Precalculus
11th Edition
ISBN: 9780135189405
Author: Michael Sullivan
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 9, Problem 28RE
To determine
To graph: The
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
a is done please show b
A homeware company has been approached to manufacture a cake tin in the shape
of a "ghost" from the Pac-Man video game to celebrate the 45th Anniversary of the
games launch. The base of the cake tin has a characteristic dimension / and is
illustrated in Figure 1 below, you should assume the top and bottom of the shape
can be represented by semi-circles. The vertical sides of the cake tin have a height of
h. As the company's resident mathematician, you need to find the values of r and h
that minimise the internal surface area of the cake tin given that the volume of the
tin is Vfixed-
2r
Figure 1 - Plan view of the "ghost" cake tin base.
(a) Show that the Volume (V) of the cake tin as a function of r and his
2(+1)²h
V = 2
15. Please solve this and show each and every step please. PLEASE no chatgpt can I have a real person solve it please!! I am stuck. I am doing pratice problems and I do not even know where to start with this. The question is Please compute the indicated functional value.
Chapter 9 Solutions
Precalculus
Ch. 9.1 - Plot the point whose rectangular coordinates are (...Ch. 9.1 - 2. The distance between two pointsand is
Ch. 9.1 - To complete the square of x 2 +6x , add ______ .Ch. 9.1 - 4. Draw the angle in standard position.
Ch. 9.1 - If P=(x,y) is a point on the terminal side of the...Ch. 9.1 - tan 1 ( 1 )= ______ .Ch. 9.1 - Prob. 7AYUCh. 9.1 - Prob. 8AYUCh. 9.1 - For the point with polar coordinates ( 1, 2 ) ,...Ch. 9.1 - The point ( 5, 6 ) can also be represented by...
Ch. 9.1 - True or False In the polar coordinates ( r, ) , r...Ch. 9.1 - True or False The polar coordinates of a point are...Ch. 9.1 - In Problems 11-18, match each point in polar...Ch. 9.1 - Prob. 14AYUCh. 9.1 - Prob. 15AYUCh. 9.1 - In Problems 11-18, match each point in polar...Ch. 9.1 - In Problems 11-18, match each point in polar...Ch. 9.1 - In Problems 11-18, match each point in polar...Ch. 9.1 - In Problems 11-18, match each point in polar...Ch. 9.1 - In Problems 11-18, match each point in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems plot each point given in polar...Ch. 9.1 - In Problems plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 19-32, plot each point given in polar...Ch. 9.1 - In Problems 33-40, plot each point given in polar...Ch. 9.1 - In Problems 33-40, plot each point given in polar...Ch. 9.1 - In Problems 33-40, plot each point given in polar...Ch. 9.1 - In Problems 33-40, plot each point given in polar...Ch. 9.1 - In Problems 33-40, plot each point given in polar...Ch. 9.1 - In Problems 33-40, plot each point given in polar...Ch. 9.1 - In Problems 33-40, plot each point given in polar...Ch. 9.1 - In Problems 33-40, plot each point given in polar...Ch. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - In Problems 4358, plot coordinates of a point...Ch. 9.1 - In Problems 4358, polar coordinates of a point are...Ch. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - Prob. 51AYUCh. 9.1 - Prob. 52AYUCh. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - Prob. 54AYUCh. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - In Problems 41-56, polar coordinates of a point...Ch. 9.1 - Prob. 58AYUCh. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems , the rectangular coordinates of a...Ch. 9.1 - In Problems 5970, the rectangular coordinates of a...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - In Problems 57-68, the rectangular coordinates of...Ch. 9.1 - Prob. 71AYUCh. 9.1 - In Problems 69-76, the letters xandy represent...Ch. 9.1 - In Problems 69-76, the letters xandy represent...Ch. 9.1 - In Problems 69-76, the letters xandy represent...Ch. 9.1 - Prob. 75AYUCh. 9.1 - Prob. 76AYUCh. 9.1 - In Problems 69-76, the letters xandy represent...Ch. 9.1 - In Problems 69-76, the letters xandy represent...Ch. 9.1 - In Problems 69-76, the letters rand represent...Ch. 9.1 - In Problems 69-76, the letters rand represent...Ch. 9.1 - In Problems 69-76, the letters rand represent...Ch. 9.1 - Prob. 82AYUCh. 9.1 - In Problems 69-76, the letters rand represent...Ch. 9.1 - In Problems 69-76, the letters rand represent...Ch. 9.1 - Prob. 85AYUCh. 9.1 - In Problems 69-76, the letters rand represent...Ch. 9.1 - Chicago ln Chicago, the road system is set up like...Ch. 9.1 - Prob. 88AYUCh. 9.1 - Prob. 89AYUCh. 9.1 - Prob. 90AYUCh. 9.1 - Prob. 91AYUCh. 9.1 - Prob. 92AYUCh. 9.1 - Is the street system in your town based on a...Ch. 9.1 - Prob. 94AYUCh. 9.1 - Prob. 95AYUCh. 9.1 - Prob. 96AYUCh. 9.1 - Prob. 97AYUCh. 9.1 - Prob. 98AYUCh. 9.1 - Prob. 99AYUCh. 9.1 - Problems 94103 are based on material learned...Ch. 9.1 - Prob. 101AYUCh. 9.1 - Prob. 102AYUCh. 9.1 - Prob. 103AYUCh. 9.2 - Prob. 1AYUCh. 9.2 - Prob. 2AYUCh. 9.2 - Prob. 3AYUCh. 9.2 - Prob. 4AYUCh. 9.2 - Prob. 5AYUCh. 9.2 - Prob. 6AYUCh. 9.2 - Prob. 7AYUCh. 9.2 - Prob. 8AYUCh. 9.2 - Prob. 9AYUCh. 9.2 - Prob. 10AYUCh. 9.2 - Rose curves are characterized by equations of the...Ch. 9.2 - True or False A cardioid passes through the pole.Ch. 9.2 - Prob. 13AYUCh. 9.2 - In polar coordinates, the points ( r, )and( r, )...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - In Problems 15-30, transform each polar equation...Ch. 9.2 - Prob. 31AYUCh. 9.2 - In problems 31-38, match each of the graphs ( A )...Ch. 9.2 - In problems 31-38, match each of the graphs ( A )...Ch. 9.2 - In problems 31-38, match each of the graphs ( A )...Ch. 9.2 - In problems 31-38, match each of the graphs ( A )...Ch. 9.2 - In problems 31-38, match each of the graphs ( A )...Ch. 9.2 - In problems 31-38, match each of the graphs ( A )...Ch. 9.2 - Prob. 38AYUCh. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - Prob. 52AYUCh. 9.2 - Prob. 53AYUCh. 9.2 - Prob. 54AYUCh. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - Prob. 56AYUCh. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - Prob. 58AYUCh. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - Prob. 60AYUCh. 9.2 - Prob. 61AYUCh. 9.2 - In Problems 39-62, identify and graph each polar...Ch. 9.2 - In problems 69-72, the polar equation for each...Ch. 9.2 - In problems 69-72, the polar equation for each...Ch. 9.2 - In problems 69-72, the polar equation for each...Ch. 9.2 - Prob. 66AYUCh. 9.2 - In Problems 63-68, graph each pair of polar...Ch. 9.2 - In Problems 63-68, graph each pair of polar...Ch. 9.2 - Prob. 69AYUCh. 9.2 - Prob. 70AYUCh. 9.2 - Prob. 71AYUCh. 9.2 - In Problems 63-68, graph each pair of polar...Ch. 9.2 - Prob. 73AYUCh. 9.2 - Prob. 74AYUCh. 9.2 - Prob. 75AYUCh. 9.2 - Prob. 76AYUCh. 9.2 - Prob. 77AYUCh. 9.2 - Prob. 78AYUCh. 9.2 - Prob. 79AYUCh. 9.2 - Prob. 80AYUCh. 9.2 - Prob. 81AYUCh. 9.2 - In Problems 73-82, graph each polar equation....Ch. 9.2 - Show that the graph of the equation rsin=a is a...Ch. 9.2 - Show that the graph of the equation rcos=a is a...Ch. 9.2 - Prob. 85AYUCh. 9.2 - Prob. 86AYUCh. 9.2 - Prob. 87AYUCh. 9.2 - Prob. 88AYUCh. 9.2 - Prob. 89AYUCh. 9.2 - Prob. 90AYUCh. 9.2 - Prob. 91AYUCh. 9.2 - Prob. 92AYUCh. 9.2 - Prob. 93AYUCh. 9.2 - Prob. 94AYUCh. 9.2 - Prob. 95AYUCh. 9.2 - Prob. 96AYUCh. 9.2 - Prob. 97AYUCh. 9.2 - Prob. 98AYUCh. 9.2 - Prob. 99AYUCh. 9.2 - Prob. 100AYUCh. 9.2 - Prob. 101AYUCh. 9.2 - Prob. 102AYUCh. 9.2 - Prob. 103AYUCh. 9.2 - Prob. 104AYUCh. 9.2 - Prob. 105AYUCh. 9.2 - Prob. 106AYUCh. 9.3 - The conjugate of 43i is _______. (p. A59)Ch. 9.3 - Prob. 2AYUCh. 9.3 - Prob. 3AYUCh. 9.3 - Prob. 4AYUCh. 9.3 - In the complex plane, the x-axis is referred to as...Ch. 9.3 - When a complex number z is written in the polar...Ch. 9.3 - Suppose z1=r1ei1 and z2=r2ei2 are two complex...Ch. 9.3 - True or False If is a complex number and is an...Ch. 9.3 - Every nonzero complex number will have exactly...Ch. 9.3 - True or False The polar form of a nonzero complex...Ch. 9.3 - If z=x+yi is a complex number, then | z | equals...Ch. 9.3 - If z 1 = r 1 ( cos 1 +isin 1 ) , and z 2 = r 2 (...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 13-24, plot each complex number in the...Ch. 9.3 - In Problems 25-34, write each complex number in...Ch. 9.3 - In Problems 25-34, write each complex number in...Ch. 9.3 - Prob. 27AYUCh. 9.3 - Prob. 28AYUCh. 9.3 - In Problems 25-34, write each complex number in...Ch. 9.3 - Prob. 30AYUCh. 9.3 - In Problems write each complex number in...Ch. 9.3 - Prob. 32AYUCh. 9.3 - Prob. 33AYUCh. 9.3 - Prob. 34AYUCh. 9.3 - Prob. 35AYUCh. 9.3 - Prob. 36AYUCh. 9.3 - Prob. 37AYUCh. 9.3 - In Problems 35-42, find zw and z w . Leave your...Ch. 9.3 - Prob. 39AYUCh. 9.3 - Prob. 40AYUCh. 9.3 - In Problems 35-42, find zw and z w . Leave your...Ch. 9.3 - Prob. 42AYUCh. 9.3 - In Problems 35-42, find zw and z w . Leave your...Ch. 9.3 - In Problems 35-42, find zw and z w . Leave your...Ch. 9.3 - In Problems 4556, write each expression in...Ch. 9.3 - In Problems 4556, write each expression in...Ch. 9.3 - In Problems write each expression in rectangular...Ch. 9.3 - In Problems write each expression in rectangular...Ch. 9.3 - In Problems write each expression in rectangular...Ch. 9.3 - In Problems 4556, write each expression in...Ch. 9.3 - In Problems 4556, write each expression in...Ch. 9.3 - Prob. 52AYUCh. 9.3 - In Problems 43-54, write each expression in the...Ch. 9.3 - In Problems 43-54, write each expression in the...Ch. 9.3 - In Problems 43-54, write each expression in the...Ch. 9.3 - In Problems 43-54, write each expression in the...Ch. 9.3 - In Problems 55-60, find all the complex roots....Ch. 9.3 - In Problems 55-60, find all the complex roots....Ch. 9.3 - In Problems 55-60, find all the complex roots....Ch. 9.3 - Prob. 60AYUCh. 9.3 - In Problems 55-60, find all the complex roots....Ch. 9.3 - Prob. 62AYUCh. 9.3 - Prob. 63AYUCh. 9.3 - Prob. 64AYUCh. 9.3 - Prob. 65AYUCh. 9.3 - Prob. 66AYUCh. 9.3 - Show that each complex n th root of a nonzero...Ch. 9.3 - Use the result of Problem 65 to draw the...Ch. 9.3 - Refer to Problem , Show that the complex roots of...Ch. 9.3 - Prob. 70AYUCh. 9.3 - Prob. 71AYUCh. 9.3 - Prob. 72AYUCh. 9.3 - Prove that De Moivres Theorem is true for all...Ch. 9.3 - Mandelbrot Sets (a) Consider the expression a n =...Ch. 9.3 - Prob. 75AYUCh. 9.3 - Prob. 76AYUCh. 9.3 - Prob. 77AYUCh. 9.3 - Prob. 78AYUCh. 9.3 - Prob. 79AYUCh. 9.3 - Prob. 80AYUCh. 9.3 - Problems 7786 are based on material learned...Ch. 9.3 - Prob. 82AYUCh. 9.3 - Prob. 83AYUCh. 9.3 - Prob. 84AYUCh. 9.3 - Prob. 85AYUCh. 9.3 - Prob. 86AYUCh. 9.4 - A ________ is a quantity that has both magnitude...Ch. 9.4 - If v is a vector, then v+( v )= ___.Ch. 9.4 - Prob. 3AYUCh. 9.4 - Prob. 4AYUCh. 9.4 - Prob. 5AYUCh. 9.4 - Prob. 6AYUCh. 9.4 - Prob. 7AYUCh. 9.4 - Prob. 8AYUCh. 9.4 - Prob. 9AYUCh. 9.4 - Prob. 10AYUCh. 9.4 - In Problems 11-18, use the vectors in the figure...Ch. 9.4 - In Problems 11-18, use the vectors in the figure...Ch. 9.4 - In Problems 11-18, use the vectors in the figure...Ch. 9.4 - In Problems 11-18, use the vectors in the figure...Ch. 9.4 - In Problems 11-18, use the vectors in the figure...Ch. 9.4 - In Problems 11-18, use the vectors in the figure...Ch. 9.4 - In Problems 11-18, use the vectors in the figure...Ch. 9.4 - In Problems 11-18, use the vectors in the figure...Ch. 9.4 - In Problems 19-26, use the figure at the right....Ch. 9.4 - In Problems 19-26, use the figure at the right....Ch. 9.4 - In Problems 19-26, use the figure at the right....Ch. 9.4 - In Problems 19-26, use the figure at the right....Ch. 9.4 - In Problems 19-26, use the figure at the right....Ch. 9.4 - In Problems 19-26, use the figure at the right....Ch. 9.4 - In Problems 19-26, use the figure at the right....Ch. 9.4 - In Problems 19-26, use the figure at the right....Ch. 9.4 - In Problems 29-36, the vector v has initial point...Ch. 9.4 - In Problems 29-36, the vector v has initial point...Ch. 9.4 - In Problems 29-36, the vector v has initial point...Ch. 9.4 - In Problems 29-36, the vector v has initial point...Ch. 9.4 - In Problems 29-36, the vector v has initial point...Ch. 9.4 - In Problems 29-36, the vector v has initial point...Ch. 9.4 - In Problems 29-36, the vector v has initial point...Ch. 9.4 - In Problems 29-36, the vector v has initial point...Ch. 9.4 - In Problems 37-42, find v . v=3i4jCh. 9.4 - In Problems 37-42, find v . v=5i+12jCh. 9.4 - In Problems 37-42, find v . v=ijCh. 9.4 - In Problems 37-42, find v . v=ijCh. 9.4 - In Problems 37-42, find v . v=2i+3jCh. 9.4 - In Problems 37-42, find v . v=6i+2jCh. 9.4 - Problems 3542, find v. v=cosi+sinjCh. 9.4 - Problems 3542, find v. v=i+cotjCh. 9.4 - In Problems 43-48, find each quantity if...Ch. 9.4 - In Problems 43-48, find each quantity if...Ch. 9.4 - In Problems 43-48, find each quantity if...Ch. 9.4 - In Problems 43-48, find each quantity if...Ch. 9.4 - In Problems 43-48, find each quantity if...Ch. 9.4 - In Problems 43-48, find each quantity if...Ch. 9.4 - Prob. 49AYUCh. 9.4 - In Problems 49-54, find the unit vector in the...Ch. 9.4 - Prob. 51AYUCh. 9.4 - Prob. 52AYUCh. 9.4 - In Problems 49-54, find the unit vector in the...Ch. 9.4 - In Problems 49-54, find the unit vector in the...Ch. 9.4 - Prob. 55AYUCh. 9.4 - Prob. 56AYUCh. 9.4 - Prob. 57AYUCh. 9.4 - Prob. 58AYUCh. 9.4 - If v=2ijandw=xi+3j , find all numbers x for which ...Ch. 9.4 - If P=( 3,1 )andQ=( x,4 ) , find all numbers x...Ch. 9.4 - Prob. 61AYUCh. 9.4 - Prob. 62AYUCh. 9.4 - Prob. 63AYUCh. 9.4 - Prob. 64AYUCh. 9.4 - Prob. 65AYUCh. 9.4 - Prob. 66AYUCh. 9.4 - Prob. 67AYUCh. 9.4 - Prob. 68AYUCh. 9.4 - Prob. 69AYUCh. 9.4 - Prob. 70AYUCh. 9.4 - Prob. 71AYUCh. 9.4 - Prob. 72AYUCh. 9.4 - Prob. 73AYUCh. 9.4 - Prob. 74AYUCh. 9.4 - Prob. 75AYUCh. 9.4 - Force Vectors A man pushes a wheelbarrow up an...Ch. 9.4 - Prob. 77AYUCh. 9.4 - Prob. 78AYUCh. 9.4 - Finding the Actual Speed and Direction of an...Ch. 9.4 - Finding the Actual Speed and Direction of an...Ch. 9.4 - Prob. 81AYUCh. 9.4 - Prob. 82AYUCh. 9.4 - Prob. 83AYUCh. 9.4 - Weight of a Car A magnitude of 1200 pounds of...Ch. 9.4 - Correct Direction for Crossing a River A river has...Ch. 9.4 - Finding the Correct Compass Heading The pilot of...Ch. 9.4 - Charting a Course A helicopter pilot needs to...Ch. 9.4 - Crossing a River A captain needs to pilot a boat...Ch. 9.4 - Static Equilibrium A weight of 1000 pounds is...Ch. 9.4 - Static Equilibrium A weight of 800 pounds is...Ch. 9.4 - Static Equilibrium A tightrope walker located at a...Ch. 9.4 - Static Equilibrium Repeat Problem 91 if the angle...Ch. 9.4 - Static Friction A 20-pound box sits at rest on a...Ch. 9.4 - Inclined Ramp A 2-pound weight is attached to a...Ch. 9.4 - Inclined Ramp A box sitting on a horizontal...Ch. 9.4 - Prob. 96AYUCh. 9.4 - Truck Pull At a county fair truck pull, two pickup...Ch. 9.4 - Removing a Slump A farmer wishes to remove a stump...Ch. 9.4 - Prob. 99AYUCh. 9.4 - Computer Graphics Refer to Problem 97. The points...Ch. 9.4 - Static Equilibrium Show on the following graph the...Ch. 9.4 - Challenge Problem Landscaping To drag a 500pound...Ch. 9.4 - Challenge Problem See Problem 102. If Bill pulls...Ch. 9.4 - Explain in your own words what a vector is. Give...Ch. 9.4 - Write a brief paragraph comparing the algebra of...Ch. 9.4 - Explain the difference between an algebraic vector...Ch. 9.4 - Prob. 107AYUCh. 9.4 - Prob. 108AYUCh. 9.4 - Prob. 109AYUCh. 9.4 - Problems 103-106 are based on material learned...Ch. 9.4 - Prob. 111AYUCh. 9.4 - Prob. 112AYUCh. 9.4 - Prob. 113AYUCh. 9.4 - Prob. 114AYUCh. 9.4 - Prob. 115AYUCh. 9.4 - Prob. 116AYUCh. 9.5 - In a triangle with sides a, b, c and angles A, B,...Ch. 9.5 - If w= a 2 i+ b 2 j and v= a 1 i+ b 1 j are two...Ch. 9.5 - If vw=0 , then the two vectors v and w are ______.Ch. 9.5 - If v=3w , then the two vectors v and w are _____.Ch. 9.5 - True or False Given two nonzero vectors v and w,...Ch. 9.5 - True or False Work is a physical example of a...Ch. 9.5 - Prob. 7AYUCh. 9.5 - Prob. 8AYUCh. 9.5 - Prob. 9AYUCh. 9.5 - Prob. 10AYUCh. 9.5 - Prob. 11AYUCh. 9.5 - Prob. 12AYUCh. 9.5 - Prob. 13AYUCh. 9.5 - Prob. 14AYUCh. 9.5 - Prob. 15AYUCh. 9.5 - Prob. 16AYUCh. 9.5 - Prob. 17AYUCh. 9.5 - Prob. 18AYUCh. 9.5 - Kind a SO that the vectors v=iajandw=2i+3j are...Ch. 9.5 - Find b so that the vectors v=i+jandw=i+bj are...Ch. 9.5 - In Problems 21-26, decompose v into two vectors v...Ch. 9.5 - In Problems 21-26, decompose v into two vectors v...Ch. 9.5 - In Problems 21-26, decompose v into two vectors v...Ch. 9.5 - In Problems 21-26, decompose v into two vectors v...Ch. 9.5 - In Problems 21-26, decompose v into two vectors v...Ch. 9.5 - In Problems 21-26, decompose v into two vectors v...Ch. 9.5 - Find a vector of magnitude 15 that is parallel to...Ch. 9.5 - Prob. 28AYUCh. 9.5 - Prob. 29AYUCh. 9.5 - Computing Work A wagon is pulled horizontally by...Ch. 9.5 - Prob. 31AYUCh. 9.5 - Prob. 32AYUCh. 9.5 - Prob. 33AYUCh. 9.5 - Prob. 34AYUCh. 9.5 - Prob. 35AYUCh. 9.5 - Incline Angle A bulldozer exerts 1000 pounds of...Ch. 9.5 - Prob. 37AYUCh. 9.5 - Prob. 38AYUCh. 9.5 - Prob. 39AYUCh. 9.5 - Prob. 40AYUCh. 9.5 - Prob. 41AYUCh. 9.5 - Prob. 42AYUCh. 9.5 - Prob. 43AYUCh. 9.5 - Let v and w denote two nonzero vectors. Show that...Ch. 9.5 - Prob. 45AYUCh. 9.5 - Prob. 46AYUCh. 9.5 - Prob. 47AYUCh. 9.5 - In the definition of work given in this section,...Ch. 9.5 - Prob. 49AYUCh. 9.5 - Prove the polarization identify, u+v 2 u-v 2...Ch. 9.5 - Prob. 51AYUCh. 9.5 - Problems 49-52 are based on material learned...Ch. 9.5 - Prob. 53AYUCh. 9.5 - Prob. 54AYUCh. 9.5 - Problems 49-52 are based on material learned...Ch. 9.5 - Prob. 56AYUCh. 9.5 - Prob. 57AYUCh. 9.5 - Prob. 58AYUCh. 9.5 - Find the exact value of cos80cos70sin80sin70.Ch. 9.5 - Prob. 60AYUCh. 9.5 - Prob. 61AYUCh. 9.6 - The distance d from P 1 =( x 1 , y 1 ) to P 1 =( x...Ch. 9.6 - Prob. 2AYUCh. 9.6 - Prob. 3AYUCh. 9.6 - Prob. 4AYUCh. 9.6 - Prob. 5AYUCh. 9.6 - Prob. 6AYUCh. 9.6 - In Problems 7-14, describe the set of points (...Ch. 9.6 - Prob. 8AYUCh. 9.6 - Prob. 9AYUCh. 9.6 - Prob. 10AYUCh. 9.6 - In Problems 7-14, describe the set of points (...Ch. 9.6 - Prob. 12AYUCh. 9.6 - Prob. 13AYUCh. 9.6 - Prob. 14AYUCh. 9.6 - In Problems 15-20, find the distance from P 1 to P...Ch. 9.6 - In Problems 15-20, find the distance from P 1 to P...Ch. 9.6 - In Problems 15-20, find the distance from P 1 to P...Ch. 9.6 - In Problems 15-20, find the distance from P 1 to P...Ch. 9.6 - In Problems 15-20, find the distance from P 1 to P...Ch. 9.6 - In Problems 15-20, find the distance from P 1 to P...Ch. 9.6 - In Problems 21-26, opposite vertices of a...Ch. 9.6 - In Problems 21-26, opposite vertices of a...Ch. 9.6 - In Problems 21-26, opposite vertices of a...Ch. 9.6 - In Problems 21-26, opposite vertices of a...Ch. 9.6 - In Problems 21-26, opposite vertices of a...Ch. 9.6 - In Problems 21-26, opposite vertices of a...Ch. 9.6 - In Problems 27-32, the vector v has initial point...Ch. 9.6 - In Problems 27-32, the vector v s has initial...Ch. 9.6 - In Problems 27-32, the vector v has initial point...Ch. 9.6 - In Problems 27-32, the vector v has initial point...Ch. 9.6 - In Problems 27-32, the vector v has initial point...Ch. 9.6 - In Problems 27-32, the vector v has initial point...Ch. 9.6 - In Problems 33-38, find v . v=3i6j2kCh. 9.6 - In Problems 33-38, find v . v=6i+12j+4kCh. 9.6 - In Problems 33-38, find v . v=ij+kCh. 9.6 - In Problems 33-38, find v . v=ij+kCh. 9.6 - In Problems 33-38, find v . v=2i+3j3kCh. 9.6 - In Problems 33-38, find v . v=6i+2j2kCh. 9.6 - In Problems 39-44, find each quantity if v=3i5j+2k...Ch. 9.6 - In Problems 39-44, find each quantity if v=3i5j+2k...Ch. 9.6 - In Problems 39-44, find each quantity if v=3i5j+2k...Ch. 9.6 - In Problems 39-44, find each quantity if v=3i5j+2k...Ch. 9.6 - In Problems 39-44, find each quantity if v=3i5j+2k...Ch. 9.6 - In Problems 39-44, find each quantity if v=3i5j+2k...Ch. 9.6 - Prob. 45AYUCh. 9.6 - In Problems 45-50, find the unit vector in the...Ch. 9.6 - In Problems 45-50, find the unit vector in the...Ch. 9.6 - In Problems 45-50, find the unit vector in the...Ch. 9.6 - In Problems 45-50, find the unit vector in the...Ch. 9.6 - In Problems 45-50, find the unit vector in the...Ch. 9.6 - Prob. 51AYUCh. 9.6 - Prob. 52AYUCh. 9.6 - Prob. 53AYUCh. 9.6 - Prob. 54AYUCh. 9.6 - Prob. 55AYUCh. 9.6 - Prob. 56AYUCh. 9.6 - Prob. 57AYUCh. 9.6 - Prob. 58AYUCh. 9.6 - Prob. 59AYUCh. 9.6 - Prob. 60AYUCh. 9.6 - Prob. 61AYUCh. 9.6 - Prob. 62AYUCh. 9.6 - Prob. 63AYUCh. 9.6 - Prob. 64AYUCh. 9.6 - Prob. 65AYUCh. 9.6 - Prob. 66AYUCh. 9.6 - Prob. 67AYUCh. 9.6 - Prob. 68AYUCh. 9.6 - Prob. 69AYUCh. 9.6 - Prob. 70AYUCh. 9.6 - Prob. 71AYUCh. 9.6 - Prob. 72AYUCh. 9.6 - Prob. 73AYUCh. 9.6 - Prob. 74AYUCh. 9.6 - Prob. 75AYUCh. 9.6 - Prob. 76AYUCh. 9.6 - Prob. 77AYUCh. 9.6 - Prob. 78AYUCh. 9.6 - Prob. 79AYUCh. 9.6 - solve: 3 x2 5Ch. 9.6 - Prob. 81AYUCh. 9.6 - Prob. 82AYUCh. 9.6 - Prob. 83AYUCh. 9.6 - Prob. 84AYUCh. 9.6 - Form a polynomial function with real coefficients...Ch. 9.6 - Prob. 86AYUCh. 9.6 - Prob. 87AYUCh. 9.6 - Prob. 88AYUCh. 9.7 - Prob. 1AYUCh. 9.7 - True or False For any vector v,vv=0 .Ch. 9.7 - Prob. 3AYUCh. 9.7 - True or False uv is a vector that is parallel to...Ch. 9.7 - Prob. 5AYUCh. 9.7 - Prob. 6AYUCh. 9.7 - In Problems 7-14, find the value of each...Ch. 9.7 - In Problems 7-14, find the value of each...Ch. 9.7 - In Problems 7-14, find the value of each...Ch. 9.7 - In Problems 7-14, find the value of each...Ch. 9.7 - In Problems 7-14, find the value of each...Ch. 9.7 - In Problems 7-14, find the value of each...Ch. 9.7 - In Problems 7-14, find the value of each...Ch. 9.7 - In Problems 7-14, find the value of each...Ch. 9.7 - In Problems 15-22, find (a) vw , (b) wv , (c) ww ,...Ch. 9.7 - In Problems 15-22, find (a) vw , (b) wv , (c) ww ,...Ch. 9.7 - In Problems 15-22, find (a) vw , (b) wv , (c) ww ,...Ch. 9.7 - In Problems 15-22, find (a) vw , (b) wv , (c) ww ,...Ch. 9.7 - In Problems 15-22, find (a) vw , (b) wv , (c) ww ,...Ch. 9.7 - In Problems 15-22, find (a) vw , (b) wv , (c) ww ,...Ch. 9.7 - In Problems 15-22, find (a) vw , (b) wv , (c) ww ,...Ch. 9.7 - In Problems 15-22, find (a) vw , (b) wv , (c) ww ,...Ch. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - Prob. 30AYUCh. 9.7 - Prob. 31AYUCh. 9.7 - Prob. 32AYUCh. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - Prob. 34AYUCh. 9.7 - In Problems 23-44, use the given vectors u,v,andw...Ch. 9.7 - Prob. 36AYUCh. 9.7 - Prob. 37AYUCh. 9.7 - Prob. 38AYUCh. 9.7 - Prob. 39AYUCh. 9.7 - Prob. 40AYUCh. 9.7 - Prob. 41AYUCh. 9.7 - Prob. 42AYUCh. 9.7 - Prob. 43AYUCh. 9.7 - Prob. 44AYUCh. 9.7 - Prob. 45AYUCh. 9.7 - Prob. 46AYUCh. 9.7 - Prob. 47AYUCh. 9.7 - Prob. 48AYUCh. 9.7 - Prob. 49AYUCh. 9.7 - Prob. 50AYUCh. 9.7 - Prob. 51AYUCh. 9.7 - Prob. 52AYUCh. 9.7 - Find a unit vector normal to the plane containing...Ch. 9.7 - Find a unit vector normal to the plane containing...Ch. 9.7 - Volume of a Parallelepiped A parallelepiped is a...Ch. 9.7 - Volume of a Parallelepiped Refer to Problem 55....Ch. 9.7 - Prove for vectors uandv that uv 2 = u 2 v 2 ...Ch. 9.7 - Prob. 58AYUCh. 9.7 - Show that if uandv are orthogonal unit vectors,...Ch. 9.7 - Prove property (3).Ch. 9.7 - Prove property (5).Ch. 9.7 - Prove property (9). [Hint: Use the result of...Ch. 9.7 - Prob. 63AYUCh. 9.7 - Prob. 64AYUCh. 9.7 - If uv=0anduv=0 , what, if anything, can you...Ch. 9.7 - Prob. 66AYUCh. 9.7 - Prob. 67AYUCh. 9.7 - Prob. 68AYUCh. 9.7 - Prob. 69AYUCh. 9.7 - Prob. 70AYUCh. 9.7 - Prob. 71AYUCh. 9.7 - Prob. 72AYUCh. 9.7 - Prob. 73AYUCh. 9.7 - Prob. 74AYUCh. 9.7 - Prob. 75AYUCh. 9 - In Problems , plot each point given in polar...Ch. 9 - In Problems 13, plot each point given in polar...Ch. 9 - In Problems , plot each point given in polar...Ch. 9 - In Problems , The rectangular coordinates of a...Ch. 9 - In Problems , The rectangular coordinates of a...Ch. 9 - Prob. 6RECh. 9 - In Problems 710, the variables r and represent...Ch. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - In Problems 1113, graph each polar equation. Be...Ch. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - In Problems, Plot each point given in polar...Ch. 9 - Prob. 2CTCh. 9 - Prob. 3CTCh. 9 - Prob. 4CTCh. 9 - Prob. 5CTCh. 9 - Prob. 6CTCh. 9 - Prob. 7CTCh. 9 - Prob. 8CTCh. 9 - Prob. 9CTCh. 9 - Prob. 10CTCh. 9 - Prob. 11CTCh. 9 - Prob. 12CTCh. 9 - Find all the complex cube roots of . Then plot...Ch. 9 - In Problems, and .
Find the position vector v...Ch. 9 - In Problems, and .
Find | v |.
Ch. 9 - In Problems, and .
Find the unit vector in the...Ch. 9 - Prob. 17CTCh. 9 - In Problems, and .
Write the vector in terms of...Ch. 9 - Prob. 19CTCh. 9 - Prob. 20CTCh. 9 - Prob. 21CTCh. 9 - Prob. 22CTCh. 9 - In Problems 2325, use the vectors u=2i-3j+k and...Ch. 9 - In Problems 2325, use the vectors u=2i-3j+k and...Ch. 9 - Prob. 25CTCh. 9 - Prob. 26CTCh. 9 - Find the real solutions, if any, of the equation...Ch. 9 - Find an equation for the line containing the...Ch. 9 - Prob. 3CRCh. 9 - What is the domain of the function f(x)=ln(12x)?Ch. 9 - Test the equation for symmetry with respect to...Ch. 9 - Graph the function
Ch. 9 - Graph the function y=sinx.Ch. 9 - Graph the function
Ch. 9 - Find the exact value of sin1(12)Ch. 9 - Graph the equations and on the same set of...Ch. 9 - Prob. 11CRCh. 9 - What are the amplitude and period of ?
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b). x-a f(x)= 1 - cos (4x-4) 3(x-1)² ; a = 1 a. Use a graphing utility to graph f. Select the correct graph below.. A. W → ✓ Each graph is displayed in a [- 1,3] by [0,5] window. B. in ✓ ○ C. und ☑ Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x-1 ○ A. The limit appears to be approximately ☐ . (Round to the nearest tenth as needed.) B. The limit does not exist. b. Evaluate f(x) for values of x near 1 to support your conjecture. X 0.9 0.99 0.999 1.001 1.01 1.1 f(x) ○ D. + ☑ (Round to six decimal places as needed.) Does the table from the previous step support your conjecture? A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…arrow_forwardx²-19x+90 Let f(x) = . Complete parts (a) through (c) below. x-a a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→a+ ○ A. a= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no values of a for which the limit equals a finite number. b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. (Type integers or simplified fractions) C. There are no values of a that satisfy lim f(x) = ∞. + x-a c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. Either a (Type integers or simplified fractions) B.arrow_forwardSketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions. f(2)=0 f(4) is undefined lim f(x)=1 X-6 lim f(x) = -∞ x-0+ lim f(x) = ∞ lim f(x) = ∞ x-4 _8arrow_forwardDetermine the following limit. lim 35w² +8w+4 w→∞ √49w+w³ 3 Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. ○ A. lim W→∞ 35w² +8w+4 49w+w3 (Simplify your answer.) B. The limit does not exist and is neither ∞ nor - ∞.arrow_forwardCalculate the limit lim X-a x-a 5 using the following factorization formula where n is a positive integer and x-➡a a is a real number. x-a = (x-a) (x1+x-2a+x lim x-a X - a x-a 5 = n- + xa an-2 + an−1)arrow_forwardThe function s(t) represents the position of an object at time t moving along a line. Suppose s(1) = 116 and s(5)=228. Find the average velocity of the object over the interval of time [1,5]. The average velocity over the interval [1,5] is Vav = (Simplify your answer.)arrow_forwardFor the position function s(t) = - 16t² + 105t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. Time Interval Average Velocity [1,2] Complete the following table. Time Interval Average Velocity [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] [1,2] [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] ப (Type exact answers. Type integers or decimals.) The value of the instantaneous velocity at t = 1 is (Round to the nearest integer as needed.)arrow_forwardFind the following limit or state that it does not exist. Assume b is a fixed real number. (x-b) 40 - 3x + 3b lim x-b x-b ... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (x-b) 40 -3x+3b A. lim x-b x-b B. The limit does not exist. (Type an exact answer.)arrow_forwardx4 -289 Consider the function f(x) = 2 X-17 Complete parts a and b below. a. Analyze lim f(x) and lim f(x), and then identify the horizontal asymptotes. x+x X--∞ lim 4 X-289 2 X∞ X-17 X - 289 lim = 2 ... X∞ X - 17 Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has a horizontal asymptote at y = B. The function has two horizontal asymptotes. The top asymptote is y = and the bottom asymptote is y = ☐ . C. The function has no horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote x = a, evaluate lim f(x) and lim f(x). Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. earrow_forwardExplain why lim x²-2x-35 X-7 X-7 lim (x+5), and then evaluate lim X-7 x² -2x-35 x-7 x-7 Choose the correct answer below. A. x²-2x-35 The limits lim X-7 X-7 and lim (x+5) equal the same number when evaluated using X-7 direct substitution. B. Since each limit approaches 7, it follows that the limits are equal. C. The numerator of the expression X-2x-35 X-7 simplifies to x + 5 for all x, so the limits are equal. D. Since x²-2x-35 X-7 = x + 5 whenever x 7, it follows that the two expressions evaluate to the same number as x approaches 7. Now evaluate the limit. x²-2x-35 lim X-7 X-7 = (Simplify your answer.)arrow_forwardA function f is even if f(x) = f(x) for all x in the domain of f. If f is even, with lim f(x) = 4 and x-6+ lim f(x)=-3, find the following limits. X-6 a. lim f(x) b. +9-←x lim f(x) X-6 a. lim f(x)= +9-←x (Simplify your answer.) b. lim f(x)= X→-6 (Simplify your answer.) ...arrow_forwardEvaluate the following limit. lim X-X (10+19) Select the correct answer below and, if necessary, fill in the answer box within your choice. 10 A. lim 10+ = 2 ☐ (Type an integer or a simplified fraction.) X-∞ B. The limit does not exist.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageIntermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningWhat is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY