Complex numbers Questions and Answers

X 49 0

2 5 x 3 125 2

1 2x 28

12 5 points Prove identity sin x csc x cos x csc x

The half life of Radium 226 is 1590 years If a sample contains 500 mg how many mg will remain after 1000 years Question Holni Dost to forum

9 10 31x 24 A 5 2x 5X5x 3 B 10 x 3x 8 C 2x 3 5x 8 D 205x3x 4 10 101 60 162 108 A 612x 35m 6 B 62 315 6 C 2 5n 3 x 3 D 60 3X 6

11 11 12m 2m 30 A 2 3m 5X2n 3 B 12 n 5 n 3 C 2 3m 5 2n 3 D 3 2m 5Xx 1 12 12 9 33r 10 A 6r 3r 4 B 10 4 3 c 2 2 9r 10 D 3r 1X3r 10

3 r 4 60 A r 6Xr 10 B 10 4 C Not factorable D 6 r 8X 1 4 4 x 11x 28 A x 4 x 7 B x 4x 2 C x 4 x 7 D x 8 x 6

2022 KWIN oftware LL C Factoring Quadratics Factor each completely 1 m 18m 81 A m 9 B m 10 m 7 C m 9 D m 10 m 3 3 4r 60 A r 6 r 10 B r 10 4 C Not factorable D 6 r 8 1 All rights reserved 2 4 2 k 3k A k k 3 B k 4 k 10 C Not factorable D 2 k 9 k 7 4 x 11x 28 A x 4 x 7 B x 4 x 7 C x 4 x 7 D x 8 x 6

ern city finds its residents moving to the suburbs Its population is declining 0 04t where t is time measured in years since according to the function P t 1 526 000e 2015 a What is the estimated population of the city in 2020 2 pts b In what year will the population decline to 1 000 000 3 pts 0 0001216t 10 The function P t Pe can be used for carbon 14 dating a Using the formula above what is the half life for carbon 14 Please show all work or how you determined the half life 2 pts

12 Which equation matches each graph Describe each graph in terms of its slope and y intercept a y 3 2 x 1 b y 3 x 2 d y 3 x 2 c y 3 2 x 1 Graph A Graph B 4 5 6 2 2 0 2 0 Graph C N 2 20 NO 2 X Graph D 2 0 2 6 y x

11 Write an equation for the line that passes through each pair of points Write each equation in slope point form and in slope intercept form a B 2 5 and C 1 1 b Q 4 7 and R 5 2 c U 3 7 and V 2 8 d H 7 1 and J 5 5

f x x 1 Domain of f Range of f Pomain of fl ange of f g x 2x5 Domain of g Range of g Domain of g Range of g 3 Alex is considering some options for making a deposit a What amount deposited today at 3 1 interest compounded monthly will grow to 12 000 in 5 years 3 pts b If Alex only has 10 000 to deposit now what annual interest rate compounded monthly is necessary for tho

What point represents the vertex height above ground 10 8 0 0 2 2 14 2 3 4 16 0 distance from launc

2022 Kuta Software LLC All rights reserved Factoring Quadratics Factor each completely 1 m 18m 81 A m 9 B m 10 m 7 C m 9 D m 10 m 3 3 r 4r 60 A r 6 r 10 B r 10 4 C Not factorable D 6 r 8 r 1 2 4 2 k 3k A k k 3 B k 4 k 10 C Not factorable D 2 k 9 k 7 4 x 11x 28 A x 4 x 7 B x 4 x 7 C x 4 x 7 D x 8 x 6

3 20 points Evaluate the following functions using the graphs shown f x 3 0 2 3 1 4 i g f 1 ii f g 0 1 0 14 N 3 0 3 9 D iii f f 3 1 0 0 2 1 3 0 10 5 01 0 1 g x 3 6

In this question we will use a spreadsheet to approximate the root of f x x5 3x 9 using Newton s method with o 1 The picture below shows a spreadsheet being used to perform the calculation A downwards arrow indicates the contents from the cell above will be copied down a Which entry should go in cell A1 O 5 B1 4 9 B1 2 O A1 5 3 A1 3 9 00 O 5 A1 4 9 A1 2 O B1 5 3 B1 3 9 01 b Which entry should go in cell B1 00 A1 5 3 A1 3 9 1 O 5 B1 4 9 B1 2 O B1 5 3 B1 3 9 5 A1 4 9 A1 2 c Which entry should go in cell C1 O A1 5 3 A1 3 9 B1 5 3 B1 3 9 5 B1 4 9 B1 2 5 A1 4 9 A1 2 1 1234 AC 2 A1 B1 C1 B C

15 Solve the following logarithmic equation If multiple solutions exist enter solutions using a comma separated list log3u log3 4u 12 2

11 Solve the following logarithmic equation If multiple solutions exist enter solutions using a comma separated list log 6x 17 log 4x 18 1

12 Solve the following logarithmic equation If multiple solutions exist enter solution using a comma separated list log x 8 log x 12 5

9 Rewrite the following logarithmic equation in exponential form Then solve the logarithmic equation Rewrite the following logarithmic equation in exponential form log y 6 6 is equivalent to Put work reasoning here Solve the logarithmic equation y log y 6 6 No Solution Put work reasoning here

1 Use the properties of logarithms to expand the following logarithmic expression as much as possible Where possible evaluate logarithmic expressions W203 215 logs

6 Find the exact value of the following logarithmic expression In e

Tu upus untry 1 Which figure shows ray AB O O A Line A Line B 557 A B B

Make up a problem that simplifies to this answer 3 N 3 C 3 1 p q mn5

5 If sin a 5 13 a in QII and tan a sin a 3 b cos a b 3 8 in QIII find 4

4 A sailboat is approaching a cliff The height of the cliff is known to be about 2000 m and the boat is about 3464 m from the cliff Determine the angle of elevation from the sailboat to the top of the cliff CLIFF

Module 1 For the function f x 4 3x 1 2 x 5 find the followin y intercept x intercept s leading coefficient degree of the polynomial

e Rudy Meangru Solve for x and check for any extraneous roots log x 6 log x 4

16 x y x y 5 A 51 F X B 380 C 9 D 19 E 22

P The shortest distance between the curves 2y2 x and 3 2 9x 9y 60y 91 0 is

Find the area of the triangle ABC a 105 8 m b 74 7 m c 99 8 m What is the area of the triangle m Round to the nearest square meter as needed Question 12

Question 10 7 3 65 Use an appropriate area formula to find the area of the triangle with the given side lengths a 17 m b 9m c 12 m The area of the triangle is m Round your answer to the nearest tenth

K Find the measure of 0 in the triangle Do not use a calculator 0 B A B 0 1 C

Diyagram enine izgilerle kesilen iki paralel izgi a ve b yi g stermektedir x in de eri nedir 490 to 380 a b

Diyagram enine kesilen iki paralel izgiyi g stermektedir 22 3y 10 l s ve 28 7y 30 l s B l m A Bir denklem yaz n ve y nin de erini bulmak i in z n 1 3 re 2 7 5 6 8

Using the graph and table as a reference identify the Domain of the function f x Write your answer in Interval Notation 5 4 3 10 1 2 3 4 f x 1 4 f x 0 11111111111111 0 14285714285714 0 16666666666667 0 2 0 25 0 33333 3333333 Undefined Domain of f x 2 S 32 1 L 44 PL 31 EJ D

2 Solve for x use log where necessary 41 8 a b 22 x 3x

Problem 5 Let W be the subspace of R spanned by the vectors u 1 0 1 0 u2 0 1 1 0 and u3 0 0 1 1 Use the Gram Schmidt process to transform the basis u u2 u3 into an orthonormal basis 4 v 2 0 2 0 v2 V V V 0 v3 3 V3 6 3 6 2 0 2 0 v V6 NE V6 0 V3 13 13 13 V2 3 3 D v 2 0 2 0 v2 V6 V6 6 0 v3 2 0 0 v 6 16 16 0 1 13 13 13 v3 E v V2 B v1 C v 2 0 2 0 v2 V6 V6 N 0 v3 V 3 6 F v 2 0 2 0 v2 V6 v6 6 0 v3 3 6 v3 13 2 0 2 0 v NE VE 0 13 3 V 0 6 6 G v H v 0 2 0 v2 v v 0 v3 6 3 6

Problem 4 Let v 3 1 0 1 v2 0 1 3 1 and b 1 6 1 4 Let W be the subspace or R4 spanned by v and V2 Find projw b Problem 4 Enter your answer symbolically as in these examples Enter the four components separated with commas

Prof Rudy Meangru 1 Evaluate the following without a calculator a log1000 b log 10 3 2 FI 2023 Due Monday 11 27 c In e

Find the exact values for the six trigonometric functions of the angle 0 in the figure O For the given triangle which of the following ratios represents the trigonometric function sin 0 BC AB O AC BC AB BC BC AB Find the value of sin 0 sin 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression For the given triangle which of the following ratios represents the trigonometric function cos 0 BC AC 11 5 AB AC B Find the value of cos 8 cos 0 Simplify your answer including any radicals Use integers or fractions for any num 2

Problem 6 Let S 1 4x 1 3x2 Which of the following polynomials could be added to the set S to form a basis for P2 Problem 6 1 2 4x 3x 11 5 4x12x 111 8 12x 15x s A none of them B all of them C i only D ii and iii only E ii only F iii only G i and ii only H i and iii only Select

Problem 1 Which of the following sets of vectors are independent 1 1 2 1 3 2 0 2 4 1 11 1 2 1 3 2 0 5 6 0 ii 1 2 1 3 2 0 7 10 2 A none of them B ii only C i only D i and iii only E ii and iii only F iii G all of them H i and ii only

Determine the exponential regression of the data below using either a calculator or spreadsheet program 21 6 19 23 13 33 8 47 5 54 2 62 Select the correct answer below Of x 93 264 1 106 Of x 93 264 1 106 O f x 93 264 1 106 O f x 93 264 1 106

8 Match each rational function with a description of its end behavior as x gets larger and larger A 9x B C D E F 99x X 99 x x 99x 9 x 99 9x x 1 The value of the expression gets closer and closer to 0 2 The value of the expression gets closer and closer to 1 3 The value of the expression gets closer and closer to 9 4 The value of the expression is 99 5 The value of the expression gets larger and larger in the positive direction 6 The value of the expression gets larger and larger in the negative direction

1 Use the Rational Zero Theorem to find al real zeros Enter your answers as a comma separated list 4x 7x 10x 3 0 X

6 4 2 8 6 4 0 0 0 2 y 4 6 8 2 2 2 4 6 X Graph the circle x y 4x 4y 8 0

6 2 2 4 8 6 4 2 2 0 2 6 4 0 0 2 4 16 8 X large points to move the center and change the radius so that x 3 y 4 16 4

Use the graph below to determine the equation of the circle in a center radius form and b general form 10 46 8 2 4 2 10 C a Type the equation in center radius form x 4 y 2 16 Simplify your answer b Type the equation in general form Simplify your answer