Vector Calculus Questions and Answers

1 Consider the functions f x 5x 5 and g x 5 x 5 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other a What is f g x f g x X Simplify your answer Give any values of x that need to be excluded from f g x Select the correct choice below and fill in any answer boxes within your choice A x Use a comma to separate answers as needed B No values should be excluded from the domain b What is g f x

Find the distance along the surface of the earth between City A and City B if the two cities determine a central angle of 0 88 radian Assume that the earth is a sphere of radius 4000 miles mi

Use the following functions f x x 4 and g x x 2 to solve cach of the following 10 f x g x 8 f x 0 9 g x 0

Fuerza El ctrica 2 Determine la fuerza el ctrica experimentada por la carga q 1 00 C en el arreglo que se muestra en la figura si Q 2 00 C y a 0 250m Q a a a Q

2 Here is triangle ABC Triangle XYZ is similar to ABC with scale factor 7 A 5 C B 4 a Draw what triangle XYZ might look like b How do the angle measures of triangle XYZ compare to triangle ABC Explain

2 2 1 2 cos 230 1 2 Drag each of the values given above in the appropriate area below to match with an expression 2 tan 15 1 tan 215 2 3 2 sin 30 cos 30 3 3 4 cos R00 6 2 8 T 5 4 sin COS 3 2 tan sin 1 tan 5k 12 3 5x 12 2 8 R

Attempts Average 4 4 Taxes paid for a given income level Caroline is getting ready to do her taxes She is single and lives in Miami Caroline earned 250 000 in 2020 She reviews the following table which shows the IRS tax rates for a single taxpayer in 2020 On Annual Taxable Income Up to 9 875 From 9 875 to 40 125 From 40 125 to 85 525 From 85 525 to 163 300 From 163 300 to 207 500 From 207 500 to 518 400 The Tax Rate Is Percent 10 12 17 20 23 Caroline calculates that she owes approximately 30 Based on the IRS table Caroline calculates that her marginal tax rate is when her annual income is 250 000 in income taxes for 2020 Caroline then calculates that her average tax rate is approximately owes for 2020 based on the annual income level and the amount of taxes she After figuring out what she owes in taxes in 2020 Caroline decides to ask an accountant for tax advice The accountant claims that he has found a legal way to shelter 4 000 of taxable income from the federal government The maximum amount that Caroline is willing to pay to learn this strategy and reduce her taxable income by 4 000 is Sheltering some income means finding a legal way to avoid being charged income tax on that income For example someone who has 50 000 in Hint A

Use this definition with right endpoints to find an expression for the area under the graph of f as a limit Do not evaluate the lin 7x x lim 1x n i 1 f x 1 x 3

Write the first five terms of the geometric sequence 1 4 a1 a2 a3 a4 a5 a 5 r

Write an expression for the apparent nth term of the sequence Assume that n begins with 1 4 16 64 9 27 81 an 1 3

Complete the table so that sin 0 is expressed in terms of the functions given across the top sin 0 cos 0 tan 0 cot 0 sec 0 tan 0 1 tan 0 1 tan 0 sin 0 1 cos 0 1 cot 0 1 cot 0 1 cot 0 1 cot 1 cot 0 csc 0 1 csc 0

Use the Binomial Theorem to approximate the quantity accurate to three decimal places 2 007 10

in 4 0 n 2 anthmetic O geometric Find the common difference or ratio 1 2 Find the sum of the first 15 terms 67 5 Need Help Submit Answer rose neintel Read DETAILE DREBOUE ONEINERE LARD 783097 MY

Write in Polar form r cos 0 i sin 0 0 0 2 and round to 3 decimal places 17 4i T 0

Use summation notation to write the sum 1 9 3 1 27 6 X

shembull 4 A 2 3 B 4 Y Y X2 7 2 x7 M 2 4 5 7 X S x z zh Yz 2 7 N

Find the rational number representation of the repeating decimal 0 945

A 60 m long chain hangs vertically from a cylinder attached to a winch Assume there is no friction in the system and that the chain has a density of 6 kg m Use 9 8 m s for the acceleration due to gravity a How much work is required to wind the entire chain onto the cylinder using the winch b How much work is required to wind the chain onto the cylinder if a 40 kg block is attached to the end of the chain E a Set up the integral that gives the work required to wind the entire chain onto the cylinder using the winch Use increasing limits of integration SO dy Type exact answers

OA S OB TO Model the situation on a set of axes by placing the center of the base of the cone at the origin and the cone s axis along the positive y axis Set up the integral that gives the volume of the solid using the shell method Use nonnegative and increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers dy Volume of the solid formed when a hole of radius 1 is drilled symmetrically along the axis of a right circular cone of radius 6 and height 9 dx Points 0 of 1 CD of 26 points Save

Points 0 of 1 Select the correct choices that complete the sentence below A region R is revolved about the y axis The volume of the resulting solid could in principle be found by using the disk washer method and integrating with respect to shell method and integrating with respect to Save or using

Consider a triangle ABC like the one below Suppose that c 61 a 74 and C 38 The figure is not drawn to scale Solve the triangle Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth If no such triangle exists enter No solution If there is more than one solution use the button labeled or B b a A 48 3 B 93 7 b 98 9 or A 131 7 B 10 3 b 17 71 or X No solution

Remember that rectangular form is z a bi and that polar form is z r cos0 i sin 0 Take following number in polar form and convert it to rectangular form 10 cos 84 i sin 84 Round to the nearest hundredth The angle above provided is in degrees 2

if the set Eu viw in TR is linearly independent is Euth vtwintus also linearly independent autbut w 0 where a 6 0 d u h e v w f w a 0 d f u d e vt e f w 0

Find the sum of the finite arithmetic sequence 9 14 19 24 29 34 39 44 49 STEP 1 Find the number of terms n in the finite sequence n STEP 2 Find the values of the first and last terms of the sequence 81 an STEP 3 Use your results from Step 1 and Step 2 to fill in the Sum of a Finite Arithmetic Sequence Forme 1 2 Sn n a an 2 STEP 4 Compute the sum of the sequence Sn

A hardware store makes a profit of 25 000 during its first year The store owner sets a goal of increasing profits by 8000 each year for 5 years Assuming that this goal is met find the total profit during the first 6 years of business Need Help Read It

Find a formula for an for the arithmetic sequence 70 310 55 an a5

The first two terms of the arithmetic sequence are given Find the missing term Use the table feature of a graphing utility to verify your results a 6 3 19 ag

The figure below shows f x 2 S 4 24 2 3 23 LA te 4 GO O If F x f x and F 0 0 find F b for b 1 3 6 and 8 b 1 3 6 8 F b

4 Write an equation of a polynomial with a intercepts at x 6 x 2 and x 1 and a y intercept of 4

Calculate the following limits x 3 x 2 x 1 a limx 3x 2x 1 c limx 2x 5x 7 e limx 4x 3x 2x 3x 5 g limx sin 2x X 2x 5 x 1 3x 2 b limx d limx f limx 4x 2x 5 2x3 3x 1 5x 3x 2 3x 2x 1 2 x 1 h limx x 2

Determine whether the following functions to R are injective surjective c bijective a f x 2x 1 d k x x 2 g p x x b g x x 3 e m x x h q x x x 1 1 c h x x 1 x 1 i r x 3x 1 f n x

4 Find all the points where x5 x 5x x 8x 4 0 Hint T polynomal has exactly two solutions namely 2 and 1

x 4 x 1

Given f x 7 x and g x 6x find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 Type an exact answer using radicals as needed Simplify your answer

Given f x 5 x and g x 3x find the following expressions a fog 4 b gof 2 c fof 1 d gog 0

1 Determine whether the given functions are linear or nonlinear If it is linear determine the slope a x f x 1 5 0 2 1 2 4 3 1 S 7 b x g x 2 28 1 7 0 1 5 2 155

j x 5x 2x 8

For the following function find the Taylor series centered at 7 and then give the first 5 nonzero terms of the Taylor series and the open interval of convergence f x e8e f 2 20 71 0 f x 0 0 0 0 0 The open interval of convergence is Give your answer in interval notation

This question 1 point s possib A full time worker aged 25 invests 500 a month in a fund which has an average yearly return of 8 4 compounded monthly a The worker wants to estimate what they will have for retirement when they are 60 years old if the rate stays constant Assume monthly compounding b If the worker makes no further deposits and makes no withdrawals after age 60 how much will they have for retirement at age 71 a How much money will the worker have in their fund when they are 60 years old The worker will have in their fund when they are 60 years old Round to the nearest cent as needed b If the worker makes no further deposits and makes no withdrawals after age 60 how much will they have for retirement at age 71 The worker will have in their fund Round to the nearest cent as needed

A man deposits 17 000 at the beginning of each year for 16 years in an account paying 7 compounded annually He then puts the total amount on deposit in another account paying 9 compounded semiannually for another 14 years Find the final amount on deposit after the entire 30 year period He will have a final amount of after the entire 30 year period Simplify your answer Round to the nearest cent as needed C

Find the final amount in the following retirement account in which the rate of return on the account and the regular contribution change over time 212 per month invested at 4 compounded monthly for 3 years then 799 per month invested at 6 compounded monthly for 3 years What is the amount in the account after 6 years Round to the nearest dollar as needed

order to accumulate enough money for a down payment on a house a couple deposits 790 per month into an account paying 3 compounded monthly If payments are made at the end of ch period how much money will be in the account in 4 years That is the amount in the account after 4 years Round to the nearest rent as needed

Find the fourth partial sum and the sum of the infinite series 1 2 10 i 1 a the fourth partial sum b the sum of the infinite series

Use sigma notation to write the sum 4 4 5 2 5 3 i 1 4 5 1 4 5 15

Write an expression for the apparent nth term an of the sequence Assume that n begins with 1 6 7 8 9 10 3 7 11 15 19 an

eel cylinder with a volume of 20 0 L is filled with 60 0 g of gen gas at 29 C Part A What is the pressure in atmospheres of the N gas in the cylinder P VAEO 199224 atm

2 30 L container is filled with methane gas CH4 at a pressure 3000 mmHg and a temperature of 25 C How many grams of methane are in the container m VO A O 5 15 g You have already submitted this answer Enter a new answer

Then improve your estimate by using six rectangles R6 1 Sketch the curve and the approximating rectangles for R3 a Estimate the area under the graph of f x 3 4x from x 1 to x 2 using three rectangles and right endpoints R3 15 y 10 M 5 15 II 10 e 2 X 0 1 15 10 5 15 10 y y Ih S 1 2 x

5 6 pts Use the properties of logarithms to fully expand and simplify the expression 5 x 1 25 3 Z log5

a What frequency is received by a person watching an oncoming ambulance moving at 29 2 m s and emitting a steady 713 Hz sound from its iren The speed of sound on this day is 345 m s Hz b What frequency does she receive after the ambulance has passed Hz