Vector Calculus Questions and Answers

1 Given U natural numbers from 1 to 20 P odd numbers less than 20 and Q multiples of 3 less than 20 a List the elements of i P ii Q b Find i P ii O iii PUQ iii PUQ iv PnQ iv POQ

For the following demand function find E p and determine if demand is elastic or inelastic at the indicated price 600 q p 3 p 6 2 3 Type an integer or a simplified fraction Is the demand elastic or inelastic at p 6 E 6 O A Elastic because E p 1 OB Inelastic because E p 1 OC Inelastic because E p 1 OD Elastic because E p 1 G

A cup of hot coffee is placed on a counter and allowed to cool The temperature in degrees Celsius of the coffee t minutes after being placed on the counter is given by the accompanying function Complete parts a through d T t 28 48e 0 019t a What was the original temperature of the hot coffee How can the original temperature of the hot coffee be found Select the correct choice below and fill in the answer box to complete your choice OA Evaluate T OB Solve 28 48e 0 019t for t

etermine the largest open interval s of the domain over hich the function shown in the graph below is increasing b decreasing and c constant Then ve the d domain and e range a Over what open interval s if any is the function increasing Select the correct choice below and if necessary fill in the answer box complete your choice A The function is increasing on the open interval s Type your answer in interval notation Use a comma to separate answers as needed B The function is never increasing b Over what open interval s if any is the function decreasing Select the correct choice below and if necessary fill in the answer box t complete your choice A The function is decreasing on the open interval s Type your answer in interval notation Use a comma to separate answers as needed B The function is never decreasing

C Through 0 4 parallel to 5x y 9 C y Simplify your answer Use integers or fractions for any numbers in the expression

K The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write a formula for f c Estimate the zero of f a The slope of the line is Type an integer or a simplified fraction CL

y 3x 6 Which of the following graphs does the equation most closely resemble OA Q OB Q G OC Q OD

Decide whether the relation defined by the grap and range Does the graphed relation define a function No Yes What is the domain of the graphed relation 0 00 Type your answer in interval notation What is the range of the graphed relation Type your answer in interval notation

K Find f x at the indicated value of x f x 3 x 8 1 8

Decide whether the relation defined by the graph to the right defines a function and give and range Does the graphed relation define a function No Yes What is the domain of the graphed relation Type your answer in interval notation S

Write the set x 1 x 5 using interval notation and then graph the set on a number line The interval notation for the set x 1 x 5 is

The data show the number of felony convictions in hundreds and the crime rate in crimes per 100 000 for seven randomly selected states For the given data a determine the correlation coefficient between the number of felony convictions and the crime rate b find the equation of the regression line and c approximate what crime rate can we anticipate in a state that has 12 hundred felony convictions Felony convictions 114 110 7 109 3 106 105 104 9 Crime rate 102 99 5 100 4 99 94 2 103 95 5 93 3 OA a r 0 906 b y 14 11x 0 777 c 170 1 OB a r 0 906 b y 0 777x 14 11 c 4 8 O C a r 0 906 b y 0 777x 14 11 c 4 8

Computer the correlation coefficient rounded to the nearest thousandth for the following data y 3 13 A 0 905 OB 0 750 OC 0 905 OD 0 750 2 1 19 12 15 7 0 18

Question 8 Terry is skiing down a steep hill Terry s elevation E t in feet after t seconds is given by E t 3700 40t The equation tells us that Terry started Select an answer Select an answer and his Select an answer is Select an answer by Select an answer Question Help Moc

Score 3 12 3 12 answered Question 9 If f x is a linear function f 5 5 and f 2 f x Question Help Video Message instructor 1 4 find an equation for f x

B 50 Need Help Submit Answer 0 06 0 12 Points X T X Read it Watch It DETAILS MY NOTES ASK YOUR TEACHER A graphing calculator is recommended Let f x 4e cos x a Find f x and f x PREVIOUS ANSWERS SCALCET9 3 3 034 PRACTICE ANOTHER

Consider the following functions f x 3x 5 g x 2x 1 Find f g x Find the domain of f g x Enter your answer using interval notation Find g f x Find the domain of g f x Enter your answer using interval notation Find f f x Find the domain of f f x Enter your answer using interval notation Find g g x Find the domain of g g x Enter your answer using interval notation

Find f g f g fg and f g and their domains f x x x g x x Find f g x Find the domain of f g x Enter your answer using interval notation Find f g x Find the domain of f g x Enter your answer using interval notation Find fg x Find the domain of fg x Enter your answer using interval notation Find 1 x Find the domain of x Enter your answer using interval notation

By definition f g x f g x So if g 7 11 and f 11 20 then f g 7

4 2 points Consider the curve a helix parametrized by r t cost sint at where a 0 is a positive constant As a increases does the curvature increa decrease or stay the same Justify your answer by describing what happens to curve and interpreting the formula K d where s d where s s t is the reparametrizat of r such that r s 1 You need not compute the curvature directly

4 Bonus 2 Find the circle passing through the three points 0 4 2 2 and 2 2

Use Fleury s Algorithm to find an Euler circuit Write an Euler circuit starting at A CHE D A E C LL

box with a square base is to be made from a square piece of cardboard 15 inches on a side by cutting out a square from each corner and turning up the sides See the figure Answers parts a through e a Express the volume V of the box as a function of the length x of the side of the square cut from each corner 3 V 225x 60x 4x Simplify your answer b What is the volume if a 2 inch square is cut out The volume is 60 cubic inches Simplify your answer 0 8 of 1

4 The graph of a function g is shown on the ay plane on the interval 7 7 a A table of selected values is given for a different function h which has only one real zero 3 h x 5 2 2 7 0 3 2 0 13 20 VAN

Question 4 For the following exercise write a formula for the function obtained when the graph is shifted as described 1 is shifted down 3 units and to the left 8 units H Question Help VIDEO D Post to forum

8 f 1 1 3 g t 1 Find pXr

8 A trough is 10 ft long and its ends have the shape of isos celes triangles that are 3 ft across at the top and have a height of 1 ft If the trough is being filled with water at a rate of 12 ft3 min how fast is the water level rising when the water is 6 inches deep

direction that is 165 counterclockwise from the x axis Part A Find the x component of this vector Express your answer in meters View Available Hint s Hint 2 Simplify expression for the horizontal component Hint 1 How to approach the problem Tx A O Submit Request Answer wwwww

Draw a propane 1 ol b heptane 2 ol c Ethanol d Diethyl ether e dipropyl ether f methyl ethyl ether

aume All of question 4 4 LOH HH OHH H OH H

3 Draw the following a Ethanal b Propanal C Pentanal All of question d Hexane 2 one e Octane 3 one f Decane 5 one

2 Which of the following has a point discontinuity c y x a y X b y x 1 X d y x 1 x 1

7 The height of an object thrown from a cliff is modeled by h t 4 91 3 6t 63 where tis time in seconds and h t is height in metres a What is the average velocity from time Os to time 1s A4 b What is the instantaneous velocity of the object at 1 seconds

Solve the following inequality x 6 312 0 0 x 5 Write your answer using interval notation 0 0 0 0 0 0 0 0 8 8 QUD

Divide 10 13x 8x 2x 4 Write your answer in the following form Quotient 10 13x 8x 2x 4 0 0 2x 4 Remainder 2x 4 15

A quantity P is an exponential function of timer such that P 170 when t 4 and P 150 when information about P Poe to a Find values for the parameters k and Po Round your answers to three decimal places k P per unit time b Give the initial quantity and the continuous percent rate of growth or decay Round your answer for the initial quantity to three decimal places Enter your answer for the growth or decay rate as a positive value rounded to one decimal place The initial quantity is i and the quantity is 2 Use the given at a continuous rate of

Tell whether a linear or quadratic function would be a more appropriate model for this set of graphed data If linear tell whether the slope should be positive or negative If quadratic tell whether the coefficient of x should be positive or negative 40 O Would an appropria data be linear or qu Linear Quadratic ho x Should the coefficier or negative ONegative Positive

4 Given the function f x what is the value of a f 2 b f 5 c f f 2

Jenny and Jim are standing on a riverbank at points A and B respectively See the figure below Jim is 160 meters from a house located across the river at point C Suppose that angle A angle BAC is 41 and angle B angle ABC is 73 How far are Jenny and Jim standing from one another Round your answer to the nearest tenth of a meter 4 0 meters X

sketch the triangle O LA 50 25 73 c 270 O 2C 57 B B 270 73 73 270 50 50 C A O A A Solve the triangle using the Law of Sines Round side lengths to the nearest Integer a 208 962 x b 175 34 50 50 270 270 73 73 B B

7 Assume c 0 find lim 1 X Vcx 1 1

Evaluate the integral 2 7x in x dx 7x In x dx 2

Evaluate the integral using integration by parts xetax x e x dax

3 Finding for a given e using a graph Let f x x 3 and note that lim f x 3 For each value of e use a graphing utility x 0 to find all values of 8 0 such that f x 3 whenever 0 x 0 8 Sketch graphs illustrating your work a 1 b e 0 5

Consider the function f x 2x 9x This function has an absolute minimum value equal to and an absolute maximum value equal to 108 8 6 7 4

Sketch a triangle that has acute angle tan 6 O Find the other five trigonometric ratios of 8 2 13 sin 8 cos 8 3 13 13 csc 8 2 5 x V 13 VS IN

Sketch a triangle that has acute angle 8 cot 8 2 O cos 6 tan 6 5 2 2 Find the other five trigonometric ratios of 8 sin 0 2 8 VS 2 2 2 5 s B 5

Use the Law of Cosines to determine the indicated angle 0 Assume a 69 01 b 36 67 and c 42 55 Round your answer to two decimal places 0 b A C B

Find a parabola with equation y ax bx c that has slope 14 at x 1 slope 18 at x 1 and passes through the point 2 37 y 9x 4x 9 Need Help X Read It the sewer

Find a cubic function y ax bx2 cx d whose graph has horizontal tangents at the points 2 4 and 2 2 y 3 3 X 10 T 9 4 x 1