \text{Direct Labor} & \quad & \text{Overhead Costs Applied}\\ \text{Date} & \text{Requisition No.} & \text{Amount} & \text{Time-Ticket No.} & \text{Amount} & \text{Rate} & \text{Amount}\\ \text{Mar. 8} & \text{4-129} & \text{\$5,000} & \text{T-306} & \text{\$ 700}\\ \text{Mar. 11} & \text{4-142} & \text{7,020} & \text{T-432} & \text{1,250}\\ \text{Mar. 18} & \text{4-167} & \text{3,330} & \text{T-456} & \text{1,250} & \quad & \text{\_\_\_\_\_}\\ \text{Totals} & \quad & \text{\_\_\_\_\_\_} & \quad & \text{\_\_\_\_\_\_} & \quad & \text{\_\_\_\_\_\_}\\ \end{matrix}$$

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Suppose a teaspoon of magnesium filings and a teaspoon of powdered sulfur are placed together in a metal beaker. Would this constitute a mixture or a pure substance? Suppose the magnesium filings and sulfur are heated so that they react with each other, forming magnesium sulfide. Would this still be a “mixture”? Why or why not?

Analyze the image and read the source’s headnote for Portrait of Louis XIV (1701) and answer the following: How did the historical context affect the development of the painting?

You are helping your Health teacher make fliers for Health Awareness Week. Using the phrases below, write six recommendations on the flier to the people indicated in the parentheses. Then, write six recommendations about what they should avoid. Use complete sentences. The first one has been done for you.

$$\begin{array}{ll} \text{jugar a los deportes (los jóv mmenes)} & \text{seguir las sugerencias del médico (nosotros)}\\ \text{perder peso (los estadounidenses)} & \text{pedir comida saludable (la gente)}\\ \text{acostarse temprano (tú)} & \text{dormir ocho horas (nosotros)}\\ \text{comenzar un programa de ejercicio (los estudiantes)} & \text{ }\\ \end{array}$$

LA SEMANA DE LA SALUD $\cdot$ Nos recomienda que durmamos ocho horas cada noche. Es mejor que no comamos muchas galletas. $\cdot$ _____ $\cdot$ _____ $\cdot$ _____ $\cdot$ _____ $\cdot$ _____