Vector Calculus Questions and Answers

K Determine whether the graph represents a function domain and range GE Is the given graph the graph of a function Ves

Determine whether the set of vectors in P2 is linearly independent or linearly dependent S 2x 2 5x x 4 6x x O linearly independent O linearly dependent

2 Express the following vector expression as a single endthint vector 2 A vec P P vec T X vec T 3 Vectors and a b are unit vectors The angle between and b is 53 degrees Find the magnitude of the vector 3a 4b to one decimal place You do not have to include a seale diagram with your solution Any sketch that helps you arrive at your solution is fine 3

Which of the following is equal to P 0 1 0 1 O 2 3 O 0 1 2 4 1 0 1 4

Recall that when S denotes the n interval approximation for I a f x dx from Simpson s Rule one has whenever L f 4 x on a b Determine the number of intervals n for which S approximates the exact value n with IS 1 x 10 Give the smallest even integer n that works according to the error formula I Sn I L b a 5 180 n4 6e Be dx

Researchers are conducting a survey about what brand of ice cream shoppers prefer They survey the tenth person who walks into the store and then every fifth person after that This type of sampling is called O random sampling O stratified sampling O systematic random sampling O cluster sampling

In 2011 a country s federal receipts money taken in totaled 2 01 trillion In 2013 total federal receipts were 2 75 trillion Assume that the growth of federal receipts F can be modeled by an exponential function and use 2011 as the base year t 0 a Find the growth rate k to six decimal places and write the exponential function F t for total receipts in trillions of dollars b Estimate total federal receipts in 2015 c When will total federal receipts be 10 trillion a Find the growth rate k k Do not round until the final answer Then round to six decimal places as needed

Estimate the volume of material in a cylindrical shell with length 30 in radius 7 in and shell thickness 0 3 in The estimated volume of material in the shell is Simplify your answer Type an exact answer using x as needed Use integers or decimals for any numbers in the expression 7 in 30 in

A quadratic function f is given f x 1 6x a Express fin standard form f x b Sketch a graph of f 15 10 5 15 10 10 y 15 5 10 y 15H 5 5 10 15 x 15 10 5 5 10 15 10 15 10 15 y y 5

Use the given information to find the quadrant in which 0 lies cos 0 and csc 0 0 OA Quadrant III OB Quadrant IV OC Quadrant II OD Quadrant I

K Assume that Tom s Tree and Landscape Service charges 200 for consultation fee plus 20 per hour for labor a Write a system of equations to represent the cost of the two lar b Graph both equations for 0 to 10 hours on the same axes c Use the graph to estimate the number of hours of landscaping

Find the equation of the tangent line to the curve x xy y x 2 at 1 1 ZX 9 24 1 0 x 2y dx 2x y 1 1 dy x 29 2X 3 dy J 3 M x x 9 1 x 1 41 9 12x5 4 x 2x y 1 x 2y 7 1 1 1 1 2 1

7 2 Length Area and Volum A barrel of oil has a height of 2 m and a Estimate the volume of the oil in th b Compute the actual volume of oil

D Graphs Use the equation y x 16 to answer a Determine whether the parabola wi The parabola will open upward The parabola will open downwa b Find the equation of the axis of sy The axis of symmetry is Type an equation

n PVOnline Honors Pre Calculus 2 Unit 2 Which of the following vectors describes Select one a 5 1 1

question Question 3 OC 1 2 and 2 O d 1 2 and 2 4 Find the angle between The angle is

Question 1 Not yet What is the unit ve Select one a 4 T

1 1 Graphs Draw the graph of the function and state the domain and ra y 13

Find the future value of a simple interest loan of 2 500 at 6 9 interest for 7 months S ive

What are the features of the function f x log x 4 graphed below 12 11 10 7 55351 12 11 10 9 8 7 6 5 4 3 2 1 1 y 2 3 4 5 6 7 8 9 10 11 12 The function f x is function with a 1 2 3 4 5 6 7 8 9 10 11 12 asymptote of The range of the function is and it is on its domain of behavior on the LEFT side is as the RIGHT side is as The end and the end behavior on

What are the features of the function f x 3 1 graphed below 12 11 10 9 8 7 6 5 4 3 1 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 789 7 y 8 9 10 11 12 The function f x is 1 2 3 4 5 6 7 8 9 10 11 12 function with a asymptote of The range of the function is and it is on its domain of behavior on the LEFT side is as the RIGHT side is as The end and the end behavior on

Factor the given polynomial 10x 3x 4

Fill in the blank Any set of ordered pairs is called a n Any set of ordered pairs is called a n dom ran rela

Evaluate grad at position 2 3 1 in the direction of unit vector d 1 whe 5x y z Enter your answer correct to 1 decimal place in the box provided

Simplify A B 3z y 3 2 18z6y 54 1 6x 2y 82 2 6 x 2y 2 C D 1 62 2y 6x z2

ck here to watch the video Ive the system of equations by th 2x 3y 6 5x 4y 8 e solution is x y mplify your answer Type an ord

The matrix defining the transformation is C4 1 2 1 R3 1 2 1 2 1 21 1 2 1 1 2 T x x y 2x y x 2y

ohamed Salad Attempt 1 153 90 Question 2 0 5 points Listen Determine the point on the line y 4x 8 that O 3 4 4 1 7 O 32 10 17

Graph the equation using the slope and y inte y x 2

2 4 4 2 22 definite integral that is provide a b and f x in the expression Given Rn express the limit as noo as Sos a 0 x b 1 x f x 4 2 4x 6 16x f x dx X

Graph the function by using the slop 6 f x x 2

Use the graph of y f x to answer the following y f x Part 1 of 9 3 N a Determine f 1 f 1 0 3 24 1 2 3 3

The function has two relative minima A relative minimum occurs at the point s 0 0 Part 1 2 Part 2 of 2 O The function has no relative maximum O The function has one relative maximum O The function has two relative maxima 0 0 Dando X

Use calculus to sketch the graph of the given function f x x 3x

44 Find to the nearest minute if sec 1 563 A 39 43 B 50 17 C 39 47 D 50 13

25 Given Given tane A 13 2250 25 B 1 2 2 C 8 1 20 25 13 5 12 and is in Quadrant IV find cote

15 Find the smallest positive angle coterminal with 160 Use degree measure A 200 B 560 C 20 D 380

Consider the following ordered data 255 778910 a Find the low Q median Q and high low 9 median 9 high b Find the interquartile range c Make a box and whisker plot

12 8 If sine and cose 0 find sec 0 13 A 13 6 B 13 12 C 13 C 12 D 13

2 Prove that the vectors u and v are orthogonal U 4 1 v 1 4

K Use the quadratic formula to x 6x 7 0

Graph the equation using the slope an 5x 3y 9 0

Question 5 2 points Let f t 70 0 8 a 1 point From t 0 to t 1 for f t the portion is percent is b 1 point From t x to t x 1 for f t the portion is percent is and percent change is and percent change is

O LINES AND FUNCTIONS Identifying functions from relations For each relation decide whether or not it is Domain chair Relation 1 Rand 5

The restaurant in the Space Needle in Seattle rotates at the rate of one revolution per hour Round your answers to two decimal places a Through how many radians does it turn in 70 minutes rad b How long does it take the restaurant to rotate through 8 radians min c How far does a person sitting by the window move in 70 minutes if the radius of the restaurant is 21 meters m Additional Materials

A nautical mile is a unit of distance frequently used in ocean navigation It is defined as the length of an arc s along a great circle on the earth when the subtending angle has measure 1 one minute 1 60 of one degree Assume the radius of the earth is 3 960 miles a Find the length of one nautical mile to the nearest 10 feet ft b A vessel which travels one nautical mile in one hour s time is said to have the speed of one knot this is the usual navigational measure of speed If a vessel is traveling 29 knots what is the speed in mph miles per hour Round your answer to two decimal places mph D c If a vessel is traveling 19 mph what is the speed in knots Round your answer to two decimal places knots

Find the exact value of each trigonometric function 1 tan e 60

5 points Find the vector in the direction of v 24 7 with length 4

Use the slope intercept form to graph the equation y

ions by g the Factor the trinomial 12r 2 11r 15