Complex numbers Questions and Answers

Homewor Find the indicated term of the binomial expansion 13th c 3 14 What is the 13th term Simplify your answer Question 7 12

Previous Problem BC Use the Pythagorean Theorem to determine the length of the hypotenuse Give the value for each trigonometric ratio using exact form Do not use decimal approximations sin B cos B tan B sec B csc B cot B Problem List 5 A 1 B Next Problem

Find the indicated term of the binomial expansion 7th x y 10 The 7th term is

Without using a calculator state the exact value of the following trig functions for the specified angle 53 0 a sin b sin c sin 27 0 3 d sin e sin f sin g sin h sin 4T 3 5T 3 7T 3 4 3 5T 3 2 23T

Without using a calculator state the exact value of the following trig functions for the specified angle a cos b cos 2 0 c cos 3 d cos T 3 e cos T 0 f cos 3 g cos h cos 4 3 5 3

Without using a calculator state the exact value of the following trig functions for the specified angle T a tan 3 2 b tan 3 4T 3 0 C tan d tan 5 e tan f tan 3 g tan 3 5T 3 h tan

2 27x6 35x 8 0

Exponential Growth and Decay Exponential growth and decay problems follow the model given by the equation A t Pert The model is a function of time t A t is the amount we have after time t P is the initial amount because for t 0 notice how A 0 Pe t Pe P r is the growth or decay rate It is positive for growth and negative for decay Growth and decay problems can deal with money interest compounded continuously bacteria growth radioactive decay population growth etc So A t can represent any of these depending on the problem Practice The growth of a certain bacteria population can be modeled by the function A t 350e0 0796 where A t is the number of bacteria and t represents the time in minutes a What is the initial number of bacteria 6 How long will it take for the number of bacteria to double round to the nearest whole number of bacteria b What is the number of bacteria after 20 minutes round to the nearest whole number of bacteria your answer must be acc

Given a right triangle with tan 0 1 sin 0 2 cos 0 3 sec 0 4 csc 0 5 cot 0 5 7 determine the value of the other trigonometric ratios of 0 Use exact notation not decimal approximations If you need to write a number such as 3 type out sqrt 3

The population of Brazil can be modeled by the function P t 247 1 0 0151 where P t measures the population in millions and t represents the number of years since 2000 1 Using this model what was the population of Brazil in 2014 2 Predict the population of Brazil in 2026 3 If this growth rate continues in what year will the population of Brazil rongill

hot air balloon is floating above a straight road To calculate their height above the ground the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon The angles of depression are found to be 16 and 19 How high in feet is the ballon

18 0 0 4 3 d the value of the six trigonometric functions of 0 where is the angle formed by the positive x axis and the line segment from 0 0 to 4 3

Show Transcribed Text 2 so Calculate the angle delta theta using cosine law The triangle to be considered is A BC Given that A C 23 98 A B 40 91 RC 221

Rewrite the following logarithms in expanded form by applying the properties of logarithms a log ry b log H Y c log x

Write the equation of the quadratic with Vertex 3 1 and point 7 3 Hint do the same as above

1 y 3 2 cos x Choose the correct graph O A UNS HILLE AV 10 1 IN Ay S 10 VAN loft H ON pehod interval Do not use a graphing calculator OB O C HERINE TOTTE HILLSITTE HISHHHHHH HISSITH 0 of 1 O D Ay GOO Save

Select the correct answer Consider this equation 12 42 1 2 2 Approximate the solution to the equation using three iterations of successive approximation Use the graph as a starting point N LIN 2 2 OA OB a z IN

Calculate 7 9i Give your answer in a bi form Give the solution with smallest positive angle Round both a and b to 2 decimal places

2 7i 3 4i 6 points Given the following expression a 1 point State the conjugate b 4 points Simplify the expression in a bi form

8 10 points Find the all solutions of this equation in the interval 0 2 3 tan 0 3 6 tan

points Given the following expression 5278 a a 1 point State the LCD b 4 points Simplify the complex fraction a PIA88

Solve the equation Write the solution set with the exact solutions Also give approximate solution to 4 decimal places log q 8 4 7 O There is no solution O The exact solution set is DO 9 0 0 10 O D

Select Yes or No to indicate whether each ordered pair is a point of intersection between the line y x 5 and the parabola y x 3x 10 Ordered Pair 5 0 3 8 5 10 Yes No O

What is the value of n in the equation 0 18 128n A 64 B C 64 i

Which expression is equal to 6 5 2 3i A 3 3i 7 9i DOO C 3 9i 7 3i

A radical expression is shown below What is the simplified form of this expression O 41 31 A

on of f x

4x y The fifth term of the binomial expansion is Simplify your answer

Find the indicated term of the binomial expansion 8th x y What is the 8th term Simplify your answer

Write a formula for the general term the nth term of the arithmetic sequence below Then use the formula for an to find a20 the 20th term of the sequence 3 8 13 18 The formula is a Simplify your answer

Simplify each of the following expression Write your answer as a complex number

Which of the following values of x are solutions to the equation x 4x 57 Select all that apply A 1 31 B 4 CO D 2 1 E 2 1

Simplify 2 5

6 5 4 3 2 6 B A 7 2 B 2 5 C 0 4 D 2 1 2 3 4 5 6 1 Which of the following points is on a circle centered at 3 1 with a radius of 5 units 2 3 4 5 6

8 10 2022 Kata Software LLC All rights reserved SUMMATIVE 3 12 Divide 8 91 43x 17x 5 13x 5 A 7x 6x 1 B 7x 6x 3 1 13x 5 S 13x 5 C 7x 6x 3 D 7x 6x 3 13x 5 Find each product 10 4a 3a 4 4a 3a 8 A 16a 9a 32 B 16a 24a 25a 12a 32 C 16a 7a 36a 32 D 16a 24a 25a 12a 32 9 11 11 8x 57x 10x 15x 45x 21 x 7 A No B Yes 9 2 35 90v 28 2v 7 4 2v 7 A 14v 7 7 B 14v 4 State if the given binomial is a factor of the given polynomial 5 2v 7 C 14v 4 D y 14v 3 ZO

The system of equations below is represented by which of the following graphs y x 4x 2 y x 2 A C 1 V 1 2 1 10 1 3 4 4 3 H 77 1 D M 5 B D 6 S A 19 t

What are the solutions for the given equations below

A radical expression is shown below What is the simplified form of this expression 150

What are the solutions for the given equations bel 2x 7 1

Solve the system of equations y 6x 16 y x 7

Determine if the point P 3 6 is on a circle centered at 1 3 with a radius of 5 units

The complex number 6 3i represents which radical expression below A 6 9 B 6 3 C 6 9 D 6 6

ne complex number 9 3i 5 represents which radical expression below 0 A 9 45 B 9 i 15 C 9 45 D 9 45

Choose the end behavior diagram that best describes the function f x 6 x 1x Choose the correct diagram below O A O C O B O D

The graph of a logarithmic function is given Select the function for each graph from the given options y log g x y log gx y 1 log gx y log gx 1 y log g x 1 y log g 1 x y log gx y log g x Drag each function given above into the area below the appropriate graph depending on which function is represented by which graph 65 Q 66 Q 67 Q68 12 10 8 6 4 2 X 2461 L X N 468 Q

Which expression below is equivalent to 3 2x 4 3 x 5 3x 27 03x 27 9x 27 3x 3

2 Which values for x below are solutions to the inequality 5 x 2 a 10 b 20 c 2 2 d 6 e 9

What is the value of x in the equation x 6x 12 0

Solve the equation State whether the solutions are real or non real x 6x 16

Find the type of and the number of solutions for each equation Hint Use the discriminant 4x 12x 9 0