Complex numbers Questions and Answers

5 Evaluate the following limits 3 1 3 a lim 3 b lim z 1 3 1 z z 6 x 2 c lim 1 22 1 6 1 2 d lim 2 1 z x 1 c lim

The number of milligrams D h of a certain drug that is in a patient s bloodstream h hours after the drug is injected is given by the following function 0 5h D h 20e When the number of milligrams reaches 3 the drug is to be injected again How much time is needed between injections Round your answer to the nearest tenth and do not round any intermediate computations hours

Write each expressi 6 n 3 8 00

Chau needs 9534 for a future project He can invest 6000 now at an annual rate of 8 6 compounded semiannually Assuming that no withdrawals are made how long will it take for him to have enough money for his project Do not round any intermediate computations and round your answer to the nearest hundredth years 3

Write the expression as a single natural logarithm 3 In 2 0 3 In 2 Simplify your answer

Draw the graph of an exponential function E t such that lim E t co and lim E t 3 00 2 Draw the graph of a sine function with range 4 1

You can afford to spend at most 135 dollars per month on a movie rental plan If your movie rental plan costs 30 dollars per month plus 3 dollars per movie rented how many movies can you afford to rent You can afford to rent Select an answer movies

te your knowledge from the lesso

he moose population in a park was r d again to be 3930 If the population mula for the moose population P in s your model predict the moose pop

3 points were given and combined to create 3 sets of two ordered pairs All calculations were performed accurately The distance was found for each of the 3 sets of ordered and are a listed below Determine whether the 3 distances reflect if the 3 points that were given are vertices of a right triangle D 148 D 229 D 25 Select Select Yes Not Enough Information No

K Determine whether the graph represents a function If it doe domain and range IYU Yes What is the domain Select the correct choice below and if answer box to complete your choice CA x 6 3 1 2 6 Use a comma to separate answers as needed

Choose the answer that best describes the graph O 850 8000 750 700 650 600 50 500 450 400 50 300 250 200 150 100 50 increasing O decreasing O constant neither both SOwed 4 Weeks 6 8 10 12 14 16 18 20 22

Tom deposited 3000 into an account with a 3 annual interest rate compounded monthly Assuming that no withdrawals are made how long will it take for the investment to grow to 3555 Do not round any intermediate computations and round your answer to the nearest hundredth years

Suppose that 2000 is loaned at a rate of 6 5 compounded annually Assuming that no payments are made find the amount owed after 8 years Do not round any intermediate computations and round your answer to the nearest cent 0 X 5

How long will it take for a 5000 investment to grow to 6455 at an annual rate of 9 4 compounded quarterly Assume that no withdrawals are made Do not round any intermediate computations and round your answer to the nearest hundredth Dur

The dollar value v t of a certain car model that is t years old is given by the following exponential function v t 32 000 0 88 Find the initial value of the car and the value after 12 years Round your answers to the nearest dollar as necessary Initial value Value after 12 years 0 X 5

The radioactive substance uranium 240 has a half life of 14 hours The amount A t of a sample of uranium 240 remaining in grams after t hours is given by the following exponential function 1 A t 1200 T Find the initial amount in the sample and the amount remaining after 30 hours Round your answers to the nearest gram as necessary Initial amount grams Amount after 30 hours grams X 5

If the rate of inflation is 4 1 per year the future price p t in dollars of a certain item can be modeled by the following exponential function where it is t number of years from today p t 2000 1 041 Find the current price of the item and the price 9 years from today Round your answers to the nearest dollar as necessary Current price 0 Price 9 years from today s

Tak Juan and Julissa were waiting in line at the movie theater and decided to play a game They have a bag of M Ms with 5 red and 6 green candles They decided each red would be worth 3 points and each green would be worth 1 point Each person takes a turn picking 7 candles from the bag without looking and then determines their score They return the candles to the bag after each person s turn For example if Juan picked 3 red and 4 green his score would be 3 3 4 1 9 4 13 1 Play the game with them elther using M Ms or something similar Red Green Total points 2 Label the variables then write and solve a system of equations algebraically using substitution or elimination method that would give a total of 15 points from choosing 7 M Ms Remember a system of equations means you write two different equations both with the

Consider the following formulas a sin 80 b cos B0 b sin 80 C where C arctan b a and a 0 a sin B0 b cos 80 b cos B0 C where C arctan a b and b 0 a Use the formulas given above to write the trigonometric expression in the following forms Round each C to four decimal place 6 sin 80 8 cos 80 a b a b sin 80 C 2 6 cos B0 3

Calculate the average rate of change of the given function f over the intervals a a h where h 1 0 1 0 01 0 001 and 0 0001 Technology is recommended for the cases h 0 01 0 001 and 0 0001 Round your answers to five decimal places h 1 h 0 1 h 0 01 h 0 001 h 0 0001 8 f x a 6 X 0 16667 X

A graphing calculator is recommended A man stands at a point A on the bank of a straight river 2 mi wide To reach point B L 9 mi downstream on the opposite bank he first rows his boat to point P on the opposit distance x to B as shown in the figure He can row at a speed of 2 mi h and walk at a speed of 5 mi h L mi a Find a function that models the time T needed for the trip T x b Where should he land so that he reaches B as soon as possible Round your answer to two decimal places

y Ax Bx C that fits the data given in a table Table Of Values xy 1 5 2 3 33 IMPORTANT PART B B Sketch the graph of the function you got in A Label coordinates of the vertex y intercept and x intercepts if any Using graphing calculator and or computer is not allowed Give your answer qualitatively C Applications Assume the function you got in A describes the profit for a new start up business in thousands of if x is the number of months after the business model has been first implemented What will be a minimum maximum whichever is applicable profit and how many months after the model has been implemented this profit hocam

10 Find the grade resistance F WSin 9 a if a 2700 pound car is traveling uphill grade with 9 5 7

a Given below the graph of the function f x 2 3x x 1 find the average rate of change from a 1 to z 1 1 4 fun X 0 b Given the table below find the average rate of change from a 1 tox 3 f x 1 1 2 1 0 3 3 4 9 16 Math

500 x is a function used to calculate the average cost per unit of making x units of aseball bats If the cost per unit is 1 50 how many units have been produced x 25 50 500 X125 37 5 500

Carl and Rick are traveling to a store 5 miles away Carl is riding a bike so he s going 12 mph faster than Rick If it takes Rick 45 minutes how long did it take Carl hint compare rates

Given f x x after performing the following transformations shift upward 54 units and shift 85 units to the right the new function g x

The graph of the function y f x 19 can be obtained from the graph of y f x by one of the following actions O shifting the graph of f x to the left 19 units O shifting the graph of f x to the right 19 units Oshifting the graph of f x upwards 19 units Oshifting the graph of f x downwards 19 units

A tree on a hillside casts a shadow c 240 ft down the hill If the angle of inclination of the hillside is b 18 to the horizontal ar the angle of elevation of the sun is a 48 find the height of the tree Round your answer to the nearest foot ft

Graph the function 2x 2 for x 1 2x 2 for x21

If f x x 8 g x x 7 and h x x the f g h x

Determine YES or NO if the following is a circle If yes then find its center using a comma to separate h and k and also find the radius If no then enter in DNE for the center and the radius 9x 9y2 12x 18y 23 0 Is this a circle Center Radius 1

Use the graph to find the following 2 10 f 2 f 0 f 1 f 4 1 2 3 4

Use the table below to evaluate the following X f x g x 2 0 6 0 2 4 X 5 7 2 10 025 g f 4

SYSTEMS Graphically solving a system of linear equati Graph the system below and write its solution 2x y 6 1 y x 1 Note that you can also answer No solution or Infi

For each system of linear equations shown below classify the syste best description of its solution If the system has exactly one soluti Line 1 y System A Line 2 y x 1 Syster Line 1 y x 2 Line 2 5x 2y

Knowledge Check Royal Fruit Company produ mpting to produce a fruit d

Evaluate the following Be sure to show what quadrant the angle is in what its reference angle is and what the coordinate 1 Sin 30 4 Sec 90 2 Csc 585 5 Tan 960 3 cot 5m 6 COS 2

The following table gives projections of the population of a country from 2000 to 2100 Answer parts a through c Year 2000 2010 2020 2030 HE Population millions 276 1 309 5 326 4 360 3 f x x Type integers or decimals rounded to three decimal places as needed Year 2060 2070 2080 2090 Populatic millions 434 3 464 2 506 4 542 4

nowledge Check orboat travels 244 kilomet is the rate of the current

Which of the following sentences uses the active voice Rows of lettuce wilted in the heat of a late August day Plump and juicy the tomatoes were harvested at the peak of flavor The drooping wheat was revived by a long soaking rain The corn crop is expected to turn a profit this year

Find the discriminant of the following quadratic and use that to choose the correct statement about the solutions to the quadratic 5x 7x 6 0 One real solution One imaginary solution Two real solutions Two imaginary solutions

Determine the values of b and c such that the following function is continuous on the entire real number line b 9 C Number f x 1 x 9 x 1 x bx c x 5 24 2

www7 RADICALS AN Finding the x

2 Solve the following equation 49k 21k 4 O k 1 7 k 4 7 O k 1 7 k 4 7 O k 1 7 k 4 7 O k 1 7 k 4 7

In the above CSS snippet tr is an example of a O O O a property b value c selector d declaration

Write the product as a sum sin x sin 7x

Solve Round to the nearest tenth 3 log x log 6 log 2 4 9

Weights in pounds of 20 African elephants 5878 6028 5995 6023 5999 5978 6042 6034 5976 5889 5938 6105 6077 6047 5938 5899 6022 6171 5990 6102 Using the above data a b Construct a frequency table with 5 classes Construct a histogram