Vector Calculus Questions and Answers

Use the Law of Sines to solve the triangle Let b 54 7 yd Round your answers for a and c to two decimal places C x X yd X yd am C 88 352 22 45 a

hips at an engineering firm As part of their work they get to assist in the planning of a brand new roller coaster For this assignment you help Jim and Michelle as they tackle the math behind some simple curves in the coaster s track Part A The first part of Jim and Michelle s roller coaster is a curved pattern that can be represented by a polynomial function 1 Michelle has a list of possible functions Pick one of the g x functions below and then describe to Michelle the key features of g x including the end behavior y intercept and zeros a g x x x 4x 4 Pick ONE b g x x 2x 9x 18 c g x x 3x 4x 12 d g x x3 2x 25x 50 Le g x x 7x x 7 2 Create a graph of the polynomial function you selected X6 from Question 1 Please label all intercepts and critical points art B he second part of the new coaster is a parabola 3 Jim needs help creating the second part of the coaster Create a unique parabola in the pattern f x ax bx c Describe the edirection of the parabola and determine the y intercept and zeroes Make sure this parabola will connect to the equation you selected in e Part A You may arrange the two functions in any order you choose as long as they connect and graph 4 The safety inspector notes that Jim also needs to plan for a vertical ladder through the center of the coaster s parabolic shape for access to the coaster to perform safety repairs Find the vertex and the equation for the axis of symmetry of the parabola showing your work so Jim can include it in his coaster plan PA My Drive Kneeskerm Roller Coaster Project pdf 5 Create a piecewise graph of the polynomial function you created in Question 1 and the quadratic equation from Question 4 You will need to restrict the domain on both your g x function in Part A and your f x function from Part B Please label all intercepts critical points domain restrictions and the range for each piece of the graph Part C 6 Now that the curve pieces are determined use those pieces as sections of a complete coaster By hand or by using a drawing program sketch a design of Jim and Michelle s coaster that includes the shape of the g x and f x functions that you chose in the Parts A and B You do not have to include the coordinate plane in the drawing Be sure to label each section of the graph with the corresponding function for your instructor to view Part D 7 Create an ad campaign to promote Jim and Michelle s roller coaster It can be a 15 second advertisement for television or radio an interview for a magazine or news report or a song poem or slideshow presentation for a company These are just examples you are not limited to how you prepare your advertisement so be creative Make sure to include a script of what you will say if you are preparing an interview or a report The purpose of this ad is to get everyone excited about the roller coaster 8 On a half sheet of poster board build your presentation that would be used to win the award of getting your roller coaster built The poster board should include a The first polynomial equation and graph g x with its key characteristics explained and labeled b The second quadratic equation and graph f x with its key motni I

Refer to the functions f and g and evaluate the function for the given value of x Select Undefined If applicable f 4 2 1 1 3 3 3 1 2 1 and g 0 3 5 8 1 1 4 6 g f 3 is Undefined

Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive L lim Van Enter inf for o 11 700 is A convergent B divergent C The Root Test is inconclusive n 6n

Given f x 2x 1 if x 0 find f 3 06 07 01 O 10 O x 2x x 1ifx 0

A given function has 3 complex zeros Two of the zeros are 3 and 2 4i What is the missing zero O 2 4i O 3 O 2 4i O 2 4i

Question 10 If 6000 dollars is invested in a bank account at an interest rate of 7 per cent per year Find the amount in the bank after 6 years if interest is compounded annually Find the amount in the bank after 6 years if interest is compounded quarterly Find the amount in the bank after 6 years if interest is compounded monthly Finally find the amount in the bank after 6 years if interest is compounded continuously Question Help Video Message instructor

R G B K Match each equation with a graph above 3 1 43 3 0 8 4 1 22 3 1 22 3 0 68 a red R b blue B c green G d orange 0 e black K Question Help Video Message instructor Submit Question

Question 9 Given that a cubic function has the zeros 4 and 8 4i what is the missing zero

X Find the real zeros of the given function Round to one decimal place as needed 4 x 2x Solution 1 Solution 2

Homework Find the slope for each line 22 2x y 14 23 3x 2y 51 24 13 20x 5y

Consider a w N weight suspended by two wires as shown in the accompanying figure If the magnitude of vector F2 is 150 N find w and the magnitude of vector F N 42 F What is the weight w W N Type an integer or decimal rounded to three decimal places as needed W 31 F2

cosh x ex e x 2 a Sketch the graphs of the functions y e and y y 3 y cosh x 2 y BES 3 2 1 y 2 2 3 2 1 cosh x y 2 1 2 3 y 3 y cosh x 2 y 2 ex on the same axes and use graphical addition see Section 2 7 to sketch the graph of y cosh x y 3 y cosh x 2 b Use the definition to show that cosh x cosh x e x 1 2 3 X X 3 y 2 y 2 2 1 3 2 1 18 y 1 1 3 y cosh x 2 2 2 2 3 1 2 3 X X

The function f x 3 is an exponential function with base Need Help Read It f 2 f 0 f 2 and f 6

0 B 22 Match each equation with a graph above 2 2 2 G R Question Help Video a red R b orange 0 c green G d blue B

Solve the trigonometric equation in the interval 0 27 Give the exact value if possible otherwise round your answer to two decimal places Enter your answers as comma separated list 2 cos 0 17 cos 0 8 0 0

TU Make the indicated trigonometric substitution in the given algebraic expression and simplify Assume 0 t 2 tan t O cos t 01 O sin t X 1 x X sin t

Simplify the following trigonometric expression as much as possible sec y tan y csc y csc y tan y sin y sec y

Let A x represent the area bounded by the graph the horizontal axis and the vertical lines at t 0 and t x for the graph below Evaluate A x for x 1 2 3 and 4 5 4 3 2 1 A 1 A 2 A 3 A 4 2 Question Help Video Add Work 3 4 5

3 2 f x x 4x 4x

The pie chart to the right shows how adults rate their financial shape Suppose 18 people are chosen at random from a group of 500 What is the probability that none of the 18 people would rate their financial shape as fair Make the assumption that the 500 people are represented by the pie chart The probability that none of the 18 people would rate their financial shape as fair is Round to six decimal places as needed Excellent 4 Good 42 Fair 38 Poor 14 Other 2

Find the equation of the slant asymptote of the rational function 2x 10x2 7x 24 f x 2x 5 The equation of the slant asymptote is y

Find the horizontal asymptote of f x y 4x 3x 5 5c3 c2 3

Suppose 30 of the people in your town talk on their cell phones and drive at the same time If you stood on a busy street corner and watched 50 people drive by about what proportion would you expect to see talking on their cell phones Choose the correct answer below OA 0 30 OB 50 O C 15 OD Not enough information is given to answer the question Submit quiz CLOS

among circular functions to find cos 1 22 7 50 2 1 0 2x 3x 3 49 2 4 4 NO MIN 0 AY 0 1 3x Ne KI3 wa 0 1 MI4 5x 4 7x 8 KIO 11x 3 F 1 0 X Q COS 3 Type an integer a exact answer usin

the trigonometric function at the indicated real number s or state that the expression is undefined 11x 6 sec 42 42 1 0 7x 4 2 2 2 0 1 2x 3 3x 42 2 5x 4 6 6 5x 4x 3 K 2 73 5x 3 74 4 x 6 0 11x 1 0 3x 2 0 1 9 2 4 x y 1 7x 6 4 60 fill in the answer box to comple O A 11x 6 Simplify your answer radicals Use integers C numbers in the express B The expression is under sec

S 2 Select the correct choice below and if necessary fill in the answer box to complete your c 7x 2 B The function is undefined OA sin Type an integer or a fraction

Suppose the average yearly salary of an individual whose final degree is a master s is 55 thousand less than twice that of an individual whose final degree is a bachelor s Combined two people with each of these educational attainments earn 116 thousand Find the aw yearly salary of an individual with each of these final degrees GED The average yearly salary for an individual whose final degree is a bachelor s is thousand and the average yearly salary for an individual whose final degree is a master s is thousand

ert the following degree measure to radians 90 radians Simplify your answer Type an exact answer using z

The angle 120 corresponds to 0 of a complete rotation Type an integer or a simplified fraction

The angle is Simplify your answer Type an integer or a simplified fraction 9 B

Determine the surface area of the solid obtained by rotating the following parametric curve about the x axis x cos 0 y sin 0 0 0 2

roblem 1 A box with an open top is to be constructed from a square piece of cardboard 4 ft wide by cutting out a square from each of the four corners and bending up the sides Find the largest volume that such a box can have

Determine the surface area of the solid obtained by rotating the following parametric curve about the x axis x cos 0 y sin 0 0 0

Consider the function Rewrite f in the form b a T a 1 bx 2 What are a a and b f x Find T4 a the fourth degree Taylor polynomial for f centered at 0 4 5 202

Find the range of the function f x 3 sin 3x 1 5 x Orange 8 2 Correct Answer range 8 2 range 9 2 range 8 2 range 2 8 range 2 9

71 72 The acceleration function in m s and the initial velocity are given for a particle moving along a line Find a the velocity at time t and b the distance traveled during the given time interval 71 a t t 4 v 0 5 0 t 10

Problemy 1 Use left or right Riemann sums with 4 rectangles to estimate the following areas 1 f x x from 0 2

Find the equation of the line segment between Po 3 1 4 and P 0 5 2

Solve the inequality Enter your answer using interval notation 1 7 1 X X 6 VI

For the exponential function f x 6 5 1 find f 6 f 6 24300000

9 3 Problem 4 1 point Use the limit comparison test to determine whether diverges an lim n 00 bn a Choose a series n 19 your answer as a fully simplified fraction For n 19 72 19 lim 1 400 an lim 100 tr bn with terms of the form b an 71 19 8n 2n 19 2 3n4 converges or 1 and apply the limit comparison test Write np b Evaluate the limit in the previous part Enter o as infinity and o as infinity If the limit does not exist enter DNE Note You can earn 40 partial credit for 2 3 correct answers c By the limit comparison test does the series converge diverge or is the test inconclusive Choose

Follow the steps for graphing a rational function to graph the function P x X X 0 x 6 x 6 B P x cannot be factored further A P x Type your answer in factored form Do not simplify X X 6 36 What is the domain of P x Select the correct choice below and if necessary fill in the answer box to complete your choice OA xx B xlx C x x 6 6 Type an integer or a simplified fraction Use a comma to separate answers as needed OD The domain is the set of all real numbers Type an integer or a simplified fraction Type an integer or a simplified fraction OA P x Simplify your answer OB P x is already in lowest terms Write P x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice

low the steps for graphing a rational function to graph the function R x x 2x 63 x 4x 21 X

24 25 Find the magnitude of the resultant force and the angle it makes with the positive x axis 24 YA 0 45 30 20 lb 16 lb X 25 till hirido su 300 N YA 0 1 200 N 60 XOX

2 8 points Using transformations sketch the graph of y f x 1 3 labeling all points Plea place your final answer to the right the other graphs below are for intermediate one if needed FINAL ANSWER 4 0 2 4 3 y f x 0 0 4 0 1 2 3 4 5 2 2 12345 3

9 Determine whether the points lie on a straight line a A 2 4 2 B 3 7 2 C 1 3 3

Minutes Cost 400 525 600 It takes you 4 seconds to climb up a 4 foot ladder that you are using to do a job You walt a seconds before climbing back down the ladder at the same rate Let x represent time and y represent height A Graph the function that models this problem B Write the piecewise function that represents the graph c Identify your domain and range 5 Height feet

You are walking from home to the grocery store which is 2 miles away Twenty minutes later and halfway to the store you realize that you forgot to bring money so you turn around return home and then walk back to the store Distance miles A Draw a graph that models your distance from home over time Assume that you are walking the same speed the entire trip B Your friend calls you 70 minutes after you began your trip and asks you how far away from home you are 2 0 La

an You ride a bus that travels a total distance of 8 miles from the first bus stop to the last bus stop It takes the bus 4 minutes to travel 2 miles between each stop The bus walts 2 minutes at each stop There are 4 stops altogether Distance miles A Draw a graph that models the bus s distance over time beginning when the bus starts to wait a the first stop B How long does it take you to arrive at the last bus stop 10