Complex numbers Questions and Answers

Open Ended Describe a real world situation that each expression might model Tell what each variable represents 36 5t 37 b 3 38 40 h

3 The table shows pork production in China from 2000 to 2007 Use a calculator to answer the questions Let 2000 year 0 Pork Production in China Year 2000 2001 2002 2003 2004 2005 2006 2007 Production metric tons 40 475 42 010 43 413 45 331 47 177 50 254 52 407 54 491 SOURCE USDA Foreign Agricultural Service GAIN Report a Find the equation for the line of best fit b Use your linear model to predict how many metric tons of pork will be produced in 2025 c Use your linear model to predict when productions is likely to reach 100 000 metric tons

Learning Goal from Lesson 12 8 I can compute the annual net income the annual yield and monthly rent to charge on an investment in real estate rental property How I Did Circle one I got it I m still learning it 10 Phillipe Isaacs bought a three bedroom two bath house as a rental property He paid 149 600 with a 75 000 down payment The annual expenses totaled 8 750 Phillipe rented the house for 975 per month a What annual net income did Philippe earn b What was his annual yield 2 points

I can compute the loading charge and number of shares purchased when you sell a mutual fund I got it one I m still learning it 8 Baza Grycza invested 30 000 in the Hansen Ryder Mutual Fund Type A The net asset value is 16 80 per sh The fund is front loaded with a loading rate of 3 5 a What is the loading charge b How many share dide buy 1 point

Use a graphing calculator to make a scatter plot for the following set of points Describe the correlation 1 1 1 5 1 5 2 1 2 5 1 5 3 2 3 5 3 4 3 5 3 5 5 3 5 6 4 O positive correlation O negative correlation no correlation

Name the rational numbers that are not integers from the list below 1 8 0 79 5 81 6 25 17 43 2 1 4848848884 The rational numbers that are not integers are Use commas to separate answers

Which numbers below are integers but not natural numbers 15 13 8 88 12 0 3 27 7 List the number s Use a comma to separate answers as needed

For a particular exotic animal it is estimated that there are no more than 370 of these anima left in the wild and approximately the same number in captivity Of the thirteen subspecies of this animal five are extinct and the remaining eight are endangered a What is the percentage of subspecies of the animal that have become extinct b What is the percentage of subspecies of the animal that are endangered c How many subspecies of the animal are not extinct and are not endangered

Use the commission schedule from Company B shown in the table to find the annual rate of interest earned on the investment Note commisions are rounded to the nearest cent Principal Value of Stock Under 3 000 3 000 10 000 Over 10 000 Commissi 32 1 8 of princi 56 1 of princi 106 0 5 of princi An investor purchases 494 shares at 36 53 a share holds the stock for 262 days and then sells the stock for 50 34 a share Assume a 360 day year The annual rate of interest is Round to three decimal places

nd the quadratic 1 5 1 3 2 3 hose graph passe

roblem 7 If A 4 and B 3 then find B a C

y3z6 Joga 2 1 2 2 4 Simplify y z6 3 6 2 4 gs x

3 6 1 1 Practice 3 Draw copies of the rectangle to show how a rectangle could 1 tile the plane Line To X

03 O 3 O 1 3 Show Transcribed Text

Let S be the surface in R defined by f x y z 0 The tangent plane of S at 2 9 1 is defined by 7 x 2 9 y 9 z 1 0 a Given the equation of the tangent plane to S enter in the box below a column vector v that can be the gradient of fat 2 9 1 V IE V Enter the column vector in the form 1 2 3 b Let g x y z 14x 4y 4z 384 Prove that the surface T defined by g x y z 0 is tangent to the surface S at the point 2 9 1 You don t need to show all computations but you must describe the steps of your proof 1 4

Name the rational numbers from the list below 1 3 10 0 74 1 04 3 49 3 9 A 1 3737737773 C What are the rational numbers Select all that apply 3 5 5 E 10 G 49 DI 3 5 1 3737737773 B 74 D O F 1 04 H 1

Determine if the following expression is a polynomial

5 Consider the ring Z with ideal 5 Give the ring tables of Z 5 4 points 6 Consider the ring Z12 with ideal I 0 3 6 9 Give the ring tables of Z12 1 4 points

a Recall the definition of 1 for all n Find k making sure to justify your answer from the lessons in 4C There is a fixed real number k so that 2 km n 2 1 n kn 2kn k n

Problem 4 Given that A 12 B 6 and y find the missing sides and angles A C a B

Question 2 Math 105 Berry wants to start a small cookie business He will spend 250 this year for a booth to start up the business He has determined that it will cost him 2 35 to produce each cookie He is planning to sell the cookies at the summer festivals for 5 00 per cookie Using a linear equations determine the cost revenue and profit functions Explain how you would help a student to determine which information should be used for each function

A uniform magnetic field B has constant strength b teslas in the z direction i e B 0 0 b a Verify that A B x r is a vector potential for B where r x y 0 b Calculate the flux of B through the rectangle with vertices A B C and D in Figure 17 Flux B A Z B FIGURE 17 A 5 0 2 B 5 2 0 C 0 2 0 D 0 0 2 F 5 0 0

M 7 r 1 All lengths radius curved surface O whicho be assumed radius are same Find arec of this shape

Determine whether the series is 00 n 1 1 3 n 1 absolutely convergent O conditionally convergent O divergent

3 ft 2 5 ft 2 ft Trenton will need Trenton is building a skateboarding ramp in the shape of a triangular prism According to his plan the ramp would have a base of 2 feet a height of 1 5 feet and a length of 3 feet The riding surface would measure 2 5 feet 1 5 ft If Trenton wants to cover all faces of the ramp with plywood how much plywood will he need to buy ft 2 of plywood

When a cyclist pedals he turns a gear called a chainring The angular velocity of the chainring will determine the linear speed at which the chain travels The chain connects the chainring to a smaller gear called a sprocket which is attached to the rear wheel see figure below The angular velocity of the sprocket depends upon the linear speed of the chain The sprocket and rear wheel rotate at the same rate and the diameter of the rear wheel is 700 millimeters The speed at which the cyclist travels is determined by the angular velocity of his rear wheel Use this information to answer the following Rear wheel Sprocket diameter Chain Chainring diameter A pro cyclist is climbing Mount Ventoux equipped with a 150 millimeter diameter chainring and a 95 millimeter diameter sprocket If he was pedaling at a rate of 100 revolutions per minute find his speed in kilometers per hour 1 km 1 000 000 mm Round your answer to one decimal place km hr

Using the expansion for the binomial x We wish to find the coefficient for the term with xy24 The number of the term is The coefficient for this term is

Disprove the following statement by letting y equal 5 and using a graphing utility to graph the function on each side of the equal sign The two functions should have different graphs showing that the equation is not true in g log x logy log Let y 5 and graph the function on the left side of the equation Each graph below uses a 0 10 1 by 4 4 1 viewing rectangle Choose the correct graph below SOA OA ON OB Let y 5 and graph the function on the right side of the equation Each graph below uses a 0 10 1 by 4 4 1 viewing rectangle Choose the correct graph below O C OB O C SOU Q Q O D OD Q Q Q Q

Find the exact value of the expression tan sin cos

Show ALL work in order to receive any credit Solve the triangle with the given parts Round answers to one decimal place B 11 2 C 131 6 92 4

Over a period of time a hot object cools to the temperature of the surrounding air This is described mathematically by Newton s Law of Cooling T C To C e kt where t is the time it takes for an object to cool from temperature To to temperature T C is the surrounding ajr temperature and k is a positive constant that is associated with the cooling object A cake removed from the oven has a temperature of 210 F and is left to cool in a room that has a temperature of 70 F After 40 minutes the temperature of the cake is 140 F What is the temperature of the cake after 60 minutes After 60 minutes the temperature of the cake is F Do not round until the final answer Then round to the nearest whole number as needed CL

Use the formal definition of a limit to show that 1 lim x 6 5 3x 2 3 lim 4 X 1 7 7 7

1 1 point The matrix A 2 1 4 2 2 2 2 4 2 1 1 2 2 0 The eigenvalue is and has multiplicity k For this eigenvalue the eigenvector v has components a and b that satisfy 2 2 a 1 b 0 1 a 4 2 b 0 which is the system such that a 8 Since there is no other linearly independent solution this eigenvalue is defective Following the algorithm for defective multiplicity 2 eigen values find a nonzero solution v2 of the equation A 2 v 0 Let V2 has characteristic equation det Choosing a 1 for the eigenvector is v b a b 0 a b 0 A 2 V V C a where c d are to be determined Then A 2 v2 v is the system c d c d Choosing c 1 V2 1 12 11 1 A general solution of the differential equation x t Ax is given by x t C x1 1 c x2 1 where x t vie x2 1 v te v e Answer s submitted incorrect 41

What are the advantages of switching a quadratic function from standard form into vertex form Please answer using complete sentences Bi U Font Family AA A E E

I can compute health insurance premiums How I Did Circle one I got it I m still learning it 1 Boris Heban is single and pays into an HMO The total cost is 8 190 annually and the employer pays 90 of the total cost Boris also pays 50 of the optional annual dental premium of 662 and 50 of the optional annual vision premium of 288 How much is deducted each week from his paycheck 1 point

1 IRA Fair Market Value 260 000 546 000 186 400 418 680 328 840 284 348 Amount Withdrawn at Age 55 50 000 35 000 10 000 a 35 000 a Penalty for Early Withdrawal a 23 780 a 5 000 3 500 Required Minimum Age Distribution 73 a 72 a 74 b 80 b 77 b 71 b Penalty If Not Withdrawn b b C O 25E C C C pige

Example Bob Bains had saved 2 000 00 per year in his IRA for 35 years At age 70 the fair market value of his IRA was 256 202 89 Using the Uniform Life Table on p 47 what is his required minimum distribution What penalty would he pay if he did not take the distribution If Bob had withdrawn 25 000 00 at age 50 for vacation purposes what would have been his penalty What if he had used the 25 000 00 for his children s college expenses Step 1 Find the required minimum distribution Fair Market Value 9 350 47037 Life Expectancy Factor Bob s required minimum distribution is 9 350 47 Step 2 Find the penalty for failure to take a distribution 50 Required Minimum 0 50 256 202 89 27 4 0 10 Distribution 9 350 47 Step 3 Find the penalty for each withdrawal 10 Amount of Distribution 25 000 4 675 24 penalty 2 500 Step 4 Determine the penalty for making an early withdrawal for his children s college expenses No penalty for making an early withdrawal for his children s college expenses Concept Check Complete the problems 1 May Kawasaki is 72 and has an IRA with a fair market value of 98 000 a Use the Uniform Life Table on p 47 to determine her required minimum distribution b What penalty would she incur if she failed to take the distribution c What penalty would she have paid if she had made an early withdrawal of 10 000 to take a vacation 2 Amir Bahoud is 70 and has a Roth IRA with a fair market value of 156 800 a Use the Uniform Life Table p 46 to determine her required minimum distribution b What penalty would he incur if he failed to take t distribution c What penalty would he have paid if he had made an early withdrawal of 20 000 to help pa his grandchildren s college education Personal Finance B Pa

Learning Goal from Lesson 11 2 I can calculate the amount the patient pays for health care How I Did Circle one I m still learning it I got it Find the a deductible b co payment amount e hospital charges and d total paid by the insured Use the figure on p 10 to help you 2 Sofia Carbondale has a network single plan After meeting her annual deductible she had these co payment 18 physician visits 15 specialist visits and 15 physical therapy visits at 90 each Sofia also had 1 emergency room visit and a hospital charge of 24 660 1 point

2 Consider two linear transformations T and S from R R defined as T x y 2x y x y and S x y x cy x 2y Let A and B be matrix representations of linear transformations T and S with respect to the standard bases of R2 respectively Consider the following statements P If c 1 then A and B are similar matrices Q If c 2 then A and B are similar matrices R If c 1 and P AP B then P can be the matrix S If c 1 and P AP B then P can be the matrix T If c 1 then there are infinitely many P satisfying the equation P AP B Which of the following options are true P is true but Q is false Both P and Q are true Both R and S are true R is false but S is true 10 12 1 2 Tis true

A dihedral group is the group of symmetries of a regular polygon which includes rotations and reflections Let D refers to the symmetries of n gon with 2n elements a Sketch a regular pentagon D5 Using dotted lines label all the reflection lines b List all elements of D5 and determine their orders c Give H a nontrivial normal subgroup of D5 d What is the factor groun Dr H2

The exponential models describe the population of the indicated country A in millions t years after 2006 Which country has the greatest growth rate By what percentage is the population of that country increasing each year Country has the greatest growth rate Country 1 Country 2 Country 3 Country 4 A 130 9e A 1098 4e 0 0011 0 0121 A 144 5e 0 001t A 27 3 0 028t

in a country were equipped with a camera The data can be modeled by the function f x 8 36 In x where f x is the percentage of new cellphones with cameras x years after 2002 CILE 80 70 60 50 40 30 20 10 0 34 Cempriones with Cameras 50 63 68 8 2003 2004 2005 2006 2007 a Use the function to determine the percentage of new cellphones with cameras in 2005 Does this overestimate or underestimate the percent displayed by the graph By how much Determine the percentage of new cellphones with cameras in 2005 using the given function Round to the nearest percent as needed

Use your graphing utility to graph each side of the following equation in the same viewing rectangle Then use the x coordinate of the intersection point to find the equation s solution set Verity this value by direct subsutution Inte equation log 3 3x 9 2 Choose the correct graph below All graphs are 0 10 1 by 5 5 1 OA What is the equation s solution set O C Q U OD Q Q

Solve the equation Use a calculator to obtain a decimal approximation correct to two decimal places for the solution In 2x 1 In x 1 2 lnx 0 4 The solution set is Round to two decimal places Use a comma to separate answers as needed

Solve the exponential equation Express the solution set in terms of natural logarithms Then use a calculator to obtain a decimal approximation correct to two decimal places for the so 90 7x 664 XXX What is the solution in terms of natural logarithms The solution set is Use a comma to separate answers as needed Simplify your answer Use integers or decimals for any numbers in the expression

Use transformations of the graph of f x ex to graph the given function Be sure to give the equation of the asymptote Use the graph to determine the function s domain and range h x ex Graph h x e Use the graphing tool to graph the function What equation represents the asymptote of h x ex Type an equation 10 5 Ay

Prove that 0 1 has the same cardinal number as 0 2 U 7 9

Express the difference as product of sin and or cos sin 30 sin 20 26

Determine which of the four quadrants I II III IV angle is located in a given cose 0 and tan 0 b given sin 0 and cot 0 c given cos 0 and tan 0

The loudness level of a sound can be expressed by intensity of a sound barely audible to the human ear The formula D 10 log 1 logo describes the loudness level of a sound D in decibels where I is the intensity of the sounc in watts per meter and I is the intensity of a sound barely audible to the human ear Use this information to answer parts a and b below a Express the formula so that the expression in parentheses is written as a single logarithm Choose your answer below OA C D log 170 0 8 D 10 log B D 10 log 11 OD D 10 log 1 0 b Use the form of the formula from part a to answer this question If a sound has an intensity 1 100th of the intensity of a louder sound how much smaller on the decibel scale is the loudness level of the less intense sound decibels softer