Math in Our World
3rd Edition
ISBN: 9780073519678
Author: David Sobecki Professor, Allan G. Bluman
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 12, Problem 9RE
Twelve batteries were tested to see how many hours they would last. The frequency distribution is shown here.
| Hours | Frequency |
| 1–3 | 1 |
| 4–6 | 4 |
| 7–9 | 5 |
| 10–12 | 1 |
| 13–15 | 1 |
Find the mean.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Remix
4. Direction Fields/Phase Portraits. Use the given direction fields to plot solution curves
to each of the given initial value problems.
(a)
x = x+2y
1111
y = -3x+y
with x(0) = 1, y(0) = -1
(b) Consider the initial value problem corresponding to the given phase portrait.
x = y
y' = 3x + 2y
Draw two "straight line solutions"
passing through (0,0)
(c) Make guesses for the equations of the straight line solutions: y = ax.
It was homework
No chatgpt pls will upvote
Chapter 12 Solutions
Math in Our World
Ch. 12.1 - To study the number of credit hours taken by a...Ch. 12.1 - A health-food store recorded the type of vitamin...Ch. 12.1 - In one math class, the data below represent the...Ch. 12.1 - Prob. 4TTOCh. 12.1 - What are data?Ch. 12.1 - Define statistics.Ch. 12.1 - Explain the difference between a population and a...Ch. 12.1 - How is a random sample selected?Ch. 12.1 - How is a systematic sample selected?Ch. 12.1 - How is a stratified sample selected?
Ch. 12.1 - How is a cluster sample selected?Ch. 12.1 - Prob. 8ECh. 12.1 - Describe the difference between descriptive and...Ch. 12.1 - How do inductive and deductive reasoning play a...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - In Exercises 172, decide if you think the method...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - At a college financial aid office students who...Ch. 12.1 - A questionnaire about how students primarily get...Ch. 12.1 - Twenty-five fans of reality TV were asked to rate...Ch. 12.1 - A small independent developer of apps for...Ch. 12.1 - The ages of the signers of the Declaration of...Ch. 12.1 - The percentage of traffic fatalities in which at...Ch. 12.1 - The data shown are the cigarette taxes per pack in...Ch. 12.1 - The acreage (in thousands of acres) of the 39 U.S....Ch. 12.1 - The heights in feet above sea level of the major...Ch. 12.1 - During the 1998 baseball season. Mark McGwire and...Ch. 12.1 - The data (in millions of dollars) are the values...Ch. 12.1 - Twenty-nine executives reported the number of...Ch. 12.1 - The National Insurance Crime Bureau reported that...Ch. 12.1 - Prob. 36ECh. 12.1 - The data shown represent the percentage of...Ch. 12.1 - Prob. 38ECh. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - Prob. 44ECh. 12.1 - In addition to the four basic sampling methods,...Ch. 12.1 - For the data in Exercise 33, draw a stem and leaf...Ch. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.2 - The frequency distribution below represents...Ch. 12.2 - Prob. 2TTOCh. 12.2 - Prob. 3TTOCh. 12.2 - Prob. 4TTOCh. 12.2 - Prob. 5TTOCh. 12.2 - Describe how to draw a bar graph and a pie chart...Ch. 12.2 - Explain why bar graphs and pie charts are...Ch. 12.2 - How are histograms and frequency polygons similar?...Ch. 12.2 - Describe the purpose of a time series graph.Ch. 12.2 - Draw a bar graph for the number of transplants of...Ch. 12.2 - The data below show the number of students...Ch. 12.2 - Draw a bar graph for the number of registered...Ch. 12.2 - Prob. 8ECh. 12.2 - The number of students at one campus who had a 4.0...Ch. 12.2 - In an insurance company study of the causes of...Ch. 12.2 - In a survey of 100 college students, the numbers...Ch. 12.2 - Prob. 12ECh. 12.2 - For 108 randomly selected college applicants, the...Ch. 12.2 - Prob. 14ECh. 12.2 - Thirty cars and trucks were tested by the EPA for...Ch. 12.2 - Prob. 16ECh. 12.2 - The data below represent the number of people...Ch. 12.2 - Prob. 18ECh. 12.2 - The following data represent the number of...Ch. 12.2 - Prob. 20ECh. 12.2 - The data below are the avenge daily temperatures...Ch. 12.2 - The data below are the average daily temperatures...Ch. 12.2 - The number of employed registered nurses tin...Ch. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Make up your own frequency polygon problem: using...Ch. 12.3 - To test a customers Internet connection, a tech...Ch. 12.3 - Prob. 2TTOCh. 12.3 - Prob. 3TTOCh. 12.3 - Prob. 4TTOCh. 12.3 - Prob. 5TTOCh. 12.3 - Prob. 6TTOCh. 12.3 - Prob. 7TTOCh. 12.3 - The number of earthquakes worldwide measuring at...Ch. 12.3 - Prob. 9TTOCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Which of the measures of average can be used to...Ch. 12.3 - In Questions 710, describe some strengths and...Ch. 12.3 - In Questions 710, describe some strengths and...Ch. 12.3 - In Questions 710, describe some strengths and...Ch. 12.3 - In Questions 710, describe some strengths and...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - Prob. 26ECh. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - Prob. 28ECh. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - For these situations, state which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.4 - The monthly average high temperatures from January...Ch. 12.4 - Prob. 2TTOCh. 12.4 - Prob. 3TTOCh. 12.4 - Prob. 4TTOCh. 12.4 - Name three measures of variation.Ch. 12.4 - What is the range?Ch. 12.4 - Why is the range not usually the best measure...Ch. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - For Exercises 710, discuss the relative sizes of...Ch. 12.4 - For Exercises 710, discuss the relative sizes of...Ch. 12.4 - For Exercises 710, discuss the relative sizes of...Ch. 12.4 - Prob. 10ECh. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - The three data sets have the same mean and range,...Ch. 12.4 - Prob. 28ECh. 12.5 - The weights in pounds for the 12 members of a...Ch. 12.5 - Prob. 2TTOCh. 12.5 - Prob. 3TTOCh. 12.5 - Prob. 4TTOCh. 12.5 - Prob. 5TTOCh. 12.5 - If your score in your math class puts you in the...Ch. 12.5 - Does a score in the 90th percentile mean that you...Ch. 12.5 - Explain what quartiles are.Ch. 12.5 - Prob. 4ECh. 12.5 - What does the portion inside the box in a box plot...Ch. 12.5 - What is meant by the term outlier? How can you...Ch. 12.5 - The scores for 20 students on a 50-point math test...Ch. 12.5 - The heights (in inches) of the 12 students in a...Ch. 12.5 - In a class of 500 students, Carvetas rank was 125....Ch. 12.5 - In a class of 400 students, Johns rank was 80....Ch. 12.5 - In a charity marathon to raise money for AIDS...Ch. 12.5 - An investor decides to buy stock only in companies...Ch. 12.5 - On an exam, Angela scored in the 20th percentile....Ch. 12.5 - Out of 600 applicants to a graduate program at an...Ch. 12.5 - Eldrick finished at the 77th percentile of a mens...Ch. 12.5 - Tinas application for a nursing position is ranked...Ch. 12.5 - Leas percentile rank on an exam in a class of 600...Ch. 12.5 - In an English class of 30 students, Audrelias...Ch. 12.5 - The Bowling Green State University mens basketball...Ch. 12.5 - A pro golfer is ranked 48th out of 230 players...Ch. 12.5 - In an evening statistics class, the ages of 20...Ch. 12.5 - Twenty subjects in a psychology class experiment...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - In Problems 2932, draw a box plot for the data,...Ch. 12.5 - Prob. 30ECh. 12.5 - In Problems 2932, draw a box plot for the data,...Ch. 12.5 - In Problems 2932, draw a box plot for the data,...Ch. 12.5 - Is it possible to score 90% on a test and have a...Ch. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.6 - A standard test of intelligence is scaled so that...Ch. 12.6 - Prob. 2TTOCh. 12.6 - Find the area under the standard normal...Ch. 12.6 - Find the area under the standard normal...Ch. 12.6 - Prob. 5TTOCh. 12.6 - What is the distinguishing characteristic of a...Ch. 12.6 - Prob. 2ECh. 12.6 - What does the area under a portion of a normal...Ch. 12.6 - Explain what the empirical rule says.Ch. 12.6 - What percentage of the area under a normal curve...Ch. 12.6 - Why does it make sense that the total area under a...Ch. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - For Exercises 1116, the data set described is...Ch. 12.6 - Prob. 12ECh. 12.6 - For Exercises 1116, the data set described is...Ch. 12.6 - Prob. 14ECh. 12.6 - For Exercises 1116, the data set described is...Ch. 12.6 - Prob. 16ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 18ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 20ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 22ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 24ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 26ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 28ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 30ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 32ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 34ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 38ECh. 12.6 - As we know from Chapter 11, the probability of an...Ch. 12.6 - As we know from Chapter 11, the probability of an...Ch. 12.6 - As we know from Chapter 11, the probability of an...Ch. 12.6 - As we know from Chapter 11, the probability of an...Ch. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - Find two z values, one positive and one negative...Ch. 12.7 - Based on data compiled by the World Health...Ch. 12.7 - The Statistical Abstract also indicates that of...Ch. 12.7 - The mean for a reading test given nationwide is...Ch. 12.7 - The ages of 33 randomly selected inmates at a...Ch. 12.7 - Explain why the normal distribution can be used to...Ch. 12.7 - Given a data set, how could you decide if the...Ch. 12.7 - Describe the connection between area under a...Ch. 12.7 - Prob. 4ECh. 12.7 - The average hourly wage for all workers in the...Ch. 12.7 - Prob. 6ECh. 12.7 - The average cost for two people to go to a movie...Ch. 12.7 - Average sales for an online textbook distributor...Ch. 12.7 - A survey found that people keep their televisions...Ch. 12.7 - The average age of CEOs is 56 years. Assume the...Ch. 12.7 - The average life of a brand of automobile tires is...Ch. 12.7 - The average time a person spends in each visit to...Ch. 12.7 - The average amount of snow per season in Trafford...Ch. 12.7 - The average waiting time for a drive-in window at...Ch. 12.7 - The average time it takes college freshmen to...Ch. 12.7 - A brisk walk at 4 miles per hour burns an average...Ch. 12.7 - During September, the average temperature of...Ch. 12.7 - If the systolic blood pressure for a certain group...Ch. 12.7 - An IQ test has a mean of 100 and a standard...Ch. 12.7 - The average size (in square feet) of homes built...Ch. 12.7 - According to the National Association of Realtors,...Ch. 12.7 - The average price of Stephen King paperbacks sold...Ch. 12.7 - Refer to Exercise 5. If your buddy Earl gets a job...Ch. 12.7 - Refer to Exercise 9. If you buy a TV for your dorm...Ch. 12.7 - Refer to Exercise 12. Suppose that your grades...Ch. 12.7 - Refer to Exercise 20. When the one-hit wonder band...Ch. 12.7 - In Problems 2730, (a) construct a histogram for...Ch. 12.7 - In Problems 2730, (a) construct a histogram for...Ch. 12.7 - In Problems 2730, (a) construct a histogram for...Ch. 12.7 - In Problems 2730, (a) construct a histogram for...Ch. 12.7 - Discuss whether or not you think each of the given...Ch. 12.7 - The number of incoming students at two campuses of...Ch. 12.7 - If a distribution of raw scores were plotted and...Ch. 12.7 - A researcher who is in charge of an educational...Ch. 12.7 - For the data provided in Exercise 27, find the...Ch. 12.7 - Prob. 38ECh. 12.8 - The data below represent the heights in feet and...Ch. 12.8 - Find the correlation coefficient for the data in...Ch. 12.8 - Prob. 3TTOCh. 12.8 - Find the equation of the regression line for the...Ch. 12.8 - Use the equation of the regression line found in...Ch. 12.8 - Describe what a scatter plot is and how one is...Ch. 12.8 - Explain what is meant when two variables are...Ch. 12.8 - Explain what is meant when two variables are...Ch. 12.8 - Prob. 4ECh. 12.8 - Prob. 5ECh. 12.8 - Prob. 6ECh. 12.8 - Describe the key difference between correlation...Ch. 12.8 - Prob. 8ECh. 12.8 - Prob. 9ECh. 12.8 - Prob. 10ECh. 12.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 12.8 - Prob. 12ECh. 12.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 12.8 - Prob. 14ECh. 12.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 12.8 - Prob. 16ECh. 12.8 - Prob. 17ECh. 12.8 - Prob. 18ECh. 12.8 - For the data sets in Exercises 1926, (a) Draw a...Ch. 12.8 - Prob. 20ECh. 12.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 12.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 12.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 12.8 - Prob. 24ECh. 12.8 - Prob. 25ECh. 12.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 12.8 - Prob. 27ECh. 12.8 - Prob. 28ECh. 12.8 - Prob. 29ECh. 12.8 - Design your own correlation problem. Think of two...Ch. 12.8 - Prob. 31ECh. 12.8 - Prob. 32ECh. 12.8 - Prob. 33ECh. 12.8 - Prob. 34ECh. 12.8 - Prob. 35ECh. 12.8 - Prob. 36ECh. 12.8 - Prob. 37ECh. 12.8 - Prob. 38ECh. 12.8 - Prob. 39ECh. 12.8 - Prob. 40ECh. 12 - A sporting goods store kept a record of sales of...Ch. 12 - The data set shown below represents the time in...Ch. 12 - During June, a local theater company recorded the...Ch. 12 - Construct a bar graph for the number of homicides...Ch. 12 - Draw a pie chart for the data in Exercies 4....Ch. 12 - Draw a histogram and frequency polygon for the...Ch. 12 - The data set shown below indicates how much Janine...Ch. 12 - The data below are the number of U.S. citizens (in...Ch. 12 - Twelve batteries were tested to see how many hours...Ch. 12 - In your own words, explain the difference between...Ch. 12 - The data below are the number of beds at the eight...Ch. 12 - Which data set do you think would have a greater...Ch. 12 - For the census data in Problem 8, (a)Find the...Ch. 12 - Find the quartiles for the data in Problem 8, then...Ch. 12 - Find the area under the standard normal...Ch. 12 - A doctor has treated 45 male patients this week....Ch. 12 - For a data set with 90 values that is normally...Ch. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - The average weight of an airline passengers...Ch. 12 - The average cost of Cheetah brand running shoes is...Ch. 12 - Prob. 22RECh. 12 - A study is done to see whether there is a...Ch. 12 - Prob. 24RECh. 12 - Prob. 1CTCh. 12 - Prob. 2CTCh. 12 - Prob. 3CTCh. 12 - The data (in millions of dollars) are the values...Ch. 12 - Prob. 5CTCh. 12 - Prob. 6CTCh. 12 - These temperatures were recorded in Pasadena for a...Ch. 12 - Prob. 8CTCh. 12 - Prob. 9CTCh. 12 - Prob. 10CTCh. 12 - A major brand of potato chips sells its product in...Ch. 12 - A study is conducted to determine the relationship...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- (7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.arrow_forward(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =arrow_forward(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward
- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
- (8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward(4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward
- (2) (12 points) Let f(x,y) = x²e¯. (a) (4 points) Calculate Vf. (b) (4 points) Given x directional derivative 0, find the line of vectors u = D₁f(x, y) = 0. (u1, 2) such that the - (c) (4 points) Let u= (1+3√3). Show that Duƒ(1, 0) = ¦|▼ƒ(1,0)| . What is the angle between Vf(1,0) and the vector u? Explain.arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a b 29 39 66.50 C 17.40 d 0 54.0 126° a Ꮎ b darrow_forwardAnswer the following questions related to the following matrix A = 3 ³).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License