Linear Algebra Questions and Answers

Part B Which expressions are equivalent to 8x2 9x2 8x2 3x 8x for x 0 9 for x 0 9 9x 9x 1 for x 0 x 3x 8x 3x Select all that apply

Name Date 3 24 23 Class 802 ALL WORK IS SHOWN ON LOOSE LEAF DIRECTIONS PLEASE READ THE FOLLOWING SCENARIO TO ANSWER THE PROMPTS THAT FOLLOW I Ms Karla was driving to Las Vegas in her electric vehicle Her vehicle gets 250 miles for every 4 5 of battery life a What is the rate of change b Grapn the function Sur com use your equation rate of change to answer q6 If ms karla drives 600 miles how much life will she have used battery 0 miles can ms karla drive on

2122 Need Help Read It 2 Points DETAILS SALGTRIG4 8 3 056 Find the product z1z2 and the quotient Express your answers in polar form Z cos 45 sin 45 22 cos 120 sin 120

Question 3 Is that are on the east side n How many different ca

Find the work done by the force field F 2 2 x in moving a par ticle along the curve C where C is the intersection curve of the plane x z 1 and the ellipsoid x 2y z 1 oriented counterclockwise when viewed from positive z axis

S Trigonometry Spring 2023 Sp23 MAT Watch It

Ultrasound is used in medicine both for diagnostic imaging Fig P17 9 page 526 and for therapy For diagnosis short pulses of ultrasound are passed through the patient s body An echo reflected from a structure of interest is recorded and the distance to the structure can be determined from the time delay for the echo s return To reveal detail the wavelength of the reflected ultrasound must be small compared to the size of the object reflecting the wave The speed of ultrasound in human tissue is about 1 500 m s nearly the same as the speed of sound in water a What is the wavelength of ultrasound with a frequency of 2 40 MHz b In the whole set of imaging techniques frequencies in the range 1 00 MHz to 20 0 MHz are used What is the range of wavelengths corresponding to this range of frequencies B Benoit Photo Researchers Inc Figure P1794 view of a fatur

50 1 0 0 1 0 1 0 1 0 0 0 0 0 0 10 1 0 0 1 1 0 Exercise 10 0 9 B level Consider the transpose matrix to the one above 50 and call it do Show that this matrix represents the linear map do R X R X which is induced by sending basis element 1 ej to the vector 1 p 1 Pi Exercise 10 0 10 C level Compute the determinant of 60 above What does this tell us about the kernel of 50 B12 B02 B01 to12 The matrix which is Similarly I can define a linear map 6 R x R X by Bij eij associated to this linear map is 6 1 1 1 0 0

a relationship is impossible So by the above lemma we have an injective linear map Exercise 10 0 5 C level Let X A Give 5 elements in R X Can you write something down using scalars el from X and other familiar symbols but that is not in R X

Let P2 be the vector space of all real polynomials of degree at most 2 Let P P2 P3 E P2 be given by pi z 2 p2 x 2x x and p3 x x ar a 4 marks Find the condition on a ER that ensures that P1 P2 P3 is a basis for P2 You are free to assume that the polynomials 1 2 and are linearly independent b 2 marks In the case that a 4 write the polynomial p x 4 write the polynomial p x combination of p1 p2 and p3 Can you write the polynomial p x 2 r r as a linear combination of p p2 and P3 when a Justify your answer 2 1 as a linear

Question 3 Jaden throws a ball straight up in the air with an initial speed of 40 ft sec from a height of 7 ft Fill in the parametric equation that describes the vertical motion of the ball as a function of time t y t 16t2 Select Select Select 2 pt Select

The figure shows a medicine wheel which is a Native The central angle in Type an integer or a simplified traction The central angle in degrees is approximately inal spokes in the wheel al equally spacedure The figure shows a medicine wheel which is a Native American structure This circular structurebis perhaps 2500 yr old There are 27 aboriginal spokes in the wheel all equally spaced a Find the measure of each central angle in degrees and in radians The central angle in degrees is approximately Type an integer or a simplified fraction The central angle in radians is approximately Simplify your answer O Type an exact answer in terms of n Use integers or

26 IV fluids 1000 mL blood transfusion 2 units 360 mL per unit 6 oz water

25 IV fluids 1200 mL water 2 oz broth 4 oz 6 ice cubes 120

6 3 Points DETAILS SMITHNM13 13 1 For the spinner below assume that the pointer can r B

Factor cach and find all rational roots x 3 5x 2 4x 20 0

1 Let V1 span V V 2 3 1 and v2 2 1 2 Which of the following vectors are i 4 2 1 ii 6 1 4 iii 10 3 4 A i and iii only B i only C ii only D iii only E all of them 7 ii and iii only G i and ii only H none of them

1 Fully factor the following a f x x 3x 2x 6 K2 marks b f x 8x 125 k 2

5 4r4s 4t 4 4r s 2t 5 3r3s 4t 16 7 x y 2z 6 3x 2y 25 4x y z 12 6 x 6y 4z 12 2 x y 42 12 5 26 28 82 2x 2y 5z 8 5a 5b 5c 20 4a 3b 3c 6 4a 3b 3c 9 C x 24 52 1 132 B 3

D Question 10 A reader can get lost or lose interest in material that is too dense and many run on sentences Select the letter of the revision that corrects The report is due on Wednesday but we re flying back from Miami th would be able to get the report to her later that day she suggested th done and I told her we had meetings until our flight took off

Question 3 Identifying run on sentences is the first step in eliminating them in your writing Sel that contains a run on O John hit the baseball very far it went over the right field fence O Be careful not to spill the milk it will ruin your new dress We went to the movies but after the movies we went home Question 4 The following sentence is a run on sentence because of incorrect punctuation at th Choose the correct way to fix the underlined problem so that the sentence is corre orna did not last long in Mr Wolcott s busy office her long fingernails made accur

Determine whether 1 3 is a solution of the system 2x 4y 8 5x 3y 1 Is 1 3 a solution of the system Choose the correct answer below Yes No

Consider the following data in the table x y 1 11 428571 08 1 5 6 2 3 92 Is the dataset in the table representative of a linear function exponential function O Exponential O Linear Find the function that creates the data above If linear express your answer in the form y mx b If exponential express your answer in the form y a b y

be how to graph a line using the slope and y intercept Provide an original example with this description To graph a line y mx b using the slope and y intercept plot the point containing the y intercept on the This is the point Obtain a second point using the slope Write Vas a fraction and use starting at the point containing the y intercept to plot this point Use a straightedge to draw a line the two points Draw arrowheads at the ends of the line to show that the line continues indefinitely in both directions Graph the line y 2x 3 using this process Use the graphing tool to graph the equation Click to enlarge graph 10 lesti n 1 point s possible 10 lo 6 Ay

Describe how to graph a line using the slope and y intercept Provide an original example with this description BLEEM Click to enlarge graph This is the point starting at the point containing the two points Draw arrowheads at the ends of the To graph a line y mx b using the slope and y intercept plot the point containing the y intercept on the Obtain a second point using the slope Write as a fraction and use the y intercept to plot this point Use a straightedge to draw a line line to show that the line continues indefinitely in both directions Graph the line y 2x 3 using this process Use the graphing tool to graph the equation This question 1 point s possible 50 10 Ay

What does it mean if the slope of a line is 0 Choose the correct answer below A A line is horizontal when its slope is 0 OB A line is neither vertical nor horizontal when its slope is 0 OC A line is vertical when its slope is 0 OD It is impossible for a line to have a slope of 0

a slope point 1 5 O No Solution 3 4 Help 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Fill Grap Afte can prop

9 1 Points 4x 50 DETAILS 3x 10 O 5x 400 Use algebra to find the value of x in the triangle X 3x 50

What is the relationship between multiplying polynomials and factoring How are these two concepts related How can they be used to check your work Give an example and work it out to explain your reasoning Be sure to explain how your example shows the relationship you describe Things you MUST include A verbal written explanation that describes the relationship between the two concepts 3 points An example that shows how multiplying polynomials and factoring are connected Explain each step Explain how your example shows the relationship 2 points You may either type your answer in the text box below OR upload a file picture or scan of handwritten answers All files should be saved using the following template Last Name First Name Assignment Name Question Number Refer to Orientation for help with file uploads Show ALL work For uploaded files label your paper with the assignment title AND your name

Solve the given initial value problem 1 2 2 X X 3 4 2 X t X 0 6

4 Solve the following binomial problem using the normal curve Be sure to use the 5 step process as outlined in Module 9 Round to 4 decimal points P X 24 n 30 and p 58

Determine whether A and B are inverse matrices Example 4 4 5 M 5 6 19 A B 21 A B 12 5 3 5 12 5 7 3 7 12 3 6 4 4 3 65 20 A B 6 5 5 4 8 4 22 2 83 A 6 3 B 3 4 68

Transcribed image text Let the density function of a random variable X be given by Sx x ex OSXS1 Suppose X X X be a random sample taken from above population Define an estimator log x Here the new random variable w follows b c Poisson distribution with mean Gamma distribution with mean 98 Gamma distribution with mean Exponential distribution with mean

ind all roots One root h x 3 3x 2 8x 10 0

Let M 036 41 2 1 7 and b invertible where p q r ands are constants If the system of linear equations Mx b is consistent show that the matrix N 2 2 1 p 0369 414 r 217 S is singular i e not

p 4 3p 7 3 Write your answer using only positive

3 Find the eigenvalues and their corresponding eigenspaces of the matrix A 0 0 0 u a Enter X the eigenvalue with algebraic multiplicity one and then X the eigenvalue with algebraic multiplicity tw A1 A Note Enter two numbers separated by a comma b Enter an eigenvector for the eigenvalue X which has multiplicity one 13 M v or v w 2 5 1 Note Your answer should be a vector of the form 11 12 13 c Enter eigenvector s for the eigenvalue X which has multiplicity two If all the eigenvectors are proportional to each other then enter only one eigenvector If there are two eigenvectors not proportional to each other then enter these two eigenvectors Note Your answer should be either one vector the form 1 12 13 or two vectors separated by commas

1 At the beginning of the week Miguel s odometer reads 86 845 At the end of the week his odometer reads 87 033 How many miles did Miguel travel that week

This module is intended to help you understand fractional exponents Rewrite the expression below as 16 to a single power 168 5 1640 167 16 4 16 16 Let x 16 x 16 x 16 Use the two different equations for x above to express 16 as a radical in the answer form below 16

Casey cuts a 2 pound meton into two pieces and puts each piece on a plate as shown Does that mean the weight of the pieces on eac ate is 1 pound Yes because each plate has 1 part of the melon Yes because 2 2 1 CLEAR CHECK No because the pieces of the melon are not the same Size No because 2 parts of a melon weigh more than 1 whole melon

The number of shark attacks can be modeled by the equation y 50 1 03 If the shark attacks continue to increase at the current rate approximatley how long will it take for the number of attacks to reach 125 O 10 years O 31 years O 33 years O 28 years

4 Complete the missing entries in the following pay stub EARNINGS PERIOD WEEKLY 18 DEDUCTIONS TAX TYPE Social Security Medicare Federal Tax State Tax ADJUSTMENTS ITEM Union Dues Family Health Ins AMOUNT AMOUNT b d 322 65 191 20 AMOUNT f 23 95 YTD AMOUNT 21 510 YTD AMOUNT C 5 807 70 3 441 60 YTD AMOUNT 216 00 a As indicated in the paycheck number box this is the 18th paycheck of the year Determine the current gross pay b What is the Social Security tax for this pay period c What is the year to date Social Security tax

0 18 31 AM A group consisting of 28 aggressive zombies triples in size every hour Which equation matches the number of zombies after 7 hours OZ 3 1 28 7 OZ 3 28 7 Z 28 1 3 7 OZ 28 3 7 Submit Answer

his angle in radians to degrees 1 DETAILS

DETAILS gle in degrees to radians Express your answ radians

Plot the point 0 6 in a rectangular coordinate system Plot 0 6 10 B 6 441 2 4 6 co 40 72 8 10 x

Fill in the blanks 160 14x 2 01 A x D B Enter only the NUMBER values for A B C and D to be automatically scored and to create a true statement

13 Mechanics Create a crease of 1 for each

Let T P3 P3 be the linear transformation satisfying T 1 4x 1 T x 3x 9 T x 5x x 8 Find the image of an arbitrary quadratic polynomial ax bx c T ax bx c

Time Left 1 43 09 Citlali Medrano Attempt 1 Question 8 5 points You decide grow your own garden to are some startup costs associated wit you find that not only have you been a but you have also saved 2 400 in gro