Question Solved1 Answer Part A For the two vectors in the figure (Figure 1) , find the magnitude of the vector product A⃗ ×B⃗ . Part B Find the direction of the vector product A⃗ ×B⃗ . Find the direction of the vector product . +z-direction

One of the many interesting fundamental particles in nature is the muon ?. This particle acts very much like a heavy electron and has a mass of 106MeV/c2, compared to the electron's mass of just 0.511MeV/c2. (Here we are using E=mc2 to obtain the mass in units of energy and the speed of light c). Unlike the electron, the muon has a finite lifetime, after which it decays into an electron and two very light neutrinos ( ?). We'll ignore the neutrinos throughout this problem. If the muon is at rest the characteristic time that it takes to decay is about 2.2?s (??=2.2×10?6s). Most of the time though, particles such as muons are not at rest and, if moving relativistically, their lifetimes will be increased by time dilation. In this problem we will explore some of these relativistic effects. Let's begin by looking at some muons moving at various speeds relative to a stationary observer. Part A If a muon is traveling at 70% the speed of light, how long will it take to decay in the observer's rest frame (i.e., what is the observed lifetime)? Express your answer in microseconds to two significant figures. View Available Hint(s) ?? = ?s SubmitPrevious Answers Incorrect; Try Again; 4 attempts remaining Part B If a muon is traveling at 99.9% the speed of light, how long will it take to decay in the observer's rest frame? Express your answer in microseconds to two significant figures. ?? = 49•10?649{\cdot}10^{-6} ?s SubmitPrevious AnswersRequest Answer Incorrect; Try Again; 5 attempts remaining Part C What is the total energy E of a muon traveling at 99.9% the speed of light? Recall that the rest energy of the muon is approximately 106MeV. Note that 1GeV=1000MeV. Express your answer in billions of electron volts to three significant figures. View Available Hint(s) E = GeV Submit Cosmic rays are constantly raining down on the earth from outer space. (Figure 1)The majority of these cosmic rays are protons, and when they crash into the upper atmosphere, they can convert into particles called pions ( ?), which subsequently decay into muons with a characteristic lifetime of ??=2.6×10?8s (in their rest frame). These muons can then continue down toward the earth until they too decay (into electrons, which are so light that they stop very quickly in the atmosphere). Let's look at how time dilation affects these cosmic rays. Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere, 45 km above the earth's surface, producing a pion that decays into a muon. Assume that the pion has a velocity of 99.99% the speed of light and decays into a muon, which, owing to kinematics, has a downward velocity of 99.9943% the speed of light. Part D How far would the pion travel before it decayed, if there were no time dilation? Express your answer in meters to two significant figures. d? = m SubmitRequest Answer Part E How far would the muon travel before it decayed, if there were no time dilation? Express your answer in meters to three significant figures. d? = m SubmitRequest Answer Part F Now, let's consider the effects of time dilation. How far would the pion actually travel before decaying? Express your answer in meters to three significant figures. d? = m SubmitRequest Answer Part G How far would the muon travel, taking time dilation into account? Express your answer in kilometers to two significant figures. d? = km SubmitRequest Answer Provide Feedback

Q.17: Heat in the amount of 7.5 kJ is added to a closed system while its internal energy decreases by 12 kJ. How much energy is transferred as work? For a process causing the same change of state but for which the work is zero, how much heat is transferred?

Blue Spruce Corp. has decided to expand its operations. The bookkeeper recently completed the following statement of financial position in order to obtain additional funds for expansion:obligation is considered a long-term liability. (List Current Assets in order of liquidity. List Property, Plant and Equipment in order of Buildings, and Equipment.)

(15 points): Consider (again) the complex function G: C+C defined by 8 +2 G(8) 32 +63 + 18 (a) By hand, draw a pole-zero map of G (i.e., in the complex plane, draw a "o" to indicate points where G evaluates to zero and an "x" to indicate points where the magnitude of G tends to infinity).

The problem is Customers arrive at a tool crib according to a Poisson process of rate $\lambda = 5$ per hour. There is a single tool crib employee, and the individual service times are exponentially distributed with a mean service time of 10 minutes. In the long run, what is the probability that two or more workers are at the tool crib being served or waiting to be served? It is given that $\lambda = 5$, and I believe that $\mu = 6$ customers per hour. Then, I think the answer is $$1-\frac{1}{6}-\frac{1}{6}\left(\frac{5}{6}\right)-\frac{1}{6}\left(\frac{5}{6}\right)^2 = \frac{125}{216}.$$ However, the answer in the back is $\frac{25}{36}$. I was wondering what I did wrong. Or is the answer in the back wrong? Thanks.

26. EMPLOYEE POPULATION BASE In a large metropolitan area, 81% of the employed population is enrolled in a health maintenance organization (HMO). If 700,650 employees are enrolled, find the total number of people in the employed population. 28. VOTER REGISTRATION Registered Republican voters make up 13.8% of the population of one county, If there are 345,000 registered Republican voters in the county, find the total population in the county 30. DRIVING TESTS In analyzing the success of driver's license applicants, the state finds that Sa 3% of those examined received a passing mark. If the records show that 8370 new driver's licenses were issued, what was the number of applicants? Round to the nearest whole number 32. FAMILY SIZE One survey among college students found that 28.4% grew up in a home with two or more siblings and 44.7% grew up in a home with one sibling. If 194 students grew up in a home with no siblings, find the size of the survey group 34. HIRING Apple, Inc. recently announced that it will be hiring 5000 employees. If this is about 4.3% of the current workforce, estimate the number of people who work for Apple. 36. SMOKING OR NONSMOKING A casino hotel in Barbados states that 70% of its rooms are for nonsmokers. If the resort allows smoking in 264 rooms, find the total number of rooms. 22. JOB CUTS One Carrier Corporation factory builds air conditioning systems for commercial buildings. Sales are traditionally low as summer draws to an end and the manager decides he must lay off 80 of the 760 employees working on the assembly lines. Find the percent of workers that will be laid off. 24. VOCABULARY There are 55,000-plus words in Webster's Dictionary, but most educated people can identify only 20,000 of these words. What percent of the words in the diction-ary can these people identify 26. TANNING SALON Only 250 of Thai Beach's 1100 customers tan regularly. Find the per cent that tan regularly 28. MOTORCYCLISTS Of the 2380 motorcycle riders that participated in a recent bike rally through the California mountains, 2041 were men. Find the percent who were men. 30. WIND ENERGY In the early 1980s, wind-generated electricity cost about 30 cents per kilo-watt hour. Today, the best wind systems can produce electricity for 2 cents per kilowatt hour Find today's cost as a percent of the cost in the 1980s. p104 4,6 4. GLOBAL WARMING Periodically, 50% or more of all species of animals have gone extinct in a relatively short period of time. Many scientists believe we are entering such a period now as Earth warms. In fact, one scientist predicts that as many as 5 million out of the estimated 8.7 million species on Earth will disappear by 2100. Find the percent that may go extinct 6. LIGHTS OUT There are still 88,000 households in the United States that do not have electricity. If this is 08% of the homes, find the total number of households.