Complex numbers Questions and Answers

Find 3 matrices to multiply to A so that you obtain an upper triangular matrix That is find My M and My such that M M M A is an upper triangular matrix Let a b c be real numbers Define the following matrices A a a ab and C aaa 87c Recall that you cannot divide by zero a Show that A 1 is invertible is a 0 and ab State the pivots of A b Find two values for e such that C is not invertible

Boris opened a savings account with 500 and was paid simple interest at an annual rate of 7 When Boris closed the account he was paid 70 in interest How long was the account open for in years If necessary refer to the list of financial formulas years X

Jim is in charge of planning a reception for 2800 people He is trying to decide which snacks to buy He has asked a random sample of people who are coming to the reception what their favorite snack is Here are the results Favorite Snack Brownies Pretzels Potato chips Other Number of People 35 28 49 63 Based on the above sample predict the number of the people at the reception whose favorite snack will be brownies Round your answer to the nearest whole number Do not round any intermediate calculations people X Esp

Find the area of the figure Sides meet at right angles 5 cm 9 cm 3 cm 4 cm 6 cm cm 2

Choose the property of addition that justifies the equation 0 8 8 5 b b 5 6 y 8 6 v 8 Choose one Commutative Property Associative Property Additive Identity Property Additive Inverse Property Choose one

Use the quadratic formula to solve for x 2x 7x 5 Round your answer to the nearest hundredth If there is more than one solution separate them with commas 8

Divide 6x 13x 15x 8 2x 1 Your answer should give the quotient and the remainder Quotient Remainder 09

The average rate of change between 1997 and 2001 was Simplify your answer Type an integer or a decimal in 1997 to 1 3 billion in 2001 Find the average rate of change in the number of public library visits from billion visits years years per library years per book books books per year libraries years per visit libraries per year

K Find the slope and the y intercept of the line with the following equation 4 y 5x 7 Find the slope of the line Select the correct choice below and if necessary fill in the answer box O A The slope is Type an integer or a simplified fraction OB The slope is undefined

Find the slope if it exists of the line Select the correct choice below and if necessary fill in the answer box to complete your choice OA m Type an integer or a simplified fraction OB The slope is undefined 1 3 3 3

Determine the slope if it exists of the graph of the linear equation y 6 8x Select the correct choice below and fill in any answer boxes within your choice A The slope is B The slope is undefined Type an integer or a decimal

Find the slope of the line Select the correct choice below and if necessary fill in the answer box to complete your choice O A The slope of the line is m www Simplify your answer Type an integer or fraction OB The slope is undefined C B 64 2 2 s 6 8 10

Find power series solutions in power of x of each of the differential equation x 1 y xy 2xy 0 y 0 2 y 0 3

Find the domain of the following function Do not use a graphing calculator 1 2 x 2x 8 f x The domain is po your answer in interval notation

Given that g x a g 8 X 7 X 8 find each of the following b g 7 c g 8 OA g 8 Simplify your answer B g 8 does not exist Oc g 8 is not a real number d g 11 25 a Select the correct choice below and if necessary fill in the answer box to complete your choice e g x h

b A 41 5 4 6 3 8 B M 6 0 The base of a vertical flagpole CM is at vertex C of the flower bed The flagpole is held in place by two cables AM and BM CM 6 0m i Show that AM 7 10m correct to 2 decimal places ii Given that BM 6 95 m find the angle of elevation of M from B iii Find angle AMB the angle between the two cables

1 point There are more inches on a football field 100 yards than there are centimeters on a 28 meter basketball court True False

B 1 point The oil tank in your car is leaking at a rate of 1 2 oz per mile driven You drove 15 miles over to your grandma s house How many cups of oil did your car leak 2 cups 2 25 cups 18 cups 144 cups

1 point A square has side lengths of 9 use the Pythagorean theorem to find the length of the diagonal 18 2 18 9

15 1 point Simplify the radical expression 100 49 10 7 10 7 not possible 10 27 Previous

1 1 point Which of the following numbers can be classified as rational numbers 33 3000 3 0 1 1 234

10 1 point Multiply 2x 1 x x 3 2x 2x 6x 3 2x x 5x 3 2x 3x 7x 3 2x x 5x 3

8 1 point Square the binomial below x 4 0 0 0 0 x 16 3 2 8x 16 Previous 8x 16 16

3 1 point 62 can be classified as a natural number True False

1 5 4 2 M 10 8 6 2 0 1 2 4 6 8 10 1 3 4 a State the domain in interval notation b State the range in interval notation c State the end behavior d State the local maxima e State the local minima f State the x intercepts g State the y intercepts h State the intervals where the graph is increasing

Describe the end behavior of each function b C 10 2 4 ty AA 4 3 4 3 2 10 M 234x As x f x As x f x As x f x x As x f x As x f x As x f x Choose Choose Choose

MODEL The height of a fish t seconds after it is thrown to a dolphin from a 64 foot tall platform can be modeled by the equation h t 16t2 48t 64 where h t is the height of the fish in feet The graph of the function is shown th t 100 80 60 40 20 0 1 2 3 4t At about The maximum height of the fish is Check seconds the fish reaches its maximum height Select one True feet Temperature C 0 50 100 150 200 Density g cm 1 000 0 988 0 958 0 917 0 865 0 799 True False As temperature approaches infinity increases the density decreases 350 0 713 0 573 250 300

f 2 Check g x 2x 3 g 3 Check h x 3x 4

engineering students built a catapult for a class project They tested the catapult by launching a watermelon and modeled the height h of the watermelon in feet over time t in seconds 24 MO What is the appropriate domain in context of the problem O 0 2 5 0 25 0 2 5 Check 2010 ENGINEERING Several engineering students built a catapult for a project They tested the catapult by launching a watermelon and modeled the height h of the watermelon in feet over time t in sec It takes the watermelon less than 2 seconds to reach its maximum height Select one

CONSTRUCT ARGUMENTS Sheena says that in the graph of f x shown below the graph has relative maxima at B and G and a relative minimum at A Is she correct Explain B A S 43 50 40 30 20 10 O NOVE F D E 20 30 40 50 2 Sheena is correct 9 Sheena is not correct because she has the relative maxima incorrect Sheena is not correct because A is not a relative minimum Sheena is not correct because there are relative minima at D and 1 Choose Choose Choose Choose

Identify the coordinates of the extrema Input minimum on the left first ty O Relative Max Relative Min and

Multiple Choice Question A car travels 30 miles on one gallon of gasoline Gasoline costs 4 00 per gallon Calculate the cost of driving the car 300 miles

Answer Attempt 1 out of 5 1 6 7x 9x x The expression represents a quadratic is the leading term is polynomial with 4 terms The constar and the leading coefficient is V

Note The vector a b C in Maple syntax should be entered as a b c b Geometrically U is a plane through the origin in R4 and v is the position vector of a point A in R4 Find the exact value of the shortest distance of A from the plane U Enter your answer in Maple syntax in the box below

Find the following sum and write it in lowest terms 6 3 11 11 6 3 11 11 Type an integer or a simplified fraction

Find the difference and write in lowest terms 7 5 4

Evaluate and write in lowest terms 64 7 16

Replace the with the correct symbol 2 3 2 3 318 318 V

List all elements of the set Select all that apply A 3 73773777 C 7 E 7 6 7 8 0 7 3 73773777 that are also elements of the set of irrational numbers 6 B D O F No elements in the set are in the set of irrational numbers 8

Find the least common multiple LCM of the following numbers 117 and 72 The LCM of 117 and 72 is

Write as a fraction 0 2

The number 0 351 rounded to the nearest hundredth is

Write as a decimal 9 8

Rewrite the fraction 1 with 35 as the denominator 7

Replace the question mark by or whichever is correct 667 0 9 0 9

Write the fraction as a terminating or repeating decimal 6 7 Choose the correct answer below OA 0 85714 OB 0 857142 OC 0 857142 OD 0 85714

Write the fraction as a decimal 6100 8

Find the prime factorization of the following number Write any repeated factors using exponents 392 The prime factorization of 392 is

Write the following fraction in lowest terms 10 77 Select the correct choice below and if necessary fill in the answ O A 10 The fraction written in lowest terms is 77 Type an integer or a simplified fraction OB The fraction 10 77 is already in lowest terms

7 Write as a decimal 10 7 10 11