Complex numbers Questions and Answers

Al calcular 3 2 VI x 1 dx se obtiene 2 3 x 1 2 3 x x 1 2 C 2 3 x 1 2 3 C x 1 2 C

4 3

How do I find the GCD of the complex numbers a 24 3i b 7 i

modeled by the function P x 3x 3 90x What do the zeros of the function tell you about the number of paddleboards that Waterworks should produce Waterworks is a company that manufactures and sells paddleboards Its profit P in hundreds of dollars earned is a function of the number of paddleboards sold x measured in thousands Profit is 39x In order to make a profit Waterworks must produce more than and fewer than paddleboards

Form a polynomial f x with real coefficients having the given degree and zeros Degree 4 zeros 4 2 2 multiplicity 2 Let a represent the leading coefficient The polynomial is f x a Type an expression using x as the variable Use integers or fractions for any numbers in the expression Simplify your answer S

Write a polynomial function of least degree with rational coefficients so that P x 0 has the given root 2 7i P x x x COLLE

3 Maximum mark 5 with GDC In an arithmetic series the first term is 7 and the sum of the first 20 terms is 620 a Find the common difference b Find the value of the 78th term

Find an orthogonal matrix A where the first row is a multiple of 1 2 2 A

Suppose that bacteria growth is modelled by the DE given in the notes Suppose that the number of bacteria is observed to double after 10 days and the estimated carrying capacity is 14 times the initial population What is the estimated population as a multiple of the initial population after 27 days For example an answer of 3 5 would indicate a population 3 5 times the initial population Give the answer accurate to 2 decimal places number

Situation 3 You are trying to a build doghouse for your adorable Pomeranian The dimensions of the base of the doghouse will be needed Determine the length and width of your doghouse The roof of the house is a triangle with two sides that are the same length Decide the height of the roof

are 22 grams of the isotope a Find the function P t which gives the number of grams of the isotope after t days P t 22 1 2 t 7 Correct Good Job 9 30 b Estimate the number of grams of the isotope after 12 days Round to two decimal places 20 grams Not quite grams Preview P t 22 grams c Estimate the number of days it will take for the isotope to reach 3 grams Round to two decimal places days Preview 9 30 grams Preview 20 days

A steep mountain is inclined 75 from the horizontal and rises to a height of 3350 ft above the surrounding plain A cable car is to be installed running from a point 850 ft from the base of the mountain to the top of the mountain The shortest length of cable ft Round the final answer to 2 decimal places You can round the distance from the top of the mountain to its base to 5 3 additional decimal places or use the Ans feature on your calculator uestion Help Video Moccago instructor Bort to foru cum

wolves and 7 years later the population was 3000 wolves a Find the function P t which gives the population of wolves t years after day one P t 1600 Not quite po 2 t 3 b Estimate the number of wolves 14 years after day one Round your answer to the nearest wolf That s not it wolves 16127 wolves Preview P t 1600 wolves c Estimate the number of years it will take to reach a population of 4300 wolves Round to two decimal places years Preview p o 2 wolves Preview 16 127 years

Find an orthogonal matrix A where the first row is a multiple of 1 2 2 A

8 Find a the square roots of z 1 2 b the cube roots of z 1 j

Partner A Use the equations above to determine the key features of the graph X Intercepts Vertex Domain 2 2 Partner B Check the work from Partner A If you agree with the values in the table use the values to sketch a graph of the quadratic function 4 Y Intercept Now pass the paper to partner C End Behavior Range Partner C Use the Desmos Graphing Calculator to check Partne A and B s work Then answer the following question What is the average rate of change for the interval 0 2 Now pass the paper back partner A to review the finc work

A doctor prescribes 26 milligrams of a therapeutic drug that is absorbed by the body in such a way that the drug reduces by 30 each hour a Find the function P t which gives the number of milligrams of the drug after t hours P t e 0 3t That s not it 0 39 b Estimate the amount of drug after 14 hours Round to two decimal places milligrams Not quite 7 20 milligrams Preview P t 0 3t milligrams c Estimate the number of hours it will take for the drug amount to reach 3 milligrams Round to two decimal places hours Preview 0 39 milligrams Preview 7 20 hours

A cup of hot chocolate is taken out of the microwave and has an initial temperature of 198 F The drink is placed on the counter in a room whose temperature is 73 F After 7 minutes the temperature of the hot chocolate has dropped to 150 F a Find the function T t which gives the temperature of the hot chocolate in degrees Fahrenheit t minutes after the hot chocolate was removed from the microwave T t OF b Estimate the temperature of the hot chocolate 16 minutes after the drink was removed from the microwave Round to two decimal places c Estimate the number of minutes after removal from the microwave for the temperature of the hot chocolate to reach 91 F Round to two decimal places

Solve each equation 2 3n 2n 6n 6 6b 11 1 8b x 15 2x 7 2

The logistic function below models the population of fish in a pond as a function of time in weeks since fish were first introduced into the pond P t 780 1 19e 0 08 a Find the number of fish that were first introduced into the pond fish b Predict the number of fish in the pond 17 weeks after they were first introduced Round to the nearest fish fish c Predict when the the population will reach 530 fish Round to two decimal places weeks d Determine the maximum number of fish that can be sustained by the pond

A doctor prescribes 26 milligrams of a therapeutic drug that is absorbed by the body in such a way that the drug reduces by 30 each hour a Find the function P t which gives the number of milligrams of the drug after t hours P t milligrams b Estimate the amount of drug after 14 hours Round to two decimal places milligrams c Estimate the number of hours it will take for the drug amount to reach 3 milligrams Round to two decimal places

According to one source the world population can be modeled using the function P t 6 17e0 0123t where P t is the world population in billions of people and t is the number of years after January 1st 2000 a Predict the year during which the world population is expected to reach 10 6 billion people year b Predict the world population on January 1st 2052 Round to the nearest person population people

oints Among all unit vectors u X Y in R find the one for which the sum x 8y 7z is minimal 2

25 9 8k 9 k 10 27 7 4 x 10 6x 2 29 4 a 3 6 1 4a 31 7 2k 8 10 8k 4 26 7 6 k 5 9k 10 28 8 a 2 5 5a 3 30 7 9 6p 3 8 4p 32 3 8r 6 7 r 5

19 3n 10 n 2 21 10n 9 n 2 23 8 n 10 4 n 2 25 9 8k 9 k 10 20 3r 6 4 2r 22 7 a 6 9 24 1 10x 1 5x 26 7 6 k 5 9k 10 6

Independent Simplify each expression 1 8 6x 6x 3 7m 5m 5 9b 2 6b 7 9 10 6r 2 7r 6 6 10r 4 2x 1 6 6 4n 5n 8 5 2n 6 Dat

2 3x 5 2x 6y 7y

2 3x 5 2x 6y 7y

Distribute and combine like 1 4 2x 8y 3x 6y

5 3x 2x4 8x 10x 9

4 7 2x 4y 5 8y 10x

3 3 6y x 6x 10y

2 3 4x 7y 6 2x 2y

1 4x 5 2x 8 10 JANNE

1 3 2x 4 2 8 2x

5 Solve ex 5e 6 0

Sketch the graph of y 3 2 specify the domain range intercept s and asymptote 10 9 8 7 6 5 4 3 2 10 9 a do it 6655 on dito 9 5 1910

Let f x 2 show that f x h f x h F h

9 2x 4X3x 5 A 6x 22x 20 B 6x 20 C 6x 2x 20 D 6x 2x 20 11 11 2p 5p 3X Sp 2 10 10 7 7v 2 7v 3 A 16 20 58v 16 B 25 55 34v 16 C 49 28 7v 6 D 56 11 12v 9 12 12 4

C 4 2 25 D 4 25 5 0 6m 2 20 6 2 2 A 0 25 47 61 B 0 36m 264 4 84 C 0 36m 4 84 D 0 25m 6 9 47 61 B C D 12x 8x 16 9 3x x 8 2x 3x x 6 8 6 6 0 0 3 A 0 64 0 09 B 0 64 0 48 0 09 C 20 25 70 2x 60 84 D 0 64 0 09 8 68 7X2a 7 A 12x 56a 49 B 12a 49 C 12 284 49 D 124 56 49

Rewrite the function using the power reducing formulas f x 4 sin x f x Use a graphing utility to graph the function y 1 5 1 0 0 5 1 5 1 00 5 N y 4 0 5 0 5 1 0 1 5 1 0 1 5 X 1 5 1 0 0 5 1 5 10 0 5 y 2 2 y 2 0 5 1 0 1 5 0 5 1 0 1 5

Begin with the graph of y e and use transformations to graph the function f x ex 3 Determine its domain range and horizontal asymptote Which transformations must be applied to obtain the graph of f x ex 3 Select all that apply A Reflection about the x axis B Horizontal shift C Horizontal compression or stretch D Reflection about the y axis E Vertical compression or stretch 10 8 6 2 10 8 6 4 2 2 4 6 8 40

Approximate each number using a calculator a 83 14 b 83 141 a 83 14 b 83 141 C 83 1415 685 019 Round to three decimal places as needed Round to three decimal places as needed d 8t

Click on the base e button and uncheck the Integer Values box to graph the function f x e For all x0 the gra of f x e lies between two exponential functions y p and y q Using the b slider find the two smallest integer for p and q and estimate f 1 Use the interactive figure to find your answer Use the left and right arrow keys to move along a slider as needed Click here to launch the interactive figure The two smallest integers are and Use ascending order

9 3 7 6 7r 11 3 5 3 10 4 28x 7x 12 2 5 6 2

1 3 12 6 3 6 6 2 5 10 4 5 4 20

3 3 2 6 14 3 5 10

Subtract 23 6 162

In this problem x 0 3 4x5 32x5

3 108 2 32