Vector Calculus Questions and Answers

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

Use the Law of Cosines to solve the triangle Round your answers to two decimal places A B C b 4 A O O O C C 8 a 7 B

Solve the right triangle shown in the figure for all unknown sides and angles Round your answers to two decimal places B 76 6 a 4 8 A C b C B a C O O b A

Find x the angle of depression from the top of a lighthouse that is 190 ft above water level to the waterline of a ship 935 ft off shore Round your answer to the nearest tenth of a degree x 935 U 190 0 X

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

To find the distance across a river a surveyor chooses points A and B which are x 350 ft apart on one side of the river see the figure She then chooses a reference point C on th opposite side of the river and finds that ZBAC 82 and ZABC 52 Approximate the distance from A to C Round your answer to the nearest foot X ft A x ft 82 52 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

Solve the right triangle shown in the figure for all unknown sides and angles Round your answers to two decimal places b 21 A B C C 20 a B O O O b A

Find the derivative of the function using the definition of derivative g t g t 7 t State the domain of the function Enter your answer using interval notation State the domain of its derivative Enter your answer using interval notation Need Help Read It Submit Answer

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

Find the exact values of the six trigonometric ratios of the angle 8 in the triangle sin 8 11 cos 8 tan 0 csc 8 sec 0 cot 0 120 123

Use the graphing tool at the right to create a scatter plot for the data in the table Use the shape of the scatter plot to determine if the data are best modeled by a linear function an exponential function a logarithmic function or a quadratic function X 0 7 10 17 24 Plot each point one at a time Using the graphing tool start by plotting 0 0 Use the graphing tool to plot 7 0 8 Use the graphing tool to plot 10 1 0 Use the graphing tool to plot 17 1 2 Use the graphing tool to plot 24 1 4 Is the data best modeled by a linear function an exponential function a logarithmic function or a quadratic function y 0 0 8 1 0 1 2 1 4 A logarithmic function B quadratic function OC exponential function OD linear function B 1 5 3 1 04 4 2 0 9 0 6 0 3 0 3 AY 0 6 0 Points 0 OT 1 3 6 B C a 12 15 18 21 24 27 oo N

Use the graphing tool at the right to create a scatter plot for the data in the table Use the shape of the scatter plot to determine if the data are best modeled by a linear function an exponential function a logarithmic function or a quadratic function X 0 1 2 3 4 y 4 NOTT 2 0 2 4 Plot each point one at a time Using the graphing tool start by plotting 0 4 10 8 6 10 B f h Ay b Q

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 equations of the tangent lines to the curve X 1 x 1 that are parallel to the line x 2y 5 Enter your answers as a comma separated list of equations y

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

Submit Answer 0 07 0 13 Points DETAILS PREVIOUS ANSWERS 7 SCALCET9 3 1 064 At what exact point on the curve y 7 2e 5x is the tangent line parallel to the line 5x

Question 20 Sketch a graph of f x 5 4 3 5 4 3 2 1 Clear All Draw 2 1 1 2 3 4 5 1 12 14 x 2 4 2 2 3 4 5 ANCY

Find an equation of the tangent line to the curve y x x that is parallel to the line y 3 9x y x 12x 12 X Enhanced Feedback Please try again Find the derivative of the function set it equal to the slope of the given line then solve for x This will give you the x coordinate of the point at which the tangent line is parallel to the find the tangent line Remember that the slopes of two parallel lines are equal and the slope of the line y f a f a x a is f a

Find equations of the tangent line and normal line to the curve at the given point y x 7e 0 7 7x 7 tangent line y normal line y 7 7 Enhanced Feedback Please try again The slope of the tangent line at a point is equal to the derivative of the function a ling and the normal line

1 If a b and care unit vectors then la bl2 lb cl2 lc al does not exceed A 4 B 9 C 8 D 6 2 If vectors a 2i k b i j k and c 4i 3j 7k If dx b cx band d a 0 then d will be A 1 Bj 2k B i 8j 2k C 1 8j k D 1 8j 2k Here i j k are unit vectors in the x y and z axis

A country that is the major supplier of a certain commodity wishes to improve its balance of trade position by lowering the price of the commodity The demand function is q p a Compute E p b Will the country succeed in raising its revenue a E p Simplify your answer 4000 5

An electronic store can sell q 7 000 p 43 38 cellular phones at a price p dollars per phone The current price is 106 a Is demand elastic or inelastic at p 106 b If the price is lowered slightly will revenue increase or decrease a Is the demand elastic or inelastic at p 106 Type an integer or a decimal rounded to three decimal places as needed OA Inelastic because E p OB Elastic because E p OC Elastic because E p OD Inelastic because E p when p 106 which is greater than 1 when p 106 which is greater than 1 when p 106 which is less than 1 when p 106 which is less than 1

blem 8 Which of the below graphs is an example of a function that satisfies the following conditions g 0 1 g 1 1 g 2 0 g 3 1 g 4 0

A famous painting was sold in 1945 for 21 930 In 1993 the painting was sold for 29 5 million What rate of interest compounded continuously did this investment earn As an investment the painting earned an interest rate of Round to one decimal place as needed Points 0 of 1 SILB

1 Find AC A 118 24 22 B

2 Find AB A C 7 53 44 B

A hummingbird flies 382 m south then turns right and flies 146 m west What is the direction of the