Vector Calculus Questions and Answers

Problem 8 1 point 1 0 y 37 180 4 150 135 120 210 225 240 0 1 90 270 0 1 60 73 300 45 7 30 315 330 7 360 0 11m 1 0 Remaining time 58 20 min Use the unit circle to find two values of between 0 and 27 where sin 0 1 Separate the values with a comma Give the exact angle in radians no decimal values Enter pi for 0 Problem 9 1 point Give exact answers no decimals If more than one answer separate them with a comma Enter pi for Consider the function y 2 sin x Where are the zeros of this function on the interval 02 13 preview answers

Find the average rate of change of the function f x 2x from 2 to 8 02 O 3 07 O 3 10

3 A common inhabitant of human intestines is the bacterium Escherichia coli A cell of this bacterium in a nutrient broth medium divides into two cells every 20 minutes The initial population of a culture is 40 cells Find an expression for the number of cells after t hours

Find all the first and second order partial derivatives for the following functions Check your answers using Maple a 2 x0 1 0 4 b c f x y z 4 x y 27 g w z y w 4 y 0 2

du x at u x 0 1 u 0 t 1 du Solve 2x 2x x 0 t 0 subject to the conditions

Crossing the Horizontal or Oblic

rom the image below calculate the Thigh angle Hip 6 02 2 06 Knee 7 43 1 02 Ankle 4 45 0 45 0 shank 0 thigh

Morales Corporation produces microwave ovens The following per unit cost information is available direct materials 41 direct labor 21 variable manufacturing overhead 14 fixed manufacturing overhead 53 variable selling and administrative expenses 14 and fixed selling and administrative expenses 26 Its desired ROI per unit is 20 Compute the markup percentage using variable cost pricing Round answer to 2 decimal places e g 10 50 Markup percentage 11 83

Factoring Trinomials a 1 Factor each completely b 2 8b 7

Recall that if the cost of producing x units is C x then the average cost function is C x C x X a table at an art fair The marginal cost the cost of producing one additional pair of earrings is 9 per pair c Find C 5 and interpret your answer C 5 49 Type an integer or decimal rounded to two decimal places as needed www C When making 5 pairs the average profit is S per pair D When making 5 pairs the average cost is 13 per pair An artist who makes handmade earrings has fixed costs of 200 for Interpret the above answer Select the correct choice below and fill in the answer box to complete your choice Type an integer or decimal rounded to two decimal places as needed OA When making pairs the average cost is 5 per pair B When making 5 pairs the net income is per pair 4

To investigate a community s reading habits a newspaper conducts a poll from a table near the exit of a history museum What is the sampling method Select Does the sampling method have any bias Select Select No the sampling method has no bias because part of the population equally represents the entire population Yes because the location is at a history museum the sample may overrepresent the number of readers in the commun Yes because the location is at a history museum the sample may underrepresent the number of readers in the commu Yes because the poll is leading It suggests that a certain answer is wanted

Gabriella asked 5 of her hundreds of coworkers how much storage space they were currently using on their computer Here are their responses in gigabytes

Solve the equation Use n as an integer constant Enter your answers as a comma separated list 2 sin x 1 0 x No Response

Find the exact values of sin 2u cos 2u and tan 2u using the double angle formulas 24 cos u 25 sin 2u cos zu tan 2u F 2 U

Use the values to evaluate if possible all six trigonometric functions If an answer is undefined enter UNDEFINED 3 tan x 3 CSC x 2 sin x No Response cos x No Response sec x No Response cot x No Response

Step 2 of 2 Find the domain and ra Answer How to enter your answer opens in

hod of factoring should first be used 10s 2 t 3 3s 2

Find the maximum or minimum value of the function f x 2x 12x 5 X 47 Is this a maximum or minimum value maximum value minimum value

A telephone pole shown at the top of the next column is 60 feet tall A guy wire 80 feet long is attached from the ground to the top of the pole Find the angle between the wire and the pole to the nearest degree The angle between the wire and the pole is approximately degrees 80 ft 60 ft

What is 720 converted to radians 0 O 00 X 4s

1 Graph the solution set of the inequality where 3x 24

the most accurate results Read each question 2x 2 10x 12

Please solve the following equation 2 2 x 2 7 3 6

Consider the function and the point x y x x y 4y 9 P 1 3 a Find the unit vectors that give the direction of steepest ascent and steepest descent at P b Find a vector that points in a direction of no change in the function at P a What is the unit vector in the direction of steepest ascent at P Type exact answers using radicals as needed

When making a statistical inference about the mean of a normally distributed population based on a sample drawn from that population which of the following statements is correct all else being equal The 68 confidence interval is wider than the 90 confidence interval O The 90 confidence interval is narrower than the 95 confidence interval The 90 confidence interval is wider than the 99 confidence interval The 99 confidence interval is narrower than the 68 confidence interval

A simple random sample of size n is drawn from a normally distributed population and the mean of the sample is x while the standard deviation is s What is the 99 confidence interval for the population mean Use the table below help you answer the question Confidence Level OX z score 0 90 s OX n 0 99 s In 1 645 s n 2 58 s OX 90 1 645 95 1 96 99 2 58

According to a poll 56 of voters support funding a new community center A surveyor randomly selects 75 vot and asks each voter if he or she is in favor of the center If being in favor of the center is a success what is the probability of a success for this binomial experiment 0 34 O 0 44 O 0 56 O 0 75

Find the do the box bel Domain of

arctan x 2 x x Please enter a complete math problem so we can solve it abc x 3 V f x e log In 7 sin cos tan cot 8 4 5 9 6 lim dx o X 1 X X

An engineer is designing a pipeline which is supposed to connect two points P and S The engineer decide to do it in three sections The first section runs from point P to point Q and costs 50 a mile to lay the second section runs from point Q to point R and costs 48 mile the third runs from point R to point S ane costs 44 a mile Looking at the diagram below you see that if you know the lengths marked x and y ther you know the positions of Q and R Find the values of x and y which minimize the cost of the pipeline P 2 Miles X y 1 Mile R 10 miles miles miles S

r2x x 5 10 pts Find a critical point of the function F x 0 Does F have a local maximum or a minimum value at this critical point COS 178 1 dt

Solve the equation for solutions in the interval 0 2x by first solving for the trigonometric functic cotx 1 3 cotx 1 0

1 point Solve the system 1 2 23 8 F1 1 x X2 23 23 24 4 2 2

A randomized study compared the effectiveness of two different flea collars for dogs The dogs in the treatment group using Flea Collar A had a mean of 2 8 fleas The dogs in the treatment group using Flea Collar B had a mean of 3 3 fleas To determine if the results are significant the data are rerandomized and the differences of the means are shown in the dot plot What is the best conclusion to make based on the data The difference of the means is significant because the rerandomizations show that it is within the range of what could happen by chance The difference of the means is not significant because the rerandomizations show that it is outside the range of what could happen by chance The difference of the means is significant because O the rerandomizations show that it is outside the range of what could happen by chance The difference of the means is not significant because the rerandomizations show that it is within the range of what could happen by chance 2 Difference of Means

and any relative maxima or mini f x 8 x

42 Use the half angle formulas to find the exact values tan 67 30 OA 1 2 OB 1 2 O C 1 2 D 1 2

ou can not receive nor give help for this test This test is open book and notes no other help is allowed D Question 11 let f x 5x2 3x 2 find f 1 O none of these answers 6 10

Set up the system of equations and then solve it by using inverse matrices Ace Trucking Company has an order for three products A B and C for delivery The table gives the volume in cubic feet the w Unit volume cu ft Weight lb Value Product A 24 40 1 500 Product B 20 30 1 800 units units units Product C 40 60 2 000 a If each truck can carry 8 600 cu ft and 13 300 lb and is insured for 564 000 how many units of each product can be carr Product A units Product B units Product C units b If the insured value increases by 64 000 find the new delivery scheme Product A Product B Product C

Show that if a b is close to 1 1 then there exists a couple x y R such that left begin array y e x y a x e x y b end array right

Consider the solution of the differential equation y 9y passing through y 0 1 A Sketch the slope field for this differential equation and sketch the solution passing through the point 0 1 B Use Euler s method with step size Ax 0 2 to fill in the following table x Y 0 0 2 1 2 8 0 4 7 84 0 6 21 952 0 8 61 466 t your estimated solution on your slope field Compare the solution and the slope field Is the estimated solution an over or under estimate for actual solution over estimate D Is y e 1 a solution to the given initial value problem Yes Select a blank to input an answer

The vector u is shown below y 80 Find the component form of u X

Part 4 of 91 d Determine the y intercept s Enter your answer as an ordered pair If there is more than one answer separate them with commas Select None in applicable y intercept s 0 0 Part 4 9 Part 5 of 9 e Sketch the function X OV 3

Consider the following data regarding students

For each of the following determine whether the equation defines y as a function of x X y 5x 3 0 y 5 4 x y 3x 4 Function O Function Function Function X Not a function Not a function Not a function Not a function S

Consider the parametric surface x 4 u 3 v quad y 3 u 5 v quad z 2 u 2 A normal vector to this surface at 4 3 2 can be given by a b 1 What is a b Hint you may need to rescale your normal vector to get it in the correct form above

Consider the given function h x 3 x 1 3 a Determine whether the graph of the parabola opens upward or downward b Identify the vertex c Determine the x intercept s d Determine the y intercept s e Sketch the function f Determine the axis of symmetry g Determine the minimum or maximum value of the function h Write the domain and range in interval notation Write your answers in exact form Part 0 9 Part 1 of 9 a Determine whether the graph of the parabola opens upward or downward The graph of the parabola opens Choose one

u 7 2 Find the direction angle of u Enter your answer as an angle in degrees between 0 and 360 rounded t nearest hundredth

Particles A and B are moving along a plane Their velocities are represented by vectors a and b respectively Which option best describes the meaning of the following statement

b Find AB if B is the midpoint of AC x 4 A B 5X

Find the differential dy of the given function y x 3x dy