Complex numbers Questions and Answers

Two friends drive off in different directions from the same place One heads North at 45 miles per hour while the other heads East at 25 miles per hour Complete an equation for the distance between the friends after t hours

the perimeter of a rectangle is 48 what is the length of the sides

Eigenvalues of the matrix with the quadratic form x 4x1x2 x2 2x 4x2 5 equals a 3 b 1 c 2 d 3 Guita ic T ATO for all

8 Are the planes 3x y 2z 4 0 and x 2y 2z 3 0 orthogonal Why explain 9 Find vector and parametric equations

Definition 1 Since the y values increase as the x values increase in the example above this is what we call exponential The graph goes up the hill from left to right QUESTION In the exponential function y 3 the y values can never equal or be less than Definition 2 Since the y value can NEVER equal zero in this function there is a horizontal at y 0 Ex 2 By looking at the graph above list the domain and range of the function y 3 DOMAIN RANGE

7 Are the planes x 3y 2z 2 and 2x 6y 4z 5 parallel If yes find the distance between them

1 If Z 3 4i Z 3 2i and Z3 2 3i find a Z3

In the Linear Function what is the y intercept 0 2 0 3 2 0 3 0 f x 3x 2 as a point

Let u 3 4 v 5 4 and w 3 2 a 2 u b u v w c What do we know about vectors u and from their dot product The angle between the vectors is acute The vectors are orthogonal The angle between the vectors is obtuse The vectors are oblique Not enough information

What is the range of this logarithmic function yly 6 10 8 6 4 yly 6 1 yly 6 1 all real numbers yly 63 1 2 104 00 8 6 4 2 0 2 4 6 8 10 2 4 6 8 10

What is the area of square GHIJ 1044 6 8 Area 6 4 2 4 2 0 2 4 6 8 1 0 G H 2 4 square units 6 J I OO 8 x O 1 0

What is the perimeter of rectangle ABCD 3 B 6 4 A Perimeter 1 0 8 6 4 2 20 2 4 6 8 10 y 2 units 4 C 6 8 D

10 8 6 x x 4 x x 4 x x 4 all real numbers x x 4 4 2 P 8 6 4 2 0 2 4 6 8 10 2 4 6

Graph square UVWX with vertices U 7 5 V 7 4 W 2 4 and X 2 5 1 0 8 6 4 2 10 8 6 4 2 0 2 4 6 8 1 0 y 2 4 6 1 What is the area of square UVWX cquaro units

Write the coordinates of the vertices after a translation 5 eflect over x 4 W 10 8 V 16 4 2 104 8 6 4 2 4 2 2 6 x y y x reflect over y x 104 T 7 3 T U 6 0 U V 7 3 V W 9 0 W 3 0 10 8 6 4 2 R Q 8 6 4 2 2 4 6 2 S 4 6 8 Q 4 10 Q R 4 4 R S 1 4 S T 1 10 T 1 1

What is the range of this exponential function 10 8 6 4 yly 9 yly 9 all real numbers yly 9 yly 9 2 104 8 6 4 2 0 2 6 03 10 2 4 6 8 10 X

What is the domain of this logarithmic function 104 10 8 6 all real numbers x x 4 x x 4 9 x x 4 x x 4 4 2 8 6 t 2 0 2 4 6 B 8 2 4 6 8 10

What is the range of this exponential function 10 8 6 4 y ly 4 yly 4 yly 4 y y 4 all real numbers 2 104 8 6 4 2 0 2 4 6 8 10 2 4 6 8 V X 10

Find the Taylor polynomials of orders 0 1 2 and 3 generated by fat x a 1 f x X Po x P x P x a 4

1 cot t 1 tan t a Use Reciprocal Identities to rewrite the expression to only have sine cosine or tangent funciton Simplify to a single trig function b Times an appropriate trig function to get rid of the complex fraction IN c Cancel the common fator between the numerator and denominator d Express the final answer without fraction 1 cot t cot t 1 tan t 2

5cm imensions me sketch 3 cm 2cm 6cm 3 5 cm a make a labeled sketch of the Base and find the Area of the Base show work Area of the Base 8 b Total Surface Area show work Total Surface Area Height of the prism H d Volume Formula V show work

Graph the solution set x y 4 y 2x 4 3

Does the series shown below converge or diverge Give a reason for your answer In n 8 n 8 n 4 Choose the correct choice below OA The integral test shows that the series converges OB The integral test shows that the series diverges OC The nth term test shows that the series diverges The nth term test shows that the series convernes

Consider a variable x where x represents the whole numbers from 0 to 20 Stated mathematically the possible values of x are x 0 1 2 19 20 For the phrase x is less than 3 write an inequality Determine which values satisfy that inequality Enter your answers as a comma separated list

As x increases what happens to the instantaneous rate of change at x f x for f x log x 24 10 2 3 y log x 2 3 4 Stays the same Decreases Incroacor 5 6 7 8 9 10 11 12

In the Blank Question Your grades in biology include three quiz grades and one test grade A test is worth four times more than a quiz To get your average grade for the class you need to calculate a mean measurin Select sour

Consider the parabola given by the equation Find the following for this parabola y 4x 12x 5 A The vertex Write your coordinates as numbers decimals not fractions B The y intercept is the point 0 C Find the two values of a that correspond to the intercepts of the parabola and write them as a lis separated by commas x Round your answer s to two decimal places

Describe how to use both an equivalent trigonometric identity and a diagram to demonstrate that two trigonometric ratios are equivalent a Use one of the following equivalent trigonometric expressions sin 0 cos 0 cos 0 sin 2 tan 0 3 cot 0 sin 3 0 2 cos 37 tan 3 0 2 0 cos sin cot 0 b Using a diagram demonstrate how the related angle formulas are true Create an example to illustrate your findings in part a choose a value for and solve

Are these sets equal D 77 4 9 606 3 E 3 4 77 9 696 Select the correct answer below Yes O No

Which sentence below does not belong in a Narrative piece A George Washington born February 22 1732 in Virginia was President of the U S from 1789 1797 B At sunset the Native Americans thinking we had not left came to bring us food C It is my opinion that we should crack down on people who litter our beautiful city parks

Find the value of the following expression and round to the nearest integer 87 20 1 06 1

In the following exponential relations solve for x using logarithms Round your answers to 4 decimal places a 2 6 b 3 2 2 c 72x 52 d 43 190

Evaluate the iterated integral 3 1 8z O In x O xey dy dx dz

10 Find the slope of the line given by the table of values shown below A B C 2 2 D 2 1 2 x 0 1 2 3 4 y 12 10 8 6 4 I

FUP many species of fish the weight W is a function of the length L that can be expressed by W W L KL k constant Suppose that for a particular species k 0 01 that for this species the length in centimeters is a function of the number of years t the fish has been alive and that this function is given E L L t 45 t 16 0sts 16 10 Find Wo L t to express W as a function of the age t of the fish WOL t x 1 1 Check which variable s should be in your answer Need Help Read It X ASK YOUR TEACHER PRACTIC

For f x x 1 and g x 1 6x find the following a fog x 216x b gof x Amazing job 1 6x 18x 18x 6 Outstanding c f f x x 3x 3x 2 3 d F x f f x to 3 12 Outstanding

In its second year of operation a local Internet provider s profits were 164 500 If this amount was 486 of the company s first year profits find th first year profits to the nearest hundred dollars Step 1 If we let x represent the company s first year profits then we can set up an equation in x using the fact that 486 is written in decimal form as 4 86 4 86 Since the second year profits of 164 500 are 486 of x we have the equation 4 86 4 86 x 164 500 Step 2 Solve this equation to find x 4 86x 164 500 X 4 86 x 164 500 Enter an exact number to the nearest 100

Determine the indicated roots of the given complex number When it is possible write the roots in the form a bi where a and b are real numbers and do not involve the use of a trigonometric function Otherwise leave the roots in polar form The three cube roots of 4 cos Xo x1 4 cos 37 4 x2 i sin 3 4

Here we are multiplying a function by itself For f x x 1 2 we have the following f f x x 1 x 1 x 1 Step 2 Use properties of exponents to simplify 2 x 1 x 1 x 1 I Enter an exact number Excellent

Step 1 To compose a function f with itself substitute f x for x in the formula for f x f f x f x 1 Step 2 Evaluate f x 1 I X x 1

When there are no restrictions the domain of a function consists of all real numbers because there are no exclusions The inputs come from all values on the real number line which span from negative infinity to positive infinity Enter the domain of the function y x2 8 using interval notation 0 00 0 Nice work Step 3 The range of a function consists of all real number outputs that result from inputting the values in the domain of the function which is Because the square of a real number is nonnegative x must be nonnegative In other words x Thus x has a least value but there is no greatest value because the range increases toward infinity If our function were only y x then zero would be the least value in the range of y However the function is y x 8 which increases x by 8 This will also increase the lower limit in the range by 8 as follows x 8 0 The upper limit of the range has not changed as y increases toward infinity Enter the range for the function y x 8 using interval notation

For f x 4x and g x x 0 find the following a f g x b f g x c f g x d f g x

Step 1 We form a new function from two functions by performing algebraic operations with the functions and simplifying if possible In general f g x f x g x Step 2 If f x 7x and g x x5 then the following holds f x g x I F

Find an equation involving g h and k that makes this augmented matrix correspond to a consistent system 1 6 0 4 7 g 19 22 h 5 6 k What equation must be satisfied for the augmented matrix to correspond to a consistent system Select the correct choice below and fill in the answer box to complete your choice Simplify your answer A 4g h k B 4g h k OC 4g h k OR 4g h k

State the domain and range of the function Enter your answers using interval notatic y x 3 domain range

Brand A ham costs 12 99 and weighs 5 2 lb What is the unit price of Brand A C 0 0070 07 A 2 49 lb Speed 1x

Astore has a sale on lunch meat at 4 79 b You need 2 5 lbs of lunch meat What is the sale price for the purchase CHA 0 00 0 11 A 11 97 Speed 1x Paused

Solve the equation cos x 2 cos2x 1 for exact solutions of x over the interval 0 x 2 Show all work without a calculator

For a certain product the revenue is given by R 40x and the cost is given by C x 20x 1500 To obtain a profit the revenue must be greater than the cost For what values of x will there be a profit X Graph the solution PRACTICE ANOTHER Use the tools to enter your answer

for z 2 3pi i calculate arg e z