Vector Calculus Questions and Answers

Question 4 Perform the indicated operation simplify Express the answer as a complex number 62 5 Question Help Video 5314

Express 1 49 as a complex number 1 49

9 The graph of a piecewise function f shown in the xy plane for 8 x 8 Write the equation for f a 10 8 6 4 2 N 141 12 10 8 6 4 2 0 J 2 4 2 4 6 8 10 X

8 Let f x x 3 7 3x 15 x 2 x 2 x 2 Which of the following is true about f A f 2 1 B The graph of f x has an open circle at 2 3 C f 6 is undefined D f x has three distinct outputs at x 2

2 13x 25 x2 x The graph of f can be drawn with an open circle at 3 k Find the value of k x 3 3 x Let f x

5 Walgreens has the following pricing for 4x6 photo prints Quantity of 1 74 costs 0 37 each Quantity of 75 costs 0 25 each a Write a piecewise function C p that gives the cost of purchasing p prints b Patty ordered 70 prints then realized she was still short and ordered 10 more the next day Ho much did this mistake cost her Explain

2 The cost C in dollars of shipping a package that weighs w pounds can be modeled by the piecewise function given by 11 C w 0 w 2 2w 10 9 1 49w 6 1 99w w 10 a How much does it cost to ship a package that weighs 1 5 pounds b How much does it cost to ship a package that weighs 5 pounds c How much more does it cost to ship a package that weighs 10 pounds than a package that weighs

e prime factorization is se ascending order

6 66 Points DETAILS SCALCET8 4 7 021 Find the point on the line y 5x 2 that is closest to the origin x y

Car s speed km h 80 60 40 20 0 2 4 5 6 7 8 Distance from home km 12 A school vending machine sells cartons of milk and juice On a typical day No cartons are sold between 7 A M and 8 A M or from 5 P M onward The machine has a capacity of 100 cartons At 7 A M it is three quarters full From 8 A M to 10 A M 10 15 A M to noon and from 1 P M to 3 P M the students are in class The machine is filled at 11 A M and at 4 P M Sketch a graph of the number of cartons in the vending machine as a function of time Explain what each section of the graph represents

Write an equation of a circle with diameter AB A 3 3 B 17 17 Choose the correct answer below OA x 10 y 10 98 OC x 10 y 10 98 O E x 10 y 10 3 O G x 10 y 10 98 OB x 10 y 10 OD x 10 y 10 OF x 3 y 3 17 OH x 17 y 17

Find the value of x x 0 X X 3

Find all solutions of the equation in the interval 0 2m algebraically Use the table feature of a graphing utility to check your answer numerically Enter your answers as a comma separated list 3 sin x 2 sin x

Find the area of the shaded region Use 3 14 m 26 m r 13 m 26 m

Find the value of x 2 X Do not include the degree symbol in your answer Round to the nearest degree as need

The level curves of the surface z x y are circles in the xy plane centered at the origin Without computing the gradient what is the direction of the gradient at 1 3 and 2 1 determined up to a scalar multiple Determine the direction of the gradient at 1 3 Choose the correct answer below OA 3 1 OC 1 3 O E 1 3 Determine the direction of the gradient at 2 1 Choose the correct answer below OA 2 1 OC 1 2 OE 1 2 CCC OB 1 3 OD 3 1 OF 3 1 OB 1 2 O D 2 1 OF 2 1

The level curves of the surface z x y are circles in the xy plane centered at the origin Without computing the gradient what is the direction of the gradient at 5 4 and 1 3 determined up to a scalar multiple Determine the direction of the gradient at 5 4 Choose the correct answer below OA 5 4 OC 4 5 OE 4 5 Determine the direction of the gradient at 1 3 Choose the correct answer below OA 3 1 OC 1 3 OE 3 1 ACCES O B 5 4 OD 5 4 OF 4 5 OB 1 3 OD 1 3 OF 3 1

The campus of a college has plans to construct a rectangular parking lot on land bordered on one side by a highway There are 680 ft of fencing available to fence the other three sides Let x represent the length of each of the two parallel sides of fencing a Express the length of the remaining side to be fenced in terms of x b What are the restrictions on x c Determine a function A that represents the area of the parking lot in terms of x d Determine the values of x that will give an area between 20 000 and 40 000 ft e What dimensions will give a maximum area and what will this area be c The area of the parking lot in terms of x is A x x 680 2x Type an expression using x as the variable d For what values of x is the area between 20 000 and 40 000 O A for x between 32 52 ft and 75 66 ft or 259 34 ft and 307 48 ft B for x between 32 52 ft and 80 66 ft or 259 34 ft and 307 48 ft C for x between 32 52 ft and 75 66 ft or 264 34 ft and 307 48 ft D for x between 32 52 ft and 80 66 ft or 264 34 ft and 307 48 ft e The area is maximum when the width is feet and the length is Type whole numbers H feet

Solve the multiple angle equation Enter your answers as a comma separated list Let n be any integer sin 7x X 3 2

Beginning 145 miles directly south of the city of Hartville a car travels due west If the car is travelling at a speed of 42 miles per hour determine the rate of change of the distance between Hartville and the car when the car has been travelling for 55 miles Do not include units in your answer and round to the nearest hundredth Provide your answer below

1 Evaluate In e 2 Solve for x e 100 In 4 In 20 2 e0 025t

5 A table of selected values is given for a one to one function g At z 5 g has a vertical asymptote x g x 5 undefined 2 14 0 11 1 0 3 6 a What is the y intercept of g 9 b Write the equation for the horizo

QUESTION 9 3pts Consider f x 1 x 3 a USE Only The Definition of the DERIVATIVE to find f 1 b Find the equation of the tangent line to the graph of f at the point 1 f 1

The radius r of a sphere is expanding at a rate of 11 metres per minute Determine the rate at which the volume is changing with respect to time when r 6m The volume is changing at a rate of m min

The 15 tenure track professors in a university math department are paid an average of 90 000 per year while the 10 adjunct professors are paid an average of 60 000 per year What is the average salary among all these math professors

The graph of the function f x is displayed below Click on a point to see its coordinates a Find the value of f 12 10 b Find the value of f 11 10 0 10 10

A flush in the card game of poker occurs if a player gets five cards that are all the same suit clubs diamonds hearts or spades Complete parts a through c to obtain the probability of being dealt a flush in five cards a Initially concentrate on one suit say diamonds There are 13 diamonds in a deck Compute P five diamonds P first card is diamonds and second card is diamonds and third card is diamonds and fourth card is diamonds and fifth card is diamonds In a standard 52 card deck P five diamonds Round to six decimal places as needed b A flush can occur if a player receives five clubs or five diamonds or five hearts or five spades Compute P five clubs or five diamonds or five hearts or five spades Note that the events are mutually exclusive In a standard 52 card deck P five clubs or five diamonds or five hearts or five spades Round to three decimal places as needed c A royal flush in the game of poker occurs if the player gets the cards Ten Jack Queen King and Ace all in the same suit Use the procedure given in parts a and b to compute the probability of being dealt a royal flush In a standard 52 card deck P royal flush night decimal places as needed

Using a rock wall as one side and fencing for the other three sides a rectangular patio will be constructed Given that there are 172 feet of fencing available determine the dimensions that would create the patio of maximum area and identify the maximum area Enter only the maximum area Do not include units in your answer

Question If you want to produce an open top box from a 16 in by 22 in flat piece of cardboard what is the maximum possible volume in in of the box Round your answer to the nearest whole number and omit units Provide your answer below

4 Carry out a simulation experiment using a statistical computer package or other software to study the sam pling distribution of when the population distribution is Weibull with a 2 and 3 5 as in Example 5 20 Consider the four sample sizes n 5 10 20 and 30 and in each case use 1000 replications For which of these sample sizes does the X sampling distribution appear to be approximately normal

ell T 1 2 Statement ZU ZV TW LUV ZTWU ZTWV TW TW SATUW ATVW W Complete the proof that ATUWATVW V Reason Given Given Additive Property of Angle Measure Additive Property of Angle Measure Additive Property of Length All right angles are congruent Angles forming a linear pair sum to 180 Definition of angle bisector Definition of equilateral triangle

2 12 pts Solve the inequality Show your work sign analysis 5 7 X 3 X 4

Verify that each x value is a solution of the equation 3 csc x 12 csc x 0 a X TU 6 3 csc 7 12 csc b x 5r 6 sc 7 6 0 3 csc 5 12 csc 5 6 6 R 48 48

If 4x 4x xy 3 and y 3 15 find y 3 by implicit differentiation

Drum Tight Containers is designing an open top square based rectangular box that will have a volume of 62 5 in What dimensions will minimize surface area What is the minimum surface area

K 1 x 49 16x O 07 u 00 OA OB O C D 4 4

2x 4 OA 0 OB Oc 4 O D

1 2 1 50 0 25

If 1 x 1 y 1 and y 4 find y 4 by implicit differentiation

Use the graph shown to find the following a The domain and range of the function b The intercepts if any c Horizontal asymptotes if any d Vertical asymptotes if any e Oblique asymptotes if any A The function has two horizontal asymptotes The top asymptote is Type equations GLICE C Find the nozomial asymptotes I were are any Select the confect choice below and if necessary we answer boxes to complete your choice A The function has one vertical asymptote Type an equation and the bottom asymptote is Q B The function has one horizontal asymptote y 3 Type an equation C The function has no horizontal asymptotes d Find the vertical asymptotes if there are any Select the correct choice below and if necessary fill in the answer box es to complete your choice OB The function has two vertical asymptotes The leftmost asymptote is and the rightmost asymptote is Type equations OC The function has no vertical asymptotes

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to two decimal places where appropria cos 8 0 24 0 rad List six specific solutions 8 rad

1 Points DETAILS Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLU sin 0 2 cos 8 1 0 0

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION cos 8 cos 8 6 0 8

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION sin 8 2 cos 8 1 0 0

K 1 For the function F x 5 a graph the rational function using transformations b use the final graph to find the domain and range and c use the final graph to list any vertical horizontal or oblie X asymptotes ya moyvi vincunucuon VJU LU supru un www OC The range of the given function is yly is a real number y Type an integer or a simplified fraction OD The range of the given function is the set of all real numbers c What is are the vertical asymptote s Select the correct choice below and if necessary fill in the answer box es to complete your choice A The left vertical asymptote is The right vertical asymptote is Type equations Use integers or fractions for any numbers in the equations B There is one vertical asymptote It is x 0 Type an equation Use integers or fractions for any numbers in the equation Points 0 5 of 1 OC There is no vertical asymptote What is are the horizontal asymptote s Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The top horizontal asymptote is The bottom horizontal asymptote is Type equations Use integers or fractions for any numbers in the equations OB There is one horizontal asymptote It is Type an equation Use integers or fractions for any numbers in the equation OC There is no horizontal asymptote

8 Let g x 2x 6 a Find g b Use compositions to verify that g and g are in fact inve

1 Three teams of scientists measured the time it takes a certain beam of particles to travel a given distance Here are their results reported in milliseconds ms in random order 9 11 5 Team A Team B Team C Team A Team B 15 Team C 3 17 5 11 5 10 Which team has the lowest standard deviation 9 11 15 All teams have the same standard deviation 15 9

4 7 16 The solution set is Simplify your answer Type an integer or a fraction KEK

Determine whether the function is one to one If so a write an equation for the inverse function in the form y f x b graph f and on the same axes and c give the domain and the range of f and f If the function is not one to one say so The Uncon IS TRUL U 10 01 b Choose the correct graph for f and below The graph of f is shown in solid blue The graph of f is shown in dashed red OA Q L B OA The domain of fis Q c Give the domain and range of f and r Begin by finding the domain and range of f x Select the correct choice below and if necessary fill in any answer boxes to complete your choice and the range of fis Type your answers in interval notation B The function is not one to one D The function f x is not one to one

Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f Enter your answers as a comma separated list If an answer does not exist enter DNE T f x sin x 0 x absolute maximum value absolute minimum value local maximum value s local minimum value s Need Help Read It Du