Vector Calculus Questions and Answers

Consider the following 0 f x y z x 2yz xyz P 2 1 1 u a Find the gradient of f Vf x y z b Evaluate the gradient at the point P Vf 2 1 1 4 3 5 c Find the rate of change of f at P in the direction of the vector u

Solve the equation 6 cos 30 3 4 cos 30 4 for 0 an angle located in the first quadrant measured in degrees

Consider the function f x sin x 4 3 sin x 4 3 over the interval 0 2 Simplify the formula of this function and find its minimum value on this interval

Tina s Material Company hauls gravel to a construction site using a small truck and a large truck The carrying capacity and operating cost per load are given in the accompanying table Tina must deliver a minimum of 120 cubic yards per day to satisfy his contract with the builder The union contract with his drivers requires that the total number of loads per day is a minimum of 5 How many loads should be made in each truck per day to minimize the total cost Small Truck Large Truck 40 30 84 72 Capacity yd Cost per Load In order to minimize the total cost the number of loads in a small truck that should be made is and the number of loads in a large truck that should be made is 5

The curvature of a plane parametric curve x f t y g t is given by xy yx x y 2 K where dots indicate derivatives with respect to t Find the curvature of the following curve x 3et cos t y 3et sin t k t

6 Find the limits of the following sequences n 1 n n 1 n n 2n a lim b lim

9 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0 1 2 2 4 5 6 71 8 9 3 4 5 6 7 8 9 x Explain your reasoning and sketch a graph of the inverse f x Upload a sketch of your graph

somebody can i do not know that much about this new topic if please solve it and try to explaint to me how to get the answer i will appreciate it so much Not mandatory but will be helping lot thank you you Write clear and detailed solutions for each problem 1 a Plot the following points on the polar grid A 3 B 5 225 5m 0 Vno 210 3 41 3 1 2 118 0 me a b Convert the polar coordinates of points A and B to rectangular coordinates

Refer to the graph to complete the questions 5 4 3 2 1 5 4 3 2 11 2 3 4 5 Ty X 1 2 3 4 5 a Find f 2 b Find f 3 c What is the formula for the function when 2 d What is the formula for the function when 22

Find the sum Use the summation capabilities of a graphing utility to verify your result Step 1 6 Step 2 i 1 Use the following property of summation to find the sum 9i 8 Hence n n a b i 1 i 1 Write the sum using the above property 6 6 9i 8 i 1 i 1 n ka k i 1 Since 9 is a constant use the following property of summation to find the sum Using the above property 6 9i i 1 n II b bi i 1 i 1 3 29 E P8 i 1 i 1 i 1 2 9i 8 i 1 21 4 5 6 6 9i i 1

Thus the value of the sum 6 9i 8 i 1

What point represents failure strain for cortical bone Stress MPa 200 g 160 120 80 f 40 a 0 00 e Oi CORTICAL BONE DENSITY p 1 85 g cm 0 05 TRABECULAB BONE p 0 9 g cm p 0 3 g cm 0 10 None of the above Strain 0 15 1 1 0 20 1 P 0 25 O

in x x Which of the following shows the simplified function of csc x sin

Q1 Use Naive Gauss elimination to find the diagonal entries of upp triangular system Ux c for the given system A 3 7 10 B 3 8 12 3x10 1x2 0 2x3 0 1x 7x2 0 3x3 7 85 19 3 0 3x10 2x2 10x3 71 4 C 3 6 9 D 3 3 6 E 13 5 8 13 2 101

ite the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the ven point Let x be the independent variable and y be the dependent variable Vertex 1 3 point 1 9

Sketch the graph of the function Select Update Graph to see your response plotted on the screen Select the Submit button to grade your respons f x y 14 4x 5y y 0 0 X 3 5

Level curves isothermals are shown for the typical water temperature in C in Long Lake Minnesota as a function of depth and time of year Estimate the temperature in the lake on October 7 day 280 at a depth of 5 m and on September 17 day 260 at a depth of 10 m Depth m 0 5 10 15 12 16 120 day 280 and depth 5 m 20 160 8 20 16 240 280 200 Day of the year C

Determine the slope of the line shown in the graph 03 03 1 0 3 0 13 1 3 2 n s A 3 2 2 2 3 4

Let f x x 5 Click on the graph where the corresponding points are located for the X values of 0 1 4 and 9

Match each linear equation with its graph Equation y Y ANTEN Y y Y 1 4 K x 2 3x 2 St x 4 3 50 4 R B Q Graph Color a black K b red R c green G d blue B e purple P

Evaluate the integral 6 1 6 t t dt

b No calculators Using the Disc or Washer method only find the exact value of the volume of the solid obtained by rotating the region enclosed by y x and x y about y 1 a Sketch the two curves on the same graph and shade in the region between them Show calculations for intersection points X Sketch the 3D volume that results when you rotate the shaded area from part a about y 1 Draw a typical disc or washer on this 3D sketch

No calculators Using the Shell method only find the exact volume created by rotating the region bounded by y 12x x and y 32 about the the line x 4 No need to go through all the steps from Problem 5 you may go straight to the integral setup and evaluation

Question The function f x 2x 3x is Select WWW Question The function f x 7x 12x is Select 1 2 1 2

Find the total area of the shaded regions Ay 18 16 14 12 10 8 6 4 2 0 2 4 3 to 5 y ex 2 6 X

Construct Pivot Tables showing the counts of gender versus carrier and type versus usage in the accompanying cell phone survey data What could be concluded from this analysis Click the icon to view the cell phone survey data Type whole numbers Count of Carrier F M Grand Total AT T 1 7 8 Other Sprint Basic Camera Smart Grand Total What could be concluded from this analysis A T Mobile is the most preferred OB Verizon is the most preferred C AT T is the most preferred OD Sprint is the most preferred 2 2 4 0 2 2 T Mobile Verizon Grand Total 0 1 1 3 2 5 6 4 Construct Pivot Tables showing the counts of type versus usage in the cell phone survey data Type whole numbers Count of Signal Strength Average High Low Very high Grand Total 14 20 Cell Phone Survey Gender M M M F M M F F M M MMMMMLMFFMM Carrier AT T AT T AT T AT T Sprint Sprint Verizon Verizon T Mobile AT T AT T AT T Other Other Verizon AT T Other Other Verizon Verizon 5 4 Type Usage Signal Strength Smart High Smart High Smart Very high 3 Smart Very high 3 Smart Very high 3 Smart Very high 4 Smart Very high 4 Smart Average 3 Camera Very high 2 Camera Average 2 Camera Average 4 Camera Average 3 Camera Average 3 Camera Average 4 Camera Very high 4 Low 3 Basic Basic Low 4 2 3 4 Basic Basic Basic Average Low Average

Find the length of the curve r t 8i 2t j 3t k 0 t 1

Find the period and amplitude of the function 2 y 3 cos X 3 Give the exact values not decimal approximations Period Amplitude 7 2 X B

2 For the triangle shown below Given b 150mm a 200mm and B 45 find the angle C and the side c C A B b a C

For the robot link position shown below find the angle that the link makes with the x axis given that of the tip of the robot is at located at 9 64 11 49 Take the link length as 15 cm Motor joint Arm 0 X y End effector tip

or t 6 For the robot link position shown below find the angle that the link makes with the x axis given that of the tip of the robot is at 13 38 14 86 Also find the link lengt Arm 0 X y End effector tip

4 For the robot link position shown below find the position of the tip of the robot given the arm link angle of 70 Take the link length as 10 cm Motor joint Arm 0 X Y End effector tip

Use the Ratio Test to determine whether the series is convergent or divergent O Identify lal O O 8 O 1 n 1 10 17 24 3 n 7n 3 30 7n 3 3 n 7n 3 3 n lim 318 3 n Submit Answer 10 17 24 Evaluate the following limit n 10 17 24 an Since lim n 25 n an 7n 3 7n 3 3 n 12 7n 3 Select Select the series is convergent the series is divergent the test is inconclusive

Determine whether the sequence is increasing decreasing or not monotonic an 2 n 3 O increasing decreasing O not monotonic Is the sequence bounded Obounded Onot bounded

Find the length of the curve X x 1 y Vt 1 dt 4 x 5

Find the exact length of the curve y 3x 2 0 x 1

Should averages be taken literally What are the drawbacks Has your understanding and perceptions of averages changed If so how Discussion Board 1 B After Watching and answering questions on MyLab Statistics discuss your understanding of Quartiles Variation Measure

Find the center foci and vertices of the ellipse Graph 36x 2 25y 2 288x 200y 76 0

Find the sum of the convergent series n 0 24

graph of an exponential function passes through 1 20 and 2 80 Find the exponential function that describes e graph holours

A circular swimming pool has a diameter of 20 ft the sides are 5 ft high and the depth of the water is 4 ft How much weighs 62 5 lb ft Round your answer to the nearest integer 384845 X ft lb

Consider the functions y x and y x 8 a Sketch the graph of the pair of functions using a standard window b Describe the transformation used to obtain the graph of the second function from the first function a Use the graphing tool to graph the functions Click to enlarge graph 20 16 20 16 8 8 12 16 20

Find the particular solution for the equation dy dx 8x 9x 5x y 0 when x 1

Find the producers surplus if the supply function for pork bellies is given by the following S q q5 2 4q3 2 53 Assume supply and demand are in equilibrium at q 25 The producers surplus is Type an integer or decimal rounded to the nearest hundredth as needed

Estimate the error in using the indicated partial sum S to approximate the sum of the series Give your final answer in scientific notation with three decimal places 00 50 k 1 44 R50 S 10 12

A variable force of 6x 2 pounds moves an object along a straight line when it is x feet from the origin Calculate the work done in ft lb in moving the object from x 1 ft to x 11 ft Round your answer to two decimal places ft lb

Suppose the vector valued function r t f t g t h t is smooth on an interval containing the point to The line tangent to r t at t to is the line parallel to the tangent vector r to that pas hrough f to g to h to For the following function find an equation of the line tangent to the curve at t to Choose an orientation for the line that is the same as the direction of r r t 5t 1 8t 4 to 1 Choose the correct answer below OA 2 8t 4 5t 1 12t OB 4 5t 12 8t 1 2t OC 1 8t 4 2t 12 5t OD 4 2t 12 5t 1 8t

Hydrostatic Force A water trough 15 ft long has ends shaped like inverted isosceles triangles with base 4 ft and height 4 ft The triangular ends are built to withstand a force of 204 70 lb Assume that the trough is filled with freshwater having a weight density of 62 41b ft What is the maximum height to which the trough can be filled without exceeding the structural limitations of the triangular sides

Find the tangential and normal components of the acceleration vector r t 2eti 2 2tj 2e k ar an 2 2

Reparametrize the curve with respect to arc length measured from the point where t 0 in the direction of increasing t Enter your answer in terms of s r t 2ti 2 3t j 9 4t k r t s