Vector Calculus Questions and Answers

Find the a amplitude b penod c phase shift if any d vertical translation if any and e range of the following function Then graph the function over at least one period y cos a The amplitude is Simplify your answer b The period is Simplify your answer Type an exact answer using x as needed Use integers or fractions for any numbers in the expression SCODE c Select the correct choice below and if necessary fill in the answer box to complete your choice OA The phase shift is Type an exact answer using as needed Use integers or fractions for any numbers in the expression OB There is no phase shift d Select the correct choice below and it necessary fill in the answer box to complete your choice OA The vertical translation is unit s down Type an integer or a simplified fraction OB The vertical translation is unit s up Type an integer or a simplified fraction OC There is no vertical translation 48 G Find the a amplitude b period c phase shift if any d vertical translation if any and e range of the following function Then graph the function over at least one period y cos 0 e The range is Type your answer in interval notation Select all the transformations that are needed to graph the given function using y cos x A Reflect the graph across the x axis 1 c Stretch the graph vertically by a factor of E Translate the graph units to the left G Translate the graph units down OL Translate the graph units up Use the graphing tool to graph the function Click to enlarge graph GOLES B Stretch the graph horizontally by a factor of 2 D Translate the graph units to the right X F Reflect the graph across the y axis H Shrink the graph vertically by a factor of J Shrink the graph horizontally by a factor of 2

Suppose that in a memory experiment the rate of memorizing is given by M t 0 006t 0 3t where M t is the memory rate in words per minute How many words are memorized in the first 11 minutes words Round your answer to the nearest whole word

6 10 Find parametric equations and symmetric equations for the line 6 The line through the points 1 0 2 4 4 6 and 2 6 1 2 03 7 The line through the points 0 2 1 and 2 1 3 8 The line through 2 1 0 and perpendicular to both i j and j k 9 The line through 1 1 1 and parallel to the line x 2 y z 3

17 20 Determine whether the lines L and L are parallel skew or intersecting If they intersect find the point of intersection 17 L x 3 2t y 4 t z 1 3t L x 1 4s y 3 2s z 4 5s z 1 3t 18 L x 5 12t y 3 9t L x 3 8s y 6s z 7 2s 19 L y 3 1 z x 2 1 2 x 3 y 4 z 2

3 a Find symmetric equations for the line that passes through the point 1 5 6 and is parallel to the vector 1 2 3 b Find the points in which the required line in part a intersects the coordinate planes

How many inflection points are there f x There is are i x inflection poi

Suppose F 2 9 F 7 10 and F x f x Also suppose G 2 0 G 7 6 and G x g x 2 4f x 9g x dx

stimate the areas under the curve by computing the left Riemann sum Lg

250 mL sample of nitrogen N has a pressure of 745 mm Ig at 30 C Part A What is the mass of nitrogen VAXO

ntainer is filled with 0 77 mole of O2 at 30 C and 845 Hg What is the volume in milliliters of the container Express your answer using two significant figures C

Suppose you buy a home and finance 275 000 at 2 263 17 per month for 30 years What is the amount of interest paid Round your answer to the nearest cent

1 12 5 Points DETAILS SCALCETS 4 9 505 XP MI Find the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative f x x 3 5x 3 F x Submit Answer 2 12 5 Points Find the antiderivative F off that satisfies the given condition Check your answer by comparing the graphs of fand F DETAILS SCALCET8 4 9 023

I 74 lim X 2x 2x e x In x 1

Find the absolute extrema of the function f t te 9t Enter your answers as a comma separated list If an answer does not exist enter DNE

Powers of trigonometric functions are rewritten to be useful in calculus Verify the identity Simplify your answers completely 9 sin x 9 cos x 9 18 cos x 18 cos x 9 sin x 9 cos x 9 sin x E 9 1 cos x 1 cos x 918 cos x 18 cos x cos4 x

Verify that each x value is a solution of the equation 9 sec x 180 a x 9 3 sec 7 T b 9 18 5TT 3 sec 5 1 0 18 I 18 18

Verify the identity Simplify your answer completely 2 sec y cos y 2 2 2 sec y cos y cos y 2

Use the values to evaluate if possible all six trigonometric functions If an answer is undefined enter UNDEFINED 24 csc x 5 cos x sin x B tan x csc x sec x cot x 5

Complete the table by solving the parallelogram shown in the figure The lengths of the diagonals are given by c and d Round your answer to two decimal places b d 64 43 Nood Helen b C 0

Use Heron s Area Formula to find the area of the triangle Round your answer to two decimal places a 13 b 16 c 8

To approximate the length of a marsh a surveyor walks x 430 meters from point A to point B Then the surveyor turns 75 and walks 220 meters to point C see figure Approximate the length AC the marsh Round your answer to one decimal place m 220 m 75

A triangular parcel of ground has sides of length 750 feet 635 feet and 585 feet Find the measure of the largest angle Round your answer to one decimal place

In the triangle below x 8 Use the Law of Cosines to solve the triangle Round your answers to two decimal places A 8 C 12 cm B 18 cm x cm C

SHORT ANSWER Show all work for full credit 23 Find the total distance traveled by a particle on the x axis with velocity given by v x 3sin 2x for the interval 0 2 5 23

Write an equation of the slant or nonlinear asymptote 20x 19x 23x 4 4x 7x 1 p x The Choose one asymptote is y 010

Use the figure to find the exact value of each trigonometric function a sin b cos 7 sec 1 csc 2 X X X x x 9 2 sin cos x 24 0 7

To get a flat uniform cylindrical satellite spinning at the correct rate engineers fire four tangential rockets as shown in the figure Figure 1 Suppose that the satellite has a mass of 1200 kg and a radius of 3 0 m and that the rockets each add a mass of 250 kg Figure R 1 of 1 End view of cylindrical satellite Part A What is the steady force required of each rocket if the satellite is to reach 3 rpm in 4 5 min starting from rest Express your answer to two significant figures and include the appropriate units F A Value Submit Request Answer Provide Feedback Units Nex

Find a function f such that f x f x 2x3 and the line 2x y 0 is tangent to the graph of f

A car braked with a constant deceleration of 40 ft s2 producing skid marks measuring 80 ft before coming to a stop How fast ft s was the car traveling when the brakes were first applied ft s

What is the maximum vertical distance between the line y x 2 and the parabola y x for 1 x 2

If 30 000 cm of material is available to make a box with a square base and an open top find the largest possible volume in cm of the box cm

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm If the area of printed material the poster is fixed at 1 536 cm2 find the dimensions in cm of the poster with the smallest area width cm 121

Find the area of the largest rectangle that can be inscribed in the ellipse 1

Find the dimensions of a rectangle in m with perimeter 76 m whose area is as large as possible Enter the dimensions as a comma separated list m

Find the value of each variable b b 9 2 and d 45 C a d b c Simplify your answers Type exact answers using radicals as needed 30

Suppose the charge q on a capacitor is given by q 2 95 C e t 0 220 s a Find the value of q when t 0 0380 s C b Find the value of t when q 1 12 C

Condense the left hand side into a single logarithm Then solve the resulting equation for A log x log y 3 log z log 4 A 1 help formulas

Given nonzero vectors u v and w use dot product and cross product notation as appropriate to describe the following a The vector projection of u onto v b A vector orthogonal to u and v c A vector orthogonal to u xv and w d The volume of the parallelepiped determined by u v and w e A vector orthogonal to u xv and uxw f A vector of length u in the direction of v OB O D Vou V V U V V V vou u u u u b If k is any constant which of the following describes a vector orthogonal to u and v OA ku v V OB kuxv OC kluxv

Find the volume of the parallelepiped box determined by u v and v u 2i j Simplify vo V for 4i j 2k The volume of the parallelepiped is 4 units cubed W i 2k

Sketch the coordinate axes and then include the vectors u v and u xv as vectors starting from the origin u 9i v 8j Which of the following graphs contains u v and u xv O A O C X uxv z u z uxy O B O D uxv X x Z u z y y uxv

Given nonzero vectors u v and w use dot product and cross product notation as appropriate to describe the following a The vector projection of u onto v b A vector orthogonal to u and v c A vector orthogonal to u xv and w d The volume of the parallelepiped determined by u v and w e A vector orthogonal to u xv and uxw f A vector of length u in the direction of v a Which of the following describes the vector projection of u onto v O A OB O C U V u u V u V V V V

pv 11 nv 0 234 a Identify the individual variable random variable X and the random variable in the context of this problem The individual is a randomly selected college student The variable information collected from each individual is the percentage of 234 randomly selected college students that are left handed X The wording in context for the random variable X is as follows rv X the number of 234 randomly selected college students that are left handed The wording in context for the random variable is as follows rv p the percentage of 234 randomly selected college students that are left handed b Can we say that the sampling distribution of p is approximately normal A Yes Because np 25 74 o which is v n 1 P 208 25 x which is v B008 0 11 10 O 10 OB 8 c What is the probability that no more than 9 of the randomly selected college students are left handed Round final answer to 4 decimal places

Consider the following function If an answer does not exist enter DNE 7 x a Find the vertical asymptote s Enter your answers as a comma separated list x 0 f x 1 5 X Find the horizontal asymptote s Enter your answers as a comma separated list y 1 b Find the interval s of increase Enter your answer using interval notation Find the interval s of decrease Enter your answer using interval notation c Find the local maximum and minimum values local maximum value local minimum value d Find the interval s on which f is concave up Enter your answer using interval notation Find the interval s on which f is concave down Enter your answer using interval notation Find the inflection point x y e Use the information from parts a d to sketch the graph of f y y

Find the length of the following curve 2t 7 3 2 3 X y 3t 0sts2 The length of the curve is Simplify your answer

3 2 3 O O 6 7 8 q The graph above shows the velocity of an object as a function of time Time is measured in seconds velocity in meters per second If the object s initial location is 0 meters where is it at t 8s h 8 m If the object s initial location is 2 meters where is it at t 8s h 8 m

Next question Evaluate the integral below by interpreting it in terms of areas in the figure The areas of the labeled regions are A1 7 A2 3 A3 1 and A4 1 V f f x da V 55 5 X Get a similar question Question Help Video Add Work You can retry this question below 0 A1 y f x 3 A2 LO 5 A3 7 A4 figure is NOT to scale 10

Consider the function f x 7 defined on 7 7 a Compute the left Riemann sum L10 L1o help numbers b Compute the right Riemann sum R10 R10 help numbers c Compute the average value of L10 and R10 Average value he help numbers d Compute the area under the graph of f Area help numbers e Compare the two values found in c and d The average value is the area

Consider the function f x 100 x 10 defined on 0 10 a Compute the left Riemann sum L6 L6 help numbers b Compute the right Riemann sum R6 R6 help numbers c Compare the two values found in a and b The left Riemann sum is the right Riemann sum

The floor of a rectangular bedroom requires 288 ft of carpeting Molding is placed around the base of the floor except at two 3 ft doorways If 62 ft of molding is required around the base of the floor determine the dimensions of the floor 3 ft The floor is ft hy 3 ft ft

a 5 13 b 12 13 c 5 12 sin 8 cos 8 tan 0 d cos 20 e tan 20 5 0 12