Vector Calculus Questions and Answers

Use the Inventory Control information above to answer this question How many books should be produced during each printing run to minimize total cost books

Complete the square and find the center and radius x 2 y 2 x 6y 9 0

Kristen s financial advisor has given her a list of 13 potential investments and has asked her to select and rank her favorite five In how many different ways can she do this There are different ways Kristen can rank the five investments Type a whole number

4 Solve on a calculator but show work sec 5

se shading to show the following set on the venn diagram BU ANB C Use the graphing tool to shade the region s Click to enlarge graph B

Find the slope of the given line if it is defined The line through the origin and 12 6 Select the correct choice below and if necessary fill in the answer box to complete your OA The slope equals Simplify your answer OB The slope is undefined

Factor the polynomial 4b 21b 5 Select the correct choice below and if necessary fill in the answer bc A 4b 21b 5 4b 1 b 5 B The polynomial cannot be factored

Find the complementary angle of 30 0 1 The complementary angle of 30 is 59 2 Simplify your answer Type an integer fraction or mixed num O

Solve each equation 3x 5 log2 1024 O x 343 O x 5 X 5 3 O x 5 Question 17

Graph each function f x log x 2 O 543 ca 14 fa 3 da I m 2 Em 5 xt 8 da A I E M

A triangle Round to one decimal place as needed www 4 B

Solve the triangle CR a 10 b 1 C 150 Round to two decimal places as needed

Plot the point whose coordinates are 0 3 5 Select one Oa O b O C O d

Use this for questions 15 and 5 9 y 4 4 x 3 36

Write the polar equation for the parabola with directrix y 5 and focus at the pole Select one O a O b O C O d r r r 5 1 cos 0 r 5 1 sin 0 5 1 sin 0 5 1 cos 0

Consider the following limit statement lim 5x 11 6 X 1 Find the corresponding value of 0 when 0 005 O 5 0 001 O 6 4 995 O 0 01 6 001

2 6 For the angle of rotation 60 and the coordinates 2 2 in x y coordinate system find the coordinates in the xy coordinate system The coordinates in the xy system are Type an ordered pair Type an exact answer using radioal

If the region enclosed by the y axis the line y 2 and the curve y x is revolved about the y axis the volume of the solid generated is A 32 5 B 16T 3 C 16 5 D 5611 E T

m48 125 m49 61 m410 119 m411 125 m412 0 O O 4 64 d 6 610 9 10 78 12 11 12

17 3 cos 15 sin 37 1 A 12 cos 60 isin 148 C 0 75 cos 3 75 isin 32 25 E 81 cos 50 625 isin 1 874 161 B 81 cos 60 isin 148 D 81 sin 60 icos148 following

Determine the standard equation of the ellipse Foci at 1 3 and 5 3 vertex at 7 3 Choose the correct equation below OA O C x 2 y 3 81 72 1 x 2 y 3 72 81 1 OB SO D x 2 y 3 81 72 x 2 y 3 72 81 1 1

Predict the general term or nth term an for the sequence 3 7 11 15 19 an Simplify your answer Next q

Find the indicated term of the geometric sequence 1 a23 when a 700 and r 2 IN a23 Type an integer or a simplified fraction

Fill in the blank with the appropriate word or phrase Making generalizations or predictions from the data collected is called statistics inferential sample population

spotlight is located on the same plane as the runway 6 meters from the runway and is kept focused on the model At what rate is the spotlight rotating when the model is 4 5 meters from the point on the runway closest to the spotlight O O 6 meters de dt de dt de 944 de 24 rad dt 25 sec 11 Spotlight 1 rad 27 sec 4 rad 25 sec e 8 rad 76 Runway X

Write the equation of the line tangent to f x X O y 5x 6 1 4 y x O 5 Oy 5x 4 1 O y 5x 4 5 when x 1

8 Respondents to a randomly distributed questionnaire answered the question Do you agree that nuclear weapons should never be used because they are immoral The study that uses the results of this questionnaire will most likely suffer from which type s of bias Pearson s test prep pg 68 4 A undercoverage B voluntary response C response D nonresponse E all of the above

3 ok B ces Exercise 12 4A Algo Use the direct method to determine cash flows from operating activities LO 12 2 The following accounts and corresponding balances were drawn from Avia Company s Year 2 and Year 1 year end balance sheets Year 1 3 800 2 440 Account Title Unearned revenue Prepaid rent During the year 68 000 of unearned revenue was recognized as having been earned Rent expense for Year 2 was 25 000 Required Based on this information alone prepare the operating activities section of the statement of cash flows assuming the direct approach Is used Amounts to be deducted should be Indicated with a minus sign Cash flow from operating activities Net cash flow from operating activities Year 2 7 600 1 750 0

Calculate the slope of the line that passes through 11 6 and 1 O 01 0 6 01 O 6

Next question Find the locations and values of all relative extrema for the function with the graph below Ay 10 10 8 b 4 K 18 Q The function has a local The function has a local of 6 at x of 2 at x

Find the bearing of the ship for the given values of x and y Round to the nearest tenth of degree x 11 km y 6 km X OSE61 4 E S61 8 E S28 2 W S25 3 W y

Find the bearing from the origin to A for the given value of 0 0 31 S31 W S59 W 31 E OS5 PE 0

A weight of 800 pounds is suspended from two cables as shown in the figure What are the tensions in the two cables Round the answer to the nearest pound See Example 10 on page 648 for help 35 50 800 pounds

1 Find the general solution to the following equations a tane 1 Value 2 ton nt b sin 0 3 sin 0 2 0 Value 3 Sinx 3sinxt2 Bin 2 sing DEO no Solution a sin 20 1 0 Value 3 Sin2x 1 51 Sing Sinx 90 360 n nER 30 1

Find the volume of the oblique triangular prism below Round your answer to the nearest tenth if necessary 8 10 8

3 Find an equation in standard form for the hyperbola that satisfies the given conditions It may help to draw a picture with the given information to help you get starte a Foci 0 3 transverse axis length 4 b Center at 0 0 a 4 e 3 2 vertical focal axis c Transverse axis endpoints 5 3 and 7 3 conjugate axis length 10 d Foci 4 2 and 2 2 transverse axis endpoints 3 2 and 1 2

Determine whether or not the vector field is conservative If it is conservative find a function f such that F V If the vector field is not conservative enter DNE F x y z xyz xyz j x6y zk

aluate the expression using r 1 0 3 v 3 4 5 and w 4 3 12 a r w b w x r v w

Rogue Comet A comet following a hyperbolic path about the Sun has a perihelion of 120 Gm When the line from the comer to the Sun is perpendicular to the focal axis of the orbit the comet is 250 Gm from the Sun Calculate a b c and e What are the coordinates of the center of the Sun if the center of the hyperbolic orbit is 0 0 and the Sun lies on the positive x axis

e Stokes s Theorem to evaluate F dr In this case C is oriented counterclockwise as viewed from above Jc F x Y 2 In V x2 y2 i arctan Xj k S z 9 2x 3y over r 2 sin 20 in the first octant

Let C x be the cost to produce x batches 3 273 2 10x C x 5 5 2 R x 5 A OA Identify the y intercept of C x The y intercept of C x is at y 54 6 Simplify your answer Graph C x Choose the correct graph below Ay 80 32 0 Q 0 0 OB Ay 80 0 32 x 32 0 0 O C AY 80 0 0 16 32 Q 07 0 O D 80 Ay 0 0 80 x 32 G

imaginary zeros for the function f x 3x 4 4x 3 13x 2 4x 5

Determine a lower bound for radius of convergence of series solution of the following equation about x 0 20 x x y xy y 0 Xo 1

Use the right triangle and the given information to solve the triangle a 1 c 2 find b A and B b Round to the nearest hundredth as needed

A searchlight is shaped like a paraboloid of revolution If the light source is located 1 feet from the base along the axis of symmetry and the opening is 6 feet across how deep should searchlight be The searchlight should be feet deep Type an exact answer in simplified form

Find the number b where b 0 such that the average value of f x 3 108x2 on the interval 0 b is equal to 2 b

Select the polar trigonometric form of each of the following complex numbers Estimate all one decimal place 13 2 15 8 17 cos 28 1 isin 28 1 C 17 cos 151 9 sin 151 9 17 cos 61 9 isin 61 9 z 6 91 10 8 cos 33 7 isin 33 7 E C 10 8 cos 123 7 sin123 7 10 8 cos 236 3 isin 236 3 B 17 sin 28 1 cos 28 1 D 23 cos 28 1 isin 28 1 B 10 8 sin 56 3 icos 56 3 D z 15 sin 56 3 cos 56 3

ucy earned babysitting each month for the past five months was 225 280 240 180 and 200 Suppose the mean for six months was 220 How much did Lucy earn babysitting during the sixth month Example 2 5 The table shows the results of a survey about the number of E mails sent in one day Find and interpret the median of the data Example 3 20 27 23 Number of E mails Sent Per Day 24 22 26 22 27 21 27 20 23 20 22 24 26 27 22 27 20 25 Find the mean median and mode of each data set 7 1 2 0 5 1 1 4 3 2 0 5 3 9 5 7 8 7 6 4 4 5 6 7 9 5 7 8 6 7 9 5 4 5 4 The number of candy bars Mariah sold over the course of two weeks was 10 12 9 14 8 12 14 7 11 13 12 9 10 13 Find and interpret the mode of the data Example 5 6 The table shows the number of points scored by a basketball team in each game last season Find and interpret the median number of points scored Example 4 64 42 41 67 Number of Points 52 44 63 68 8 72 65 68 68 73 45 68 71 44 43 10 140 128 124 137 143 126 130 136 54 61

Using synthetic division select the quotient for each polynomial division below x 4x 18x 9 r 3 11 91 12 Quotient 7x 3 Remainder 18 C Quotient x 21 No remainder E Quotient x 7x 39 Remainder 108 2x 5x 6 x 2 A Quotient 2 4x 3 No remainder C Quotient 2 4r 13 Remainder 32 Quotient 2x 4x 3 Remainder 12 B Quotient r r 21 Remainder 54 D Quotient 7x 3 No remainder B Quotient 2x 4x 3 No remainder D Quotient 2 4x 3 Remainder 12

A ball is shot straight up into the air with initial velocity of 42 ft sec Assuming that the air resistance can be ignored how high does it go Hint The acceleration due to gravity is 32 ft per second squared