Vector Calculus Questions and Answers

3 f x 5x 45x 4 Write a polynomial f x that satisfies the given conditions Polynomial of lowest degree with zeros of 4 multiplicity 3 3 multiplicity 1 and with f 0 960 2 60x 400 960 5

Let P 1 1 Q 3 5 R 1 4 Part 1 Find the component form and magnitude of the vector Simplify radicals if possible Round your answers to the thousandt 1 PQ Find PQ

Let u 2 4 v 1 3 Part 2 Find the component form of the vector 4 2u 3v

Snow Day Homework elike terms to simplify the polynomial 4x 2 3x 2x 2 5 9x 18

Give the exact values of the sine and cosine of the special angles listed below sin 6 5 cos 6 sin 0 cos 0 11 cos IM sin 7 7 6 11 11

Find exact function values No decimals If undefined answer DNE a 117 6 sin 77 4 COS tan 57 4

use matrix inversion to solve the given linear system x y 2 z 2 x 3 y 2 z 0 21 4x 5y 5z 3 22 2x 6y 5z 4 2x 3y 62 9 x 4y 4z 1

1 074 Points MY NOTES DETA ASK YO Marginal Cost The following function C x 20

Obtain an equivalent system by performing the stated elementary operation on the system Multiply the first equal by 4x 8y 7x 8x 4x 8y 7x 8x 3z 8 14y 14z 14 11y 15z 40 11 3z 8 14z 14 14y 11y 15z 40 Type integers or simplified fractions y Save C

A tank contains 80 kg of salt mized in 1000 L of water A solution of concentration tank at a rate of 10 L min 0 04 kg of salt enters the The solution is mixed and drains out of the tank at the same rate Find the concentration of salt in the tank in Kg L as time approaches infinity

A quadratic function has its vertex at 9 9 When written in vertex for h k II 111

Model the curve with a sine function Note that the graph may or may not be drawn with the same scale on the two axes f x ANA 13 5 9 4 5 4 5 2 13 5 G

35 What is the answer a no solution b 38 41 c 53 8 d 36 52

21 What are the answers 5TT 3 b a Tar and C F3 F F F d TT TT and and and 11TT 6 5TT 6 211

To answer questions 22 23 find the solution set of 2 cos2x in the interval 0 x 2T 2 or when a table or calculator is used in the interval 0 x 360 22 What is the second from the last step a cos x 1 2 b cos x 1 1 C cos x 2 d cos x 1

The owner of a van installs a rear window lens that has a focal length of 0 310 m When the owner looks out through the lens at an object located directly behind the van the object appears to be 0 260 m from the back of the van and appears to be 0 320 m tall a How far from the van is the object actually located and b how tall is the object Rear window lens a Number i 1 225 Person Units m Image of person O

Find the size of the matrix Identify a square column or row matrix Give the additive in 6 86 2 42 The size of the matrix is 2 x 3 The matrix is of no special type The additive inverse of the matrix is

Conclusion A Normal plane is a palne containing the normal vector of surface at a particular point A Inclined plane is a plane inclined at an angle to the horizontal A Oblique plane is a plane surface is inclined to one of the principal plane and a side or a diogonal or diameter of a plane surface is parallel to that principal plane and inclined to other plane surface will be calkled oblique plane Do upvote and comment for more clarification

expression as a logarithm of a single expressi log 27 log 9 g 27 log 9 log log 12 Simplify your answ

Determine whether point A is inside or o

a Suppose the slope of the curve y f x at 5 8 is Find f y at y 8 b Find f 2 if f x x x

Point P 4 2 is on the terminal arm of 0 in standard position 0 means angle theta a Sketch the angle in standard position and label your diagram

sin x sin y cos x cosy Ju x du dy 0 u cos 2y for x 2 y

1 point Graph the rational function The intercept s have x The y intercept s have y Give you answer as a comma separated list e g 2 3 8 4 If there are none enter None The vertical asymptote s have y Give you answer as a comma separated list e g 2 3 8 4 If there are none enter None 2x 7x 3x 7 The horizontal asymptote s have y Give you answer as a comma separated list e g 2 3 8 4 If there are none enter None The local extrema are Give you answer as a comma separated list e g 2 3 8 4 If there are none enter None Give you answer as a comma separated list of ordered pairs correct to one decimal place e g

C intercepts as ordered pairs in ascending order Does the graph Bounce B or Cross C at each of the x intercepts List this in ascending order of intercepts type BBCC or CBCB or CBCB or End Behavior ON OM OH Off My graph looks like O Afr of the

hich values are in the domain of the function f x 6x 11 with

of co x o t t X t s F s ds solves the initial value problem X AX F t X t Xo whenever t is a fundamental matrix of the associated homogeneo system Use the above to solve the given initial value problem X t 66 X 0 X

75 According to Quantcast analytics of CrossFit com 59 of CrossFitters have children Suppose we take a random sample of 40 Crossfitters and find the sample proportion p that have children We repeat this process many times a What do you expect the mean of the p s to be b What do you expect the standard deviation of the p s to be c What do you expect the shape of the p s to be 76 According to Quantcast analytics of CrossFit com 40 of CrossFitters have post graduate de grees Suppose we take a random sample of 60 Crossfitters a Describe the sampling distribution of the sample proportion of CrossFitters who have post graduate degrees for samples of size 60

Which differentiation rule cannot be used in finding the derivative of f 1 e sin t 15 O The Power Rule O The Power Rule Combined with the Chain Rule O The Chain Rule O The Quotient Rule

When finding the margin of error for the mean of a normally distributed population from a sample what is the critical probability assuming a confidence level of 58 O 0 21 O 0 42 O 0 58 0 79

Recall that the dot product u v of two vectors u 1 2 un and v v v2 Vn from Fis U 1 V 1 U2V2 1 unvn where the addition and multiplication are those of F Let C be an n k linear code Show that C vEF vu 0 for all u E C is an n n k linear code This code is called the dual of C

1 Determine the exact value for the trig ratios of angles below on the Unit Circle No calculators allowed nese must be found by using the following steps Graph the angle in standard form Label the reference angle in degrees Draw and annotate all sides of the reference triangle Identify and simplify the trig ratio 2TT sin 3 tan

The table below shows the cumulative amount of time in hours Meghan reads over five weeks Number of Weeks Cumulative of Hours Read 1 2 3 5 If the data in the table is graphed what is the approximate slope of a line that best fits the data 2 5 7 13 Only 0 1 2 3 4 5 6 7 8 9 and are allowed in your answer Answers that are mixed numbers must be entered as an improper fraction or decimal

Evaluate the integral x dV where E is the solid tetrahedron with vertices 0 0 0 1 0 0 0 1 0 and 0 0 1

Project Ploughshares periodically sponsors public service seminars and programs Currently promotional plans are under way for this year s program Advertising alternatives include television radio and newspaper Audience estimates costs and maximum media usage limitations are as shown TV Radio Newspaper 100 000 18 000 50 000 2 000 300 600 50 40 Audience per ad Cost per ad S Maximum Media Usage 10 To ensure a balanced use of advertising media radio advertisements must not exceed 50 of the total number of advertisements authorized In addition television should account for at least 10 of the total number of advertisements authorized Formulate a linear programming model for this problem Solve with Excel solver Attach ONE PAGE solution printout and ONE PAGE sensitivity analysis report printout to your homework Answer the following questions a If the promotional budget is limited to 18 200 how many commercial messages should be run on each medium to maximize total audience contact What is the allocation of the budget among the three media and what is the total audience reached b By how much would audience contact increase if an extra 100 were allocated to the advertising budget If possible answer without resolving

the domain is set of all the values of x the range of all the values uf y D 2 4 7 1 R 10 2 8 4

Helen Ming receives a travel allowance of 170 each week from her company for time away from home If this allowance is taxable and she has a 28 percent income tax rate what amount will she have to pay in taxes for this employee benefit Round your final answer to 2 decimal places Annual tax amount

Luke Anderson is earning 29 000 a year in a city located in the Midwest He is interviewing for a position in a city with a cost of living 6 percent higher than where he currently lives What is the minimum salary Luke would need at his new job to maintain the same standard of living Minimum salary

Notations R is the set of real numbers C is the set of complex numbers Exercise 1 10 points Prove that a b ab

Q10 Following are the differential equations and their respective solutions Select the incorrect one 1 y a sin 2x sinx y a sin x cos x 9 y b log x 2 T III y 7x 3 sec 3x 5e cos 5x e sin 5x y 7 e sin 5x tan 3x a Only l b Only II c Only III d All corre

A family spends 30 000 a year for living expenses If prices increase by 2 percent a year for the next three years what amount will the family need for their living expenses after three years Use Exhibit 1 A Round time value factor to 3 decimal places and final answer to the nearest whole dollar Future living expenses

Use Lagrange multipliers to find the point on the plane x 2y 3z 6 that is closest to the point 0 5 2

Problem 6 a Let the vector u 2 3 be given Describe the set of all vectors v v1 v2 which are orthogonal to u b Let the vector u 0 1 be given Find all vectors v 1 a which are in a 300 angle to u

Answer the following by using the worksheet 6 If z i then zo is approximately 0 66 1 1i If z If z 2 3 2 1 2 3 1 3 5 13 i then 26 is approximately 2 Click for List 12 6 i then z is approximately 13 Click for List Note When zooming in on the diagram the upper the coordinates of the upper lefthand corner and lower right corner are shown when the coordinate axes cannot be seen

Calculate the integral approximations Ts and Ms for 10 30 In x 5 dx Your answers must be accurate to 8 decimal places Ts M I

Find the absolute maximum and absolute minimum of the function f x y x y 4xy 2 on the rectangular plate 0 x 3 0 y 2

What is the approx hoose the correct answer below A 1200 cm B 1200 km2 C 1200 mm

Throughout this problem consider R to be the region between the curves f x g x r in the first quadrant sliced horizontally see graph below Y y x Ay a and a Find the exact area between the two curves in R Show your steps and explain your reasoning You do not need to simplify your answer b Set up an integral for the volume of the solid obtained by rotating R around the x axis You do not need to evaluate the integral c Set up an integral for the volume of the solid obtained by rotating R around the line x 1 You do not need to evaluate the integral Notes In parts b and c your explanation should include i a rough sketch of the solid of revolution ii Label your solid and show the radius es iii Clearly state the method you are using and why and iv Clearly show and justify your steps for setting up your integral Your final integral should be clearly shown

1 6 marks Let S be the torus parametrized by G 0 p a bcos p cos 0 a bcos p sin 0 b sin for 0 9 0 2 where a b 0 and a b Calculate the surface area of S

Let f x be a function that has a Taylor Series centred at x 6 given by converges f x What is the smallest value of k for which the derivative f k 6 0 k 0 What is the value of this derivative f k 6 n 2 2nn 3n 1 x 6 n 2