Complex numbers Questions and Answers

Suppose that u v and w are vectors in an inner product space such tha u v 1 u w 5 v w 0 lu 1 v 3 w 4 Evaluate the expression 6vw 4u 6w

Is the following Please provide brief The set 6 statement true or false explanation why 5 8 0 is a linearly independent subset of R

Resolver la siguiente integral 1 3x So 4x4 x 1 2

NOTICE you only have ONE chance for this problem Jan and Monica are both solving a problem that involves an angle of depression of 22 5 from an airplane to a car Jan draws a triangle that looks like this 22 50 Monica draws a triangle that looks like this 22 5 Who is correct and why O Monica is correct because the angle needs to be in the triangle Jan is correct because the angle of depression starts from a horizontal line and swings down

Describe the end behavior of each function f x x 2x 4 O f x f x as x 00 as x 00 O f x as x f x as Xx 00 O as x as x 00 O f x as x o as x

Evaluate 10 000 Provide your answer below

For what values of x is f x x a function

Find the values of the six trigonometric functions for angle L 15 K 8

Graph the line with slope and y intercept 5 X

43 Solving a quadratic equation by completing the square Module 10 a Example Solve 2x 3x 2 0 44 Solving a quadratic equation by using the quadratic formula Module 10

Use Descartes s rule of signs to obtain information regarding the roots of the equation Select all that apply x x 6 0 The equation has no positive roots The equation has no negative roots The equation has no complex roots The equation has 4 positive roots The equation has 4 negative roots The equation has 4 complex roots Onone of these

CO A student is designing an experiment about cell size in organisms of different sizes Her hypothesis is that larger organisms will have larger cells She collects cheek cells from five different students in her class and estimates their size under the microscope Her results can be seen below Student Height in cm Cheek Cell Size In m 0 16 50 A B C D Multiple Choice What is the Independent variable in her experiment O 167 172 190 158 179 C height of human students different types of organisms size of cheek cells 76 82 97 98 88 micrometers um G

Beatrice deposits 525 in an account that pays 4 3 simple annual interest It she keeps the money in the account for 12 years how much interest will she earn

Select the correct choice below and fill in any answer box es within your choice Simplify your answer Use integers or fractions for any numbers in expressions OA x y x y and no numbers must be excluded x0 x and no numbers must be excluded for y Show Transcribed Text G

The graph of y f x is shown below dashed curve Reposition the two green draggable points to obtain the graph of y f z 1 2 solid curve Provide your answer below 76 5 4 3 2 7 5 0 1 2 3 1 2 3 4 5 7

7 9i 7 9i Simplify your answer Type your answer in the form a bi

Construction This section of a concrete skateboard ramp has the shape of a triangular prism Find the volume of the triangular prism Find the value of the concrete used in the ramp if the cost of concrete is 4 00 per cubic foot The volume of the triangular prism is ft 4ft 48 92A neip

Chips Between Functions 15 Select the correct answer Consider the function a z 3 8 and function b modeled by this graph b x No o Which statemerit describes the relationship between the intercepts of functions a and b DA The y intercept of b is less than the y intercept of a B The x intercept of bis equal to the x intercept of a C The intercept of b is greater than the x intercept of a D The y intercept of bis equal to the y intercept of

1 Find the center of the circle 3 2 1 2 1 0 1

7 4 10 sin 11 sin 9 4 12 tan 2 3

Rotate the point 680 to within 10 1 0 0 1 y 0 1 1 0 X

Consider the graph shown below Profit in dollars 200 150 100 50 50 20 Interpret the meaning of the ordered pair 60 50 in this situation The profit will be 40 60 80 100 120 140 Number of Candles Sold The profit will be candles are sold Interpret the meaning of the y intercept in this situation The profit will be dollars if dollars if candles are sold Interpret the meaning of the x intercept in this situation dollars if

from and decimal form 1 2a 5a 13 0 3 2b 6b 36 0 5 15 v v 5v 1 6 2 4n 5 11n 4 3n 24 7n 8 6 14p 14 2 6p

Compute Aut Q 2 3 with justification Give both its size and group structure

After a 10 reduction you purchase a new digital player for 292 5 What was the price of the digital player before the reduction A First write an equation you can use to answer this question Use x as your variable and express any percents in decimal form in the equation The equation is B Solve your equation in part A to find the original price of the digital player Answer The original price of the digital player was dollars

Sketch the graph to determine the number of solutions the equation has then use a graphing calculator Desmos to find the solutions 16 137 10 2 x 12 4 11 0 5 x 2 13 2 x 1

and a scalar equation of the hyperplane with vector equation 1 7 C 2 1 C C3 5 C1 C C3 R

A linear model shows that the relationship between the number of grocery items purchased and the total cost of the grocery bill has a correlation coefficient of 0 97 Which statement about the variables is true O There is a strong relationship between the number of items purchased and the total cost of and the total cost of the grocery bill Purchasing more items cause a higher cost of grocery bill O If a grocery bill has a higher cost then more items must have been purchased O There is no relationship between the numbers of items purchased and the total cost of the grocery bill

Which of the following values for a b and c will ensure f x is a function Choose all that apply b 6 Oa 3 b 6 c 4 O a 6 b 4 c 7 Oa 6 b 6 c 6 O a 8 b 8 c 8 O a 1 b 8 c 6 f x a 8 C

Perform the operations 1 2 Drovide your answer below

Consider an image with the centre pixel coordinates x y located at point 2500 1875 Given that the square pixel is 0 0016 mm wide the distorted pixel xd yd is located at 1267 2480 and we want the undistorted point xu yu to differ by only one pixel In other words xu xa y 0 0016mm What is the value of the first order distortion parameter given the above conditions and that Pin Cushion distortion is present Round your answer to 2 sf K

3 One of the following may Not be a Field division Ring a A commutative b A commutative Ring with unity where every non zero element is a unit c A commutative Ring with unity where every non zero element is a non zero divis d A finite Integral Domain

One of the following is a FALSE statement a Every Unit is a non zero divisor b Every zero divisor is Not a unit c All non trivial idempotents in Z20 are prime number d There is non trivial nilpotent elements in Z6 0 0

El n mero complejo 3 i en forma trigonom trica es O a 2 cis 300 Ob2 cis 60 Oc2 cis 30 2 cis 330

A new car is purchased for 22400 dollars The value of the car depreciates at 6 75 per year What will the value of the car be to the nearest cent after 9 years

Write an explicit formula for the sequence 1 1 1 1 1 8 9 10 11 12 an

6 5 4 3 2 1 6 5 4 3 2 7 1 34 5 6 1 2 3 4 5 6 The graph above is a transformation of the function f x x Write an equation for the function graphed above g x

The function y f x is graphed below What is the average rate of change of the function f x on the interval 2 x 8 10 9 8 7 6 5 4 3 2 20 18 16 14 12 10 1 8 6 4 2 4 6 8 10 y 14 16 18 20 1 2 3 4 5 6 7 8 9 10

4 5 points Below is the graph of a periodic function y f 0 IMA 2 T a 1 point What is the period of f KIN b 1 point What is the midline of f c 1 point What is the amplitude of d 2 points Write a function formula for f 0 2T 0

Add the following vectors v 5 0 0 V2 7 0 180 V3 3 03 150 v 4 83 0 162 v 4 83 0 18 1 v1 61 0 68 3 v 15 0 330 v 1 61 0 112

Calculate the vertex of the parabola using the equation 10 y x 4x 7 11 y x 8x 16 12 y 3x 6x

y 8 6 75 2 3 Which equation best represents the data shown in the scatterplot 8 9 X

5 be an n x m matrix and let C A be the set of columns of A Define all anl a12 00 0 an2 alm anm CR rank A dim Span C Now let V W be finite dimensional vector spaces and TV W a linear map between them Sh for any basis a of V and any basis of W we have dim im T rank T

Graph x 1 10 10 9 8 7 6 5 4 3 2 1 27 9 8 7 6 5 4 3 2 1 7 2 3 4 5 6 7 8 9 1 2 3 4 LA 5 6 7 00 8 9 10

Graph y 1 10 9 8 7 6 5 4 3 2 1 101 9 8 7 6 5 4 3 2 1 1 2 3 4 6 7 8 9 1 2 w 4 5 6 7 8 9 10

Select the appropriate inequality then fill in the equation of the line that represents the graph below y VAVIA 6 5 4 3 55 CSE 2 3 4 5 6

Choose the correct answer Peter wants to save all his earnings The goal is O unrealistic O measurable O specific

Choose the correct answer The basic step for financial planning is to O develop a plan for achievement O set the financial goal O implement the plan

Name the point that coordinates with this notation 2 G F 6 4 2 E 2 4 6 A D C B X f 0

Given this graph of the function f x Find f 4 OOOO 1 3 2 2 5