Vector Calculus Questions and Answers

a Find the slope of the line and b interpret the slope 2 3 10 0 C

Find the domain and range of the function graphed below Use interval notation S4 3 2 Domain Range 3 2 72 3 a

00000 Choose the correct equivalent Chinese numeral below OA OA an OB ETE OC yuf O B Choose the correct equivalent Greek numeral below OD the to f

1 point Relative to the graph of the graphs of the following equations have been changed in what way 1 y x 18 2 y x 18 3 y 18x 4 y x 18 A shifted 18 units down B shifted 18 units up C shifted 18 units left D shifted 18 units right E compressed horizontally by the factor 18 F stretched horizontally by the factor 18 G compressed vertically by the factor 18 H stretched vertically by the factor 18 y x

Label a ray with endpoint H Determine an appropriate name for a ray whose endpoint is H Choose the correct ray whose endpoint is H OA G OB OC OD H H G A GH OB HG OC GH H G G H Choose an appropriate name for a ray whose endpoint is H

For the given equation list the intercepts and test for symmetry y 6x 2 x 64 What are the intercept s Select the correct choice below and fill in any answer boxes within your che A The intercept s is are Type an ordered pair Use a comma to separate answers as needed

1 1 Let R be the region bounded by y the x axis x 1 and x b where b 1 I Let D be the solid formed when R is revolved about the x axis Find the volume of D c In b 1 b 1 b d 1 1 b In b I

Given u 12 5 and v 3 9 what is projvu 27 10 10 54 5 9 2 243 729 169 169 972 405 169 169

Step 1 Find f x Ax by substituting x Ax in place of x in f x 7x 2x f x Ax 7x Ax 1 1 Step 2 Simplify the above equation f x Ax x Ax x 1 x Ax XAX x Ax 4x x 24x

Please arrange each of the following groups of fractions in ascending order from smallest to largest 5 14 V 16 m 1 4

Graph the equation by hand by plotting points Verify your results using a graphing utility y x 9 Use the graphing tool to graph the equation Click to enlarge

A box with an open top is to be constructed from a rectangular piece of cardboard with length 48 inches and width 14 inches by cutting out equal squares of side length x at each corner and then folding up the sides as shown in the figure Write a completely factored polynomial whose values give the volume of the box volume length x width x height Volume Type your answer in factored form 14 in X X 48 in x

In the given right triangle find the side labeled x X X 28 21

Graph the exponential function SG Plot five points on the graph of the function and also draw the asymptote Then click on the graph a function button X 1

For each pair of functions f and g below find f g x and g f x Then determine whether fand g are inverses of each other Simplify your answers as much as possible Assume that your expressions are defined for all x in the domain of the composition You do not have to indicate the domain 3 x 0 a f x x 7 3 8 x x 0 x f g x g f x Ofand g are inverses of each other Ofand g are not inverses of each other b x 4x 3 g x 4x 3 f g x 0 8 f x 0 Of and g are inverses of each other Of and g are not inverses of each other 010

Match the point in polar coordinates with either A B C or D on the graph 3 a A b B c C D 6 25 5 4 A 3 2 1 D 3 2 1 1 2 3 4 1 B 2 C 3 4 5 r

sing Match the point in polar coordinates with either A B C or D on the graph 120T analloc 3 1 09 bao pinoTHU 6 05 03 ben in der I A B C D K 5 4 3 2 1 2 1 t 2 D 4 B C 3 4 51

Tree Mr and Mrs Frank just moved into a new home and need to do some landscaping They Elm E are going to purchase one tree one shrub and Birch B one lilac bush at random from the list to the Oak 0 right Use this list to complete parts a through e Shrubs Lilac bushes Juniper J Tinkerbelle T Primrose P Holly H a Determine the number of sample points in the sample space The number of points in the sample space is

Evaluate the function for the given value 5x g x e x 1 g 1 Type an integer or a decimal Round to the nearest thousandth as nee

Evaluate g x 4 a g 2 b g 3 c g 6 a g 2 b g 3 1 for the given values CHO Simplify your answer Type an integer or a simplified fraction Simplify your answer Type an integer or a simplified fraction

Write the equation in exponential form log 1 24 2 Write the equation log 1 24 2 in exponential form ww Use integers or simplified fractions for any numbers in the expression

Write the equation in exponential form 1 1 6 36 log 2 1 Write the equation log 1 6 36 2 in exponential form E Use integers or simplified fractions for any numbers in the expres

The circle graph shows the percent of people in a certain country with the various types of blood If one person from this country is selected at random use the graph to determine the odds in favor of the person having either O or O blood The odds in favor of the person having either O or O blood are 0 Type whole numbers Simplify your answer AB 1 AB 5 B 2 B 7 A 6 A 34 O 6 O 39

The adjacent spinner is used to play a board game What is the probability that the spinner will land on 200 1 The probability that the spinner will land on 200 is 12 Type an integer or a simplified fraction 200 450 600 Bankrupt 100 900 500 Lose turn 300 400 800 700

Translate the word phrase to an algebraic expression the product of 12 and x The translation is 12 x

Simplify the exponential expression 50x 10x 5 50x Simplify your answer Type exponential notation with positive exponents

The adjacent spinner is used to play a board game If the wheel is spun what is the probability that the spinner will land on a number greater than 200 The probability that the spinner will land on a number greater than 200 is Simplify your answer 100 230 Bankrupt 150 50 130 450 Lose turn 230 100 50 130

A cooler contains 66 cans of soda There are 24 cans of cola 9 cans of orange soda 15 cans of ginger ale 6 cans of root beer and 12 cans of club soda If one can of soda is randomly selected determine the probability that the can is not cola The probability that the can selected is not cola is Simplify your answer

Simplify the trigonometric expression 1 cot A csc A

Solve by using the square root property of equality Express all radicals in simplest form 1 125 t Simplify your answers Type exact answe using radicals as needed Use a comma separate answers as needed

A die is tossed Find the odds against rolling a number greater than 1 The odds against rolling a number greater than 1 are Simplify your answer

One card is drawn from a standard 52 card deck Determine the probability that the card selected is not a club P NOT club Type an integer or a simplified fraction

Complete the square to form a true equation x2 12x x x 12x x Simplify your answer Type an integer or a fraction

Complete the trinomial so that it is a perfect square t2 20t Find the missing term that completes the square t 20t Simplify your answer Type an integer or a fraction

O Consider the mathematical system with the single element 1 under the operation of multiplication Complete parts a to f below No O Yes d Does the associative property hold Yes No e Does the commutative property hold OYes O No f Is 1 under the operation of multiplication a commutative group No OYes CTED

D D D 5 Consider the mathematical system with the single element 1 under the operation of multiplication Complete parts a to f below a Is this system closed O No O Yes b Does the system have an identity element O No OYes c Does 1 have an inverse No a Noc

Consider the mathematical system defined in the table Assume that the associative property holds for the given operation Complete parts a to h below GREECH f Give an example to illustrate the associative property Which of the following is such an example OA ASM M A OB M 5 A 5 M SA OC A 5 SM A 5 M g Is the system commutative Give an example to verify your answer Which of the following correctly describes the system OA Yes the system is commutative An example is A 5 M A 5 M OB No the system is not commutative An example is 5 5 A 5 5 A OC No the system is not commutative An example is 5 A A 5 OD Yes the system is commutative An example is A M MSA

Click here to watch the video A fair die is rolled What is the probability of rolling an odd number The probability is Type an integer or a simplified fraction

Find all asymptotes x for vertical SON y for horizontal Stimgshal SMAKE MO17 Cos xo stos x 525 x2 f x 5 3x g x 5 3 x x 4 7x 4 D 30525 1 X C 14

Each individual letter of the word California is placed on a piece of paper and all 10 pieces of paper are placed in a hat If one letter is selected at random from the hat find the probability that a vowel is selected P vowel Type a fraction Simplify your answer

Find the opposite of 8 The opposite of 8 is

Express the number in decimal form without exponents 2 5 10

Express the number in decimal notation 1 36 10 1 36 x 100 1 36

ness drawings original work proper use of mathematics explanations etc For problems 11 14 Let f x y exy x y extrema Explain you 12 Let f be constrained by x 1 y 1 Use Lagrange multipliers to find any extrema Explain your findings

6 Evaluate the integral F dr where C is any path from 0 0 to 2 1 by finding potential function F x y 12x 3y 5y i 6xy 3y 5x j

z varies directly as the square of x and inversely as the square of y If z 163 whenx 8 andy 5 findzifx 7 andy 8 Round your answer to two decimal places if necessary Answer 2 Points Keypad Keyboard Shortcut

Evaluate y 4xy 2xy 2x d where C is the line from 0 0 to 1 5 followed by the line from 1 5 to 2 0 followed by a semicircular curve x 1 y 1 from 2 0 to 1 1 O 1 2 4 2 3 O 4

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4 Find the absolute minimum and maximum of the function f x y x 6y subject to the constraint g x y x y 16

K Part 3 of 12 Lines 1 and 12 are parallel lines Determine the mea of 1 through 12