Vectors Questions and Answers

The measure of an angle in standard position is given Find two positive angles and two negative angles that are coterminal with the given angle Enter your answers as a comma separated list T 6 rad

Solve the given differential equation by finding as in Example 4 from Section 2 4 an appropriate integrating factor 8xy dx 4y 12x dy 0

a Find parametric equations for the tangent line to the curve x t e y t 2e t z t 0 at t 0 b Find the unit tangent vector at t 0 T 0 r 0 0

A polynomial function h x with integer coefficients has a leading coefficient of 5 and a constant term of 6 According to the Rational Root Theorem which of the following are possible roots of h x 1 6 6 5 1 5 Submit

Kim claims that the solutions to the equation x 2 are rational numbers Which of the following is true about Kim s claim A It is correct because there are two solutions to the equation B It is correct because if a number squared is rational the number is also rational c It is NOT correct because there is no number a such that the square of x is 2 It is NOT correct because x 2 or x 2 and both 2 and 2 are

How many times do the graphs of y 3 sin x and y 3 sin3x intersect for x in the interval 10 20121 A 1920 B 1921 Without using tables evaluate A cos 36 cos 72 B cos 36 x cos 72 C 1922 D 1923 E 1924

2 Find a unit vector in the direction of the given vector V 1 1

Read the excerpt on Jean Jacques Rousseau then answer the following question Jean Jacques Rousseau was one of the most influential thinkers of the Enlightenment A writer of amazing breadth and depth his works of social and political theory as well as musical criticism novels and even a successful opera continue to be relevant His ideas inspired the architects of the American and French revolutions and encouraged the rise of Romanticism In 1755 Rousseau published a controversial essay entitled Discours sur l origine de l in galit Discourse on the Origin of Inequality The work expanded on the themes of his earlier Discourse In it Rousseau argued that humans had originally existed in a state of nature that was morally superior to that of the contemporary world Rousseau s dim view of human progress met sharp criticism from many sources most notably from the French philosophe Voltaire In the wake of their public disagreement the two philosophers became implacable enemies Rousseau soon fell out with a number of other prominent intellectuals of the day including his friend Diderot In The Social Contract Rousseau argues that civil liberties are natural rights of all human beings The work begins with the famous sentence Man was born free but he is everywhere in chains The philosopher insists that the sovereignty of a community does not lie in the divine right of kings but in the interests of the people as expressed in what he calls the general will In 1755 Rousseau published the Discourse on the Origin of Inequality in which he said that early humans had been better off in The Garden of Eden A monastic separation A Medieval ignorance

Population in the R888220 10 1910 Population of Town A Each Decade from 1910 to 2000 1920 1930 1940 1950 B 1960 Year 1970 1980 16 centimeter 1990 According to the figure shown above the population f Town A in 1970 was what fraction of the opulation of Town A in 2000 2000 en block is in the shape of the right circular shown above If the volume of the wooden 547 cubic centimeters what is the diameter of of the cylinder in centimeters Questions 37 and 38 refer to the following information w w 2a0 w w at 1 at time angular position 2 angular position angular velocity time angular velocity 0 w t A carousel is rotating at an angular velocity of 90 degrees per second The instant a particular point on the carousel reaches angular position 0 0 the carousel operator flips a switch causing the carousel at a constant angular acceleration to slow down and eventually change direction The equations above describe the constant acceleration motion of the carousel where w represents the initial angular velocity w is the angular velocity as it travels is the angular position of the particular point on the carousel t is the time since the switch was flipped and a is the constant angular acceleration 12 6 s 37 To the nearest degree at what angular position will the carousel change direction 38 To the nearest second how long will it take the carousel to come to a complete stop before it ch direction

Dependent Events Three cards are drawn sequentially from a shuffled deck without replacement What is the approximate probability all three drawn cards have NUMBERS on them 41 3 69 2 32 3 33 2 47 201 RE 922 24 ET TEST THIT THE THE

Quest Independent Events What is the probability of rolling a single die to the number 5 and simultaneously flipping a penny to heads 12

A telephone survey was conducted in order to determine if people in City C are more likely to work 9 to 5 office jobs than other jobs The research team called 5 000 random people between 12 P M and 4 P M on a Thursday Of the 5 000 people called 3 000 did not answer and 250 refused to participate Which of the following was the biggest flaw in the design of the survey A The time the survey was taken B Population size C Sample size The fact that the survey was done by telephono

thousands of dollars 100 90 80 70 50 40 30 20 10 Annual Profits 0 2000 2001 2002 2003 2004 2005 2006 2007 The line graph above shows the annual profit of particular clothing store from 2000 to 2007 ccording to the graph what was the greatest change n absolute value in the annual profit between two nsecutive years 25 000 30 000 35 000 40 000

9 p figure In the triangle above the cosine of p is 0 8 What is the sine of q

Find a plane containing the line lx t 5 4ty t 6 5t z t 6 t and orthogonal to the plane 4x 7y 6z 4

O B A C X D B 6 Which additional fact proves that ARST and AWJK are similar A The measure of ZJ is 40 B The measure of ZJ is 95 C The measure of ZK is 40 D The measure of ZK is 95 A R 10 X 1 point Given AABC ADEC find the value of x and y 40 C type your answer S 28 45 W y 40 T D 21 K y type your answer E

1 Give a geometric description of the span Justify your response a Span 2 2 b Span an 1 4 3 5 e Span H 8 d Span 3 4 0 2 5 3

165 33 A B Figure 4 sing Figure 4 above what is the measure of Arc CA

2 45 125 What is the measure of angle

Which of the following is equivalent to the line x t 1 1 1 1 1 2 3 A 2x y 1 OB x t 1 1 4 3 O C x t 1 1 1 3 4 OD 2 1 x 2 3 0 OE 3 4 1 1 0

30 Directions Factor out the GCF Greatest Common Factor then simplify the polyne 142 42 62 GCF Factored Form

Question 5 1 point Given MDB 79 and FE 590 determine the measure of the angle ZBCD You may assume that point A is the center of the circle OC 690 39 5 70 m dru 108 5 79 D 59 4 Figure may not be drawn to scale

Find the value of x G R 9x 6 143 9 65 6 132 14 10 F F H

1 point Select the statement that is the converse of the following statement If Alan eats peanuts then he will break out in hives If Alan doesn t break out in hives then he hasn t eaten peanuts If Alan doesn t eat peanuts then he won t break out in hives If Alan eats peanuts then he won t break out in hives If Alan breaks out in hives then he has eaten peanuts

For the following three problems let I 5 points Show that I and J are orthogonal unit vectors your 22 upload

Graph the following function y Step 2 of 2 Determine how the general shape of the graph chosen in the previous step would be shifted stretched and reflected for the given function Graph the results on the axes provided Answer x Axis Reflection Reflect graph across x axis Shift Graph Vertically O Up Down None Shift Graph Horizontally Phase Shift Left Right None 3x Keypad Keyboard Shortcuts Enable Zoom Pan

1 A man in a boat is 3 km offshore and wishes to go to a point on the shore that is 5 km from his present position The man can walk at 4 km h and row at 2 km h How far should he walk and how far should he row so that he can reach his destination in the shortest possible time Recall Time Distance speed

Given the magnitude and direction angle of a and b a sketch a graph showing u b and r b find the resultant vector F as a sum of two components c b find the resultant vector r as a magnitude and direction 21 If a 5 units at O 30 and b 9 units at 70

What is the m BDE J O O 313 86 94 47 E 47 B D

If a function f is periodic with period p then f t p Select for every t The trigonometric functions y sin x and y cos x are periodic with period Sketch a graph of y sin x on the interval 0 2 y 1 0 1 y 1 7 1 7 Sketch a graph of y cos x on the interval 0 2x y f x f 2x f p f t 2x 2x X y 1 1 y 1 y 1 R 27 2x X X and amplitude

Consider the differential equation x 2 y prime prime 5 x y prime 8 y 0 quad x 2 x 4 0 infty Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval The functions satisfy the differential equation and are linearly independent since W x x 0 for 0 x Form the general solution y

Which line intersects the parabola y x 2 6x 2 at two points

What is the equation of the line with a slope of 2 and a y intercept of 5 Oy 2x 5 Ov 5x 2 2 Ov x Or G

and the inverse transformation for the transformation given by x xcos60 ysin60 y xsin60 ycos60

4 y 3 1 18 2 Ay 16 2 14 12 10 8

7 Demonstrate using diagrams 4 marks a that vector addition is commutative ie a b b b that vector addition is associative ie a b c a a b c

For the vectors u 1 2 and v 4 1 express u as the sum u p n where p is parallel to v and n is orthogonal to v u p n 0 0 Type integers or simplified fractions List the terms in the same order as they appear in the original list

Find the perimeter of the figure below Notice that one side length is not given Assume that all intersecting sides meet at right angles Be sure to include the correct unit in your answer 14 ft 4 ft 9 ft St 6 A

Questions 37 and 38 refer to the following information A CD account contains 5 400 today The account earns an annual interest of 7 for each of the next four years The bank uses the equation A 5 400 r to determine the amount of money in the account A after y years if no other deposits or withdrawals are made 37 What numerical value should the bank use for r To the nearest dollar how much money will be in the CD account at the end of the four years Note Disregard the sign when gridding your answer

The deben an ancient Egyptian unit of weight is approximately equal to 3 21 ounces It is also equivalent to 12 smaller Egyptian units called shematies Based on these relationships 488 shematies is equal to how many pounds to the nearest 2016 1 pound hundredth 16 ounces ces 1 po

Find the length of the diagonal of a 7cmx6cmx12cm rectangular prism Round to the nearest tenth O 9 8 cm 14 1 cm O 15 1 cm 13 7 cm

2 Suppose three distinct points 2 i 2 in z plane maps onto 1 i 1 in w plane i Construct the bilinear transformation that maps these points ii Find the fixed points of the transformation

Cassandra is hanging crystal stars from the gym ceiling using string for the homecoming dance She wants the ends of the strings where the stars will be attached to be 7 feet from the floor Use the diagram to determine how long she should make the strings 10 x 2

The figure below shows two concurrent force vectors of magnitudes 400 lb and 600 lb a Express each force as a Cartesian force vector b Compute the direction cosine angles of each force vector three angles per vector in degrees c Find the resultant force expressed as a Cartesian force vector d Compute the magnitude and the direction cosine angles of the resultant force vector you found in the previous part 400 lb 40 43 600 lb 33 35 I

In the figure below mz1 52 Find m 2 1 2 m 2 O 0 X

Deductible Monthly Premium Individual Plan 1 Plan 2 0 00 1 000 00 87 32 11 77 Individual Spouse 890 00 735 00 Individual Child 750 00 606 00 Individual Family 1 600 00 1 400 00 In which plan would you end up spending more out of pocket money for an emergency room visit A Plan 1 since it requires higher monthly premium payments B Plan 2 because it has lower monthly premiums C Plan 1 since it has 0 deductible D Plan 2 because it has

Find the area bounded by the parabolas x 2 y and x 2 y 2

se the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about e y axis y 15e x y 0 x 0 X 1

points and Q and the Cartesian directions x y and z The point Q is located on the xy plane Select the answer that provides the position of the point P measured from point Q as a Cartesian vector X 111 8j 12k 11x 8y 12z 81 5j 12k 8x 5y 12z 31 131 3x 13y Z 13 P 5 8 12 Q 3 y

e numbers of domestic and international hts for three airlines for the year 2012 are en in the table Find the probability that a mestic flight is operated by Airline B Airline A B C Total Domestic Internation 517 971 120 976 729 987 96 611 527 769 135 211 1 775 727 352 798 probability that a domestic flight is operated by Airline B is und to four decimal places as needed