Precalculus
Precalculus
17th Edition
ISBN: 9780078035609
Author: Miller, Julie, Gerken, Donna.
Publisher: Mcgraw-hill Education,
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Chapter 7.2, Problem 78PE

Given r = 4 sin θ 4 ,

a. Replace r , θ by r , − θ in the equation. Does this show that the graph of the equation is symmetric with respect to the polar axis?

b. The ordered pair r , 4 π − θ is another representation of the point r , − θ . Replace r , θ by r , 4 π − θ in the equation. Does this show that the graph of the equation is symmetric with respect to the polar axis?

c. What other type of symmetry (if any) does the graph of the equation have?

d. Use a graphing utility to graph the equation on a graphing utility for 0 ≤ θ ≤ 8 π .

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Chapter 7 Solutions

Precalculus

Ch. 7.1 - Plot the points whose polar coordinates are given....Ch. 7.1 - Given 7,32 in polar coordinates, find two other...Ch. 7.1 - Convert the ordered pairs in polar coordinates to...Ch. 7.1 - Convert 2,23 from rectangular coordinates to polar...Ch. 7.1 - Prob. 5SPCh. 7.1 - Write an equivalent equation using polar...Ch. 7.1 - Prob. 1PECh. 7.1 - Given a point P represented by the ordered pair r,...Ch. 7.1 - To convert an ordered pair r, in polar coordinates...Ch. 7.1 - To convert an ordered pair x,y in polar...
Ch. 7.1 - Use an equation in polar coordinates to describe...Ch. 7.1 - Prob. 6PECh. 7.1 - Prob. 7PECh. 7.1 - For Exercises 7-14, match each point in polar...Ch. 7.1 - For Exercises 7-14, match each point in polar...Ch. 7.1 - For Exercises 7-14, match each point in polar...Ch. 7.1 - For Exercises 7-14, match each point in polar...Ch. 7.1 - For Exercises 7-14, match each point in polar...Ch. 7.1 - For Exercises 7-14, match each point in polar...Ch. 7.1 - For Exercises 7-14, match each point in polar...Ch. 7.1 - Prob. 15PECh. 7.1 - For Exercises 15-18, plot the points whose polar...Ch. 7.1 - Prob. 17PECh. 7.1 - For Exercises 15-18, plot the points whose polar...Ch. 7.1 - For Exercises 19-22, given a point in polar...Ch. 7.1 - For Exercises 19-22. given a point in polar...Ch. 7.1 - For Exercises 19-22, given a point in polar...Ch. 7.1 - For Exercises 19-22, given a point in polar...Ch. 7.1 - For Exercises 23-32, convert the ordered pair in...Ch. 7.1 - For Exercises 23-32, convert the ordered pair in...Ch. 7.1 - Prob. 25PECh. 7.1 - For Exercises 23-32, convert the ordered pair in...Ch. 7.1 - For Exercises 23-32, convert the ordered pair in...Ch. 7.1 - For Exercises 23-32, convert the ordered pair in...Ch. 7.1 - For Exercises 23-32, convert the ordered pair in...Ch. 7.1 - For Exercises 23-32, convert the ordered pair in...Ch. 7.1 - For Exercises 23-32, convert the ordered pair in...Ch. 7.1 - Prob. 32PECh. 7.1 - Prob. 33PECh. 7.1 - For Exercises 33-38, convert the ordered pair in...Ch. 7.1 - For Exercises 33-38, convert the ordered pair in...Ch. 7.1 - Prob. 36PECh. 7.1 - Prob. 37PECh. 7.1 - For Exercises 33-38, convert the ordered pair in...Ch. 7.1 - For Exercises 39-44, convert the ordered pair in...Ch. 7.1 - For Exercises 39-44, convert the ordered pair in...Ch. 7.1 - Prob. 41PECh. 7.1 - For Exercises 39-44, convert the ordered pair in...Ch. 7.1 - For Exercises 39-44, convert the ordered pair in...Ch. 7.1 - For Exercises 39-44, convert the ordered pair in...Ch. 7.1 - Prob. 45PECh. 7.1 - Prob. 46PECh. 7.1 - For Exercises 45-56, write an equivalent equation...Ch. 7.1 - For Exercises 45-56, write an equivalent equation...Ch. 7.1 - Prob. 49PECh. 7.1 - Prob. 50PECh. 7.1 - For Exercises 45-56, write an equivalent equation...Ch. 7.1 - Prob. 52PECh. 7.1 - Prob. 53PECh. 7.1 - Prob. 54PECh. 7.1 - Prob. 55PECh. 7.1 - Prob. 56PECh. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - Prob. 63PECh. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - Prob. 66PECh. 7.1 - Prob. 67PECh. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - For Exercises 57-70, convert the polar equation to...Ch. 7.1 - Suppose that the polar axis is positioned to...Ch. 7.1 - Prob. 72PECh. 7.1 - For Exercises 73-76, determine whether the two...Ch. 7.1 - Prob. 74PECh. 7.1 - For Exercises 73-76, determine whether the two...Ch. 7.1 - For Exercises 73-76, determine whether the two...Ch. 7.1 - For Exercises 77-78, determine whether the...Ch. 7.1 - For Exercises 77-78, determine whether the...Ch. 7.1 - For Exercises 79-82, a point in polar coordinates...Ch. 7.1 - Prob. 80PECh. 7.1 - For Exercises 79-82, a point in polar coordinates...Ch. 7.1 - For Exercises 79-82, a point in polar coordinates...Ch. 7.1 - For Exercises 83-88, describe the graph of the set...Ch. 7.1 - For Exercises 83-88, describe the graph of the set...Ch. 7.1 - For Exercises 83-88, describe the graph of the set...Ch. 7.1 - For Exercises 83-88, describe the graph of the set...Ch. 7.1 - For Exercises 83-88, describe the graph of the set...Ch. 7.1 - For Exercises 83-88, describe the graph of the set...Ch. 7.1 - Suppose that seating in a theater is in an area...Ch. 7.1 - A rotating sprinkler spreads water over an area...Ch. 7.1 - A player in a video game must knock out a target...Ch. 7.1 - Prob. 92PECh. 7.1 - Explain the significance of r0 in an ordered pair...Ch. 7.1 - Explain why a point in the plane can be...Ch. 7.1 - Prob. 95PECh. 7.1 - Use the results of Exercise 95. a. If 1=2 what is...Ch. 7.1 - Given points Pr1,1 and Qr2,2 represented in polar...Ch. 7.1 - Use the results of Exercise 97. Find the distance...Ch. 7.1 - Prob. 99PECh. 7.1 - For Exercises 99-102, use a graphing utility to...Ch. 7.1 - For Exercises 99-102, use a graphing utility to...Ch. 7.1 - For Exercises 99-102, use a graphing utility to...Ch. 7.2 - Graph r=4cos .Ch. 7.2 - Graph r=3+3sin .Ch. 7.2 - Graph r=1+4cos .Ch. 7.2 - Prob. 4SPCh. 7.2 - Graph r2=25cos2 .Ch. 7.2 - Graph r=0.8 for 0 .Ch. 7.2 - Prob. 1PECh. 7.2 - If replacing r, by r, in a polar equation results...Ch. 7.2 - Prob. 3PECh. 7.2 - Prob. 4PECh. 7.2 - Determining the ordered pairs for which r=0 in a...Ch. 7.2 - Prob. 6PECh. 7.2 - Prob. 7PECh. 7.2 - Prob. 8PECh. 7.2 - Prob. 9PECh. 7.2 - Prob. 10PECh. 7.2 - Prob. 11PECh. 7.2 - Prob. 12PECh. 7.2 - Prob. 13PECh. 7.2 - Prob. 14PECh. 7.2 - Prob. 15PECh. 7.2 - For Exercises 15-22, determine whether the tests...Ch. 7.2 - For Exercises 15-22, determine whether the tests...Ch. 7.2 - For Exercises 15-22, determine whether the tests...Ch. 7.2 - For Exercises 15-22, determine whether the tests...Ch. 7.2 - For Exercises 15-22, determine whether the tests...Ch. 7.2 - For Exercises 15-22, determine whether the tests...Ch. 7.2 - For Exercises 15-22, determine whether the tests...Ch. 7.2 - For Exercises 23-30, use symmetry to graph the...Ch. 7.2 - Prob. 24PECh. 7.2 - For Exercises 23-30, use symmetry to graph the...Ch. 7.2 - For Exercises 23-30, use symmetry to graph the...Ch. 7.2 - For Exercises 23-30, use symmetry to graph the...Ch. 7.2 - For Exercises 23-30, use symmetry to graph the...Ch. 7.2 - For Exercises 23-30, use symmetry to graph the...Ch. 7.2 - Prob. 30PECh. 7.2 - Prob. 31PECh. 7.2 - Prob. 32PECh. 7.2 - Prob. 33PECh. 7.2 - Prob. 34PECh. 7.2 - Prob. 35PECh. 7.2 - Prob. 36PECh. 7.2 - Prob. 37PECh. 7.2 - Prob. 38PECh. 7.2 - Prob. 39PECh. 7.2 - Prob. 40PECh. 7.2 - Prob. 41PECh. 7.2 - Prob. 42PECh. 7.2 - Prob. 43PECh. 7.2 - Prob. 44PECh. 7.2 - For Exercises 43-46, graph the polar curve. (See...Ch. 7.2 - For Exercises 43-46, graph the polar curve. (See...Ch. 7.2 - For Exercises 47-52, for the purpose of...Ch. 7.2 - For Exercises 47-52, for the purpose of...Ch. 7.2 - For Exercises 47-52, for the purpose of...Ch. 7.2 - For Exercises 47-52, for the purpose of...Ch. 7.2 - For Exercises 47-52, for the purpose of...Ch. 7.2 - For Exercises 47-52, for the purpose of...Ch. 7.2 - Prob. 53PECh. 7.2 - Prob. 54PECh. 7.2 - Prob. 55PECh. 7.2 - Prob. 56PECh. 7.2 - A quilter wants to make a design in the shape of a...Ch. 7.2 - The outline of a propeller on an airplane is in...Ch. 7.2 - a. Given r=8sin4 , determine the set of values of ...Ch. 7.2 - a. Given r=6sin3 , determine the set of values of ...Ch. 7.2 - If r=fsin , that is, if r is expressed as a...Ch. 7.2 - Prob. 62PECh. 7.2 - Prob. 63PECh. 7.2 - Prob. 64PECh. 7.2 - For Exercises 63-66, use the results of Exercises...Ch. 7.2 - For Exercises 63-66, use the results of Exercises...Ch. 7.2 - Given r=1+sec (conchoids), a. For what value(s) of...Ch. 7.2 - Given r=2 (hyperbolic spiral), a. For what value...Ch. 7.2 - Use a graphing utility to graph the equations on...Ch. 7.2 - Use a graphing utility to graph the equations on...Ch. 7.2 - A logarithmic spiral is represented by r=aeb . a....Ch. 7.2 - An Archimedean spiral is represented by r=a . a....Ch. 7.2 - Graph the limaqons given by the equation r=a+bcos...Ch. 7.2 - Graph the limacons given by the equation r=a+bcos...Ch. 7.2 - Find the values of on the interval 0,2 for which...Ch. 7.2 - Find the values of on the interval 0,2 for which...Ch. 7.2 - Given r=6cos2 , a. Replace r, by r, in the...Ch. 7.2 - Given r=4sin4 , a. Replace r, by r, in the...Ch. 7.2 - The graph of r=4cos2 is shown. a. Is 4,2 a...Ch. 7.2 - Prob. 80PECh. 7.2 - a. Match the polar or rectangular equation on the...Ch. 7.2 - Prob. 2PRECh. 7.2 - Prob. 3PRECh. 7.2 - a. Match the polar or rectangular equation on the...Ch. 7.2 - Prob. 5PRECh. 7.2 - Prob. 6PRECh. 7.2 - Prob. 7PRECh. 7.2 - a. Match the polar or rectangular equation on the...Ch. 7.2 - Prob. 9PRECh. 7.2 - Prob. 10PRECh. 7.2 - Prob. 11PRECh. 7.2 - Prob. 12PRECh. 7.2 - Prob. 13PRECh. 7.3 - Graph the complex numbers in the complex plane. a....Ch. 7.3 - Find the modulus. a. z=512i b. z=4+6iCh. 7.3 - Write the complex number in polar form. a. z=1i b....Ch. 7.3 - Write z=6cos150+isin150 in rectangular form.Ch. 7.3 - Given z1=3cos12+isin12 and z2=2cos6+isin6 , find...Ch. 7.3 - Given z1=18cos75+isin75 and z2=2cos255+isin255 ,...Ch. 7.3 - Compute 4cos70+isin703 and write the result in...Ch. 7.3 - Compute 22i4 and write the result in rectangular...Ch. 7.3 - Find the cube roots of 64 over the set of complex...Ch. 7.3 - Find the fourth roots of 3+33i over the set of...Ch. 7.3 - The complex plane has two axes. The horizontal...Ch. 7.3 - Prob. 2PECh. 7.3 - The rectangular form of a complex number z is a+bi...Ch. 7.3 - Given z=rcos+isin , the value r is called the of z...Ch. 7.3 - If z1=r1cos1+isin1 and z2=r2cos2+isin2 , then...Ch. 7.3 - If z=rcos+isin , then zn = for a positive integer...Ch. 7.3 - For Exercises 7-8, graph the complex numbers in...Ch. 7.3 - Prob. 8PECh. 7.3 - For Exercises 9-14, find the modulus of each...Ch. 7.3 - For Exercises 9-14, find the modulus of each...Ch. 7.3 - Prob. 11PECh. 7.3 - Prob. 12PECh. 7.3 - Prob. 13PECh. 7.3 - For Exercises 9-14, find the modulus of each...Ch. 7.3 - Prob. 15PECh. 7.3 - Prob. 16PECh. 7.3 - Prob. 17PECh. 7.3 - Prob. 18PECh. 7.3 - Prob. 19PECh. 7.3 - Prob. 20PECh. 7.3 - For Exercises 15-22, write the complex number in...Ch. 7.3 - Prob. 22PECh. 7.3 - For Exercises 23-30, convert the complex number...Ch. 7.3 - For Exercises 23-30, convert the complex number...Ch. 7.3 - For Exercises 23-30, convert the complex number...Ch. 7.3 - For Exercises 23-30, convert the complex number...Ch. 7.3 - For Exercises 23-30, convert the complex number...Ch. 7.3 - Prob. 28PECh. 7.3 - For Exercises 23-30, convert the complex number...Ch. 7.3 - For Exercises 23-30, convert the complex number...Ch. 7.3 - Prob. 31PECh. 7.3 - Prob. 32PECh. 7.3 - For Exercises 31-42, given complex numbers z1 and...Ch. 7.3 - For Exercises 31-42, given complex numbers z1 and...Ch. 7.3 - Prob. 35PECh. 7.3 - Prob. 36PECh. 7.3 - For Exercises 31-42, given complex numbers z1 and...Ch. 7.3 - For Exercises 31-42, given complex numbers z1 and...Ch. 7.3 - For Exercises 31-42, given complex numbers z1 and...Ch. 7.3 - Prob. 40PECh. 7.3 - Prob. 41PECh. 7.3 - For Exercises 31-42, given complex numbers z1 and...Ch. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - Prob. 45PECh. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - For Exercises 43-52, use De Moivre's theorem to...Ch. 7.3 - When expressing the fourth roots wk of a complex...Ch. 7.3 - When expressing the fifth roots Wk of a complex...Ch. 7.3 - For Exercises 55-60, the indicated complex roots...Ch. 7.3 - For Exercises 55-60, the indicated complex roots...Ch. 7.3 - For Exercises 55-60, the indicated complex roots...Ch. 7.3 - For Exercises 55-60, the indicated complex roots...Ch. 7.3 - For Exercises 55-60, the indicated complex roots...Ch. 7.3 - For Exercises 55-60, the indicated complex roots...Ch. 7.3 - For Exercises 61-64, find the indicated complex...Ch. 7.3 - For Exercises 61-64, find the indicated complex...Ch. 7.3 - For Exercises 61-64, find the indicated complex...Ch. 7.3 - For Exercises 61-64, find the indicated complex...Ch. 7.3 - For Exercises 55-60, the indicated complex roots...Ch. 7.3 - For Exercises 55-60, the indicated complex roots...Ch. 7.3 - Prob. 67PECh. 7.3 - Prob. 68PECh. 7.3 - For Exercises 65-70, find the indicated complex...Ch. 7.3 - For Exercises 65-70, find the indicated complex...Ch. 7.3 - The square roots, cube roots, and fourth roots of...Ch. 7.3 - Use the results of Exercise 71 to find the fifth...Ch. 7.3 - Prob. 73PECh. 7.3 - Use De Moivre's theorem to show that 1i is a cube...Ch. 7.3 - For Exercises 75-78, shade the area in the complex...Ch. 7.3 - Prob. 76PECh. 7.3 - Prob. 77PECh. 7.3 - Prob. 78PECh. 7.3 - Prob. 79PECh. 7.3 - Prob. 80PECh. 7.3 - Prob. 81PECh. 7.3 - For Exercises 79-82, convert the complex number...Ch. 7.3 - Prob. 83PECh. 7.3 - Given z1=2+2i and z2=3i , a. Find z1z2 by dividing...Ch. 7.3 - Let Z1=r1cos1+isin1 and Z2=r2cos2+sin2 .Prove...Ch. 7.3 - Show that Z1=rcos+isin and Z2=rcos=isin are...Ch. 7.3 - Let z=rcos+isin . a.Prove that z1=r1cos+isin b....Ch. 7.3 - Use De Moivre's theorem to find the indicated...Ch. 7.3 - For Exercises 89-92, simplify and write the...Ch. 7.3 - For Exercises 89-92, simplify and write the...Ch. 7.3 - For Exercises 89-92, simplify and write the...Ch. 7.3 - For Exercises 89-92, simplify and write the...Ch. 7.3 - Solve x6=64 by factoring and applying the zero...Ch. 7.3 - Solve x3=64 by factoring and applying the zero...Ch. 7.3 - Prob. 95PECh. 7.3 - For Exercises 95-98, find all complex solutions to...Ch. 7.3 - Prob. 97PECh. 7.3 - For Exercises 95-98, find all complex solutions to...Ch. 7.3 - How is the absolute value of a complex number...Ch. 7.3 - Is the polar representation of a complex number...Ch. 7.3 - Euler's formula states that ei=cos+isin . a....Ch. 7.3 - In calculus, we can show that...Ch. 7.3 - Show that 3ei/12 is a solution to z881z4+6561=0 .Ch. 7.3 - Show that e7i/12 is a solution to z8z4+1=0.Ch. 7.4 - Prob. 1SPCh. 7.4 - Suppose that vector v has initial point 4,5 and...Ch. 7.4 - Prob. 3SPCh. 7.4 - Given a=11,7 and b=4,6 , find a. 6a b. 3a+10bCh. 7.4 - Prob. 5SPCh. 7.4 - Prob. 6SPCh. 7.4 - Prob. 7SPCh. 7.4 - A ball is thrown from a height of 1m . At the time...Ch. 7.4 - A plane travels with an air speed of 400 knots at...Ch. 7.4 - Prob. 10SPCh. 7.4 - Prob. 11SPCh. 7.4 - Prob. 12SPCh. 7.4 - A is a quantity that has magnitude only, whereas...Ch. 7.4 - Given a vector AB the initial point is and the...Ch. 7.4 - The ofAB of is the length of the vector and is...Ch. 7.4 - For a real number k, the vector kv is in the same...Ch. 7.4 - Two vectors r=a1,b1 and s=a2,b2 are equal if .Ch. 7.4 - Prob. 9PECh. 7.4 - Prob. 10PECh. 7.4 - For Exercises 11-16, vector v has initial point P...Ch. 7.4 - For Exercises 11-16, vector v has initial point P...Ch. 7.4 - For Exercises 11-16, vector v has initial point P...Ch. 7.4 - Prob. 14PECh. 7.4 - For Exercises 11-16, vector v has initial point P...Ch. 7.4 - Prob. 16PECh. 7.4 - Prob. 17PECh. 7.4 - Prob. 18PECh. 7.4 - For Exercises 17-20, refer to vectors v and w in...Ch. 7.4 - Prob. 20PECh. 7.4 - Prob. 21PECh. 7.4 - Prob. 22PECh. 7.4 - Prob. 23PECh. 7.4 - Prob. 24PECh. 7.4 - Prob. 25PECh. 7.4 - Prob. 26PECh. 7.4 - Prob. 27PECh. 7.4 - Given vector v with initial point 17,80 and...Ch. 7.4 - Given v=17,29 with initial point 4,10 , find the...Ch. 7.4 - Given v=5,8 with initial point1,7 , find the...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - Prob. 39PECh. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - Prob. 42PECh. 7.4 - Prob. 43PECh. 7.4 - Prob. 44PECh. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 31-46, perform the indicated...Ch. 7.4 - For Exercises 47-54, let c and d be scalars and...Ch. 7.4 - For Exercises 47-54, let c and d be scalars and...Ch. 7.4 - For Exercises 47-54, let c and d be scalars and...Ch. 7.4 - For Exercises 47-54, let c and d be scalars and...Ch. 7.4 - Prob. 51PECh. 7.4 - For Exercises 47-54, let c and d be scalars and...Ch. 7.4 - Prob. 53PECh. 7.4 - For Exercises 47-54, let c and d be scalars and...Ch. 7.4 - Prob. 55PECh. 7.4 - Prob. 56PECh. 7.4 - Prob. 57PECh. 7.4 - For Exercises 55-60, find a unit vector in the...Ch. 7.4 - Prob. 59PECh. 7.4 - Prob. 60PECh. 7.4 - For Exercises 61-68, perform the indicated...Ch. 7.4 - For Exercises 61-68, perform the indicated...Ch. 7.4 - For Exercises 61-68, perform the indicated...Ch. 7.4 - For Exercises 61-68, perform the indicated...Ch. 7.4 - For Exercises 61-68, perform the indicated...Ch. 7.4 - For Exercises 61-68, perform the indicated...Ch. 7.4 - For Exercises 61-68, perform the indicated...Ch. 7.4 - For Exercises 61-68, perform the indicated...Ch. 7.4 - For Exercises 69-74.write the vector v in the form...Ch. 7.4 - Prob. 70PECh. 7.4 - Prob. 71PECh. 7.4 - Prob. 72PECh. 7.4 - Prob. 73PECh. 7.4 - Prob. 74PECh. 7.4 - Prob. 75PECh. 7.4 - Prob. 76PECh. 7.4 - Prob. 77PECh. 7.4 - Prob. 78PECh. 7.4 - Prob. 79PECh. 7.4 - Prob. 80PECh. 7.4 - Prob. 81PECh. 7.4 - Prob. 82PECh. 7.4 - A punter kicks a football with an initial velocity...Ch. 7.4 - The velocity of a ship is given by the vector...Ch. 7.4 - Prob. 85PECh. 7.4 - A plane flies at a speed of 370 mph on a bearing...Ch. 7.4 - A swimmer swims 1.5 mph in still water and wants...Ch. 7.4 - A boat that travels 6 mph in still water leaves a...Ch. 7.4 - For Exercises 89-94, the given forces (in units of...Ch. 7.4 - Prob. 90PECh. 7.4 - Prob. 91PECh. 7.4 - Prob. 92PECh. 7.4 - For Exercises 89-94, the given forces (in units of...Ch. 7.4 - For Exercises 89-94, the given forces (in units of...Ch. 7.4 - Prob. 95PECh. 7.4 - Prob. 96PECh. 7.4 - For Exercises 97-102, refer to vectors t, u, v,...Ch. 7.4 - For Exercises 97-102, refer to vectors t, u, v,...Ch. 7.4 - For Exercises 97-102, refer to vectors t, u, v,...Ch. 7.4 - For Exercises 97-102, refer to vectors t, u, v,...Ch. 7.4 - For Exercises 97-102, refer to vectors t, u, v,...Ch. 7.4 - For Exercises 97-102, refer to vectors t, u, v,...Ch. 7.4 - A kayaker paddles 3 mph in still water. If she...Ch. 7.4 - A long-distance swimmer swims 2 mph in still...Ch. 7.4 - Prob. 105PECh. 7.4 - For Exercises 105-106, two vectors v and w act on...Ch. 7.4 - Prob. 107PECh. 7.4 - Explain how the sum v+w is found geometrically.Ch. 7.4 - Prob. 109PECh. 7.4 - Prob. 110PECh. 7.4 - For Exercises 111-112, assume that the system is...Ch. 7.4 - For Exercises 111-112, assume that the system is...Ch. 7.4 - A 50 -lb box is supported by two ropes attached to...Ch. 7.4 - A tightrope walker and the balance bar together...Ch. 7.5 - Given v=2,6 andw=3,1 , find a. vw b. wv c.vv d. vCh. 7.5 - Prob. 2SPCh. 7.5 - Determine if the given vectors are orthogonal, a....Ch. 7.5 - Repeat Example 4 with v=7,3 and w=2,6 .Ch. 7.5 - Repeat Example 5 with a 1400 -lb SUV parked on a...Ch. 7.5 - Prob. 6SPCh. 7.5 - Prob. 7SPCh. 7.5 - The dot product of v = a1,b1 and w = a2,b2 equals ...Ch. 7.5 - If is the angle between two nonzero vectors v and...Ch. 7.5 - Prob. 3PECh. 7.5 - Two vectors are said to be if and only if they...Ch. 7.5 - The projection of a nonzero vector v onto a...Ch. 7.5 - Suppose that D is the displacement vector of an...Ch. 7.5 - For Exercises 7-14.for the given vectors, find a....Ch. 7.5 - For Exercises 7-14.for the given vectors, find a....Ch. 7.5 - Prob. 9PECh. 7.5 - For Exercises 7-14. for the given vectors, find a....Ch. 7.5 - Prob. 11PECh. 7.5 - For Exercises 7-14. for the given vectors, find a....Ch. 7.5 - For Exercises 7-14. for the given vectors, find a....Ch. 7.5 - For Exercises 7-14. for the given vectors, find a....Ch. 7.5 - For Exercises 15-18, use the dot product to find...Ch. 7.5 - Prob. 16PECh. 7.5 - Prob. 17PECh. 7.5 - Prob. 18PECh. 7.5 - Prob. 19PECh. 7.5 - Prob. 20PECh. 7.5 - Prob. 21PECh. 7.5 - Prob. 22PECh. 7.5 - Prob. 23PECh. 7.5 - Prob. 24PECh. 7.5 - Prob. 25PECh. 7.5 - Prob. 26PECh. 7.5 - Prob. 27PECh. 7.5 - Prob. 28PECh. 7.5 - For Exercises 29-32, let v=a1,b1,w=a2,b2,u=a3,b3 ,...Ch. 7.5 - For Exercises 29-32, let v=a1,b1,w=a2,b2,u=a3,b3 ,...Ch. 7.5 - Prob. 31PECh. 7.5 - For Exercises 29-32, let v=a1,b1,w=a2,b2,u=a3,b3 ,...Ch. 7.5 - Prob. 33PECh. 7.5 - Prob. 34PECh. 7.5 - For Exercises 35-40, find the angle between v and...Ch. 7.5 - For Exercises 35-40, find the angle between v and...Ch. 7.5 - For Exercises 35-40, find the angle between v and...Ch. 7.5 - For Exercises 35-40, find the angle between v and...Ch. 7.5 - For Exercises 35-40, find the angle between v and...Ch. 7.5 - For Exercises 35-40, find the angle between v and...Ch. 7.5 - If v=10 and w=6 and the angle between v and w is...Ch. 7.5 - If v=2.6 and w=8 and the angle between v and w is...Ch. 7.5 - Prob. 43PECh. 7.5 - For Exercises 43-50, determine if the given...Ch. 7.5 - For Exercises 43-50, determine if the given...Ch. 7.5 - Prob. 46PECh. 7.5 - For Exercises 43-50, determine if the given...Ch. 7.5 - For Exercises 43-50, determine if the given...Ch. 7.5 - Prob. 49PECh. 7.5 - For Exercises 43-50, determine if the given...Ch. 7.5 - Given v=3,6 and w=1,3 , a. Find projwv . (See...Ch. 7.5 - Given v=4,3 and w=2,2 , a. Find projwv . b. Find...Ch. 7.5 - Given v=4i+9j and w=2ij , a. Find projwv . b. Find...Ch. 7.5 - Prob. 54PECh. 7.5 - A boat and trailer weighing a total of 450lb are...Ch. 7.5 - A forklift is used to offload freight from a...Ch. 7.5 - Prob. 57PECh. 7.5 - Prob. 58PECh. 7.5 - a. Find the amount of work done in lifting a 50lb...Ch. 7.5 - a. Find the amount of work done pulling an object...Ch. 7.5 - Prob. 61PECh. 7.5 - For Exercises 61-64, find the work done by the...Ch. 7.5 - Prob. 63PECh. 7.5 - Prob. 64PECh. 7.5 - For Exercises 65-68, find the work w done by a...Ch. 7.5 - For Exercises 65-68, find the work w done by a...Ch. 7.5 - For Exercises 65-68, find the work w done by a...Ch. 7.5 - Prob. 68PECh. 7.5 - Prob. 69PECh. 7.5 - For Exercises 69-72, find the work done by a force...Ch. 7.5 - Prob. 71PECh. 7.5 - For Exercises 69-72, find the work done by a force...Ch. 7.5 - Prob. 73PECh. 7.5 - Prob. 74PECh. 7.5 - Prob. 75PECh. 7.5 - A child exerts a force of 28N on the handle of a...Ch. 7.5 - Prob. 77PECh. 7.5 - Prob. 78PECh. 7.5 - Given v=22i55j and w=4i+10j , a. Find the angle...Ch. 7.5 - Prob. 80PECh. 7.5 - Prob. 81PECh. 7.5 - Given c=5,12 and d=10,24 , a. Find the product cd...Ch. 7.5 - If projwv=v , what do you know about v and w?Ch. 7.5 - If projwv=0 , what do you know about v and w?Ch. 7.5 - Given v=4i10j , a. Find two vectors parallel to v,...Ch. 7.5 - Given v=3i9j , a. Find two vectors parallel to v,...Ch. 7.5 - The dot product of vectors can be used in business...Ch. 7.5 - Prob. 88PECh. 7.5 - Prob. 89PECh. 7.5 - Prob. 90PECh. 7.5 - Prob. 91PECh. 7.5 - The individual in Exercise 91 is directed to lose...Ch. 7.5 - Prob. 93PECh. 7.5 - Explain what is meant by decomposing a nonzero...Ch. 7.5 - Prove that v-w2=v2+w22vw .Ch. 7.5 - Prob. 98PECh. 7.5 - Prob. 99PECh. 7.5 - Prob. 100PECh. 7 - For Exercises 1-2, given a point in polar...Ch. 7 - For Exercises 1-2, given a point in polar...Ch. 7 - For Exercises 3-4, convert the ordered pair in...Ch. 7 - For Exercises 3-4, convert the ordered pair in...Ch. 7 - For Exercises 5-6, convert the ordered pair in...Ch. 7 - For Exercises 5-6, convert the ordered pair in...Ch. 7 - For Exercises 7-12, write an equivalent equation...Ch. 7 - For Exercises 7-12, write an equivalent equation...Ch. 7 - For Exercises 7-12, write an equivalent equation...Ch. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - For Exercises 7-12, write an equivalent equation...Ch. 7 - For Exercises 13-16, convert the polar equation to...Ch. 7 - For Exercises 13-16, convert the polar equation to...Ch. 7 - For Exercises 13-16, convert the polar equation to...Ch. 7 - For Exercises 13-16, convert the polar equation to...Ch. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - For Exercises 27-30, determine whether the tests...Ch. 7 - For Exercises 27-30, determine whether the tests...Ch. 7 - For Exercises 27-30, determine whether the tests...Ch. 7 - For Exercises 27-30, determine whether the tests...Ch. 7 - For Exercises 31-32, find the modulus of each...Ch. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - For Exercises 33-34, convert the complex number...Ch. 7 - For Exercises 35-36, given complex numbers z1 and...Ch. 7 - For Exercises 35-36, given complex numbers z1 and...Ch. 7 - For Exercises 37-38, use De Moivre’s theorem to...Ch. 7 - For Exercises 37-38, use De Moivre’s theorem to...Ch. 7 - For Exercises 39-40, find the indicated complex...Ch. 7 - For Exercises 39-40, find the indicated complex...Ch. 7 - For Exercises 41-42, find the indicated complex...Ch. 7 - For Exercises 41-42, find the indicated complex...Ch. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - For Exercises 47-48, refer to vectors v and w in...Ch. 7 - For Exercises 47-48, refer to vectors v and w in...Ch. 7 - For Exercises 49-54, perform the indicated...Ch. 7 - Prob. 50RECh. 7 - Prob. 51RECh. 7 - For Exercises 49-54, perform the indicated...Ch. 7 - Prob. 53RECh. 7 - For Exercises 49-54, perform the indicated...Ch. 7 - Prob. 55RECh. 7 - Prob. 56RECh. 7 - Prob. 57RECh. 7 - Prob. 58RECh. 7 - Prob. 59RECh. 7 - Prob. 60RECh. 7 - For Exercises 61-62, the given forces (in units of...Ch. 7 - For Exercises 61-62, the given forces (in units of...Ch. 7 - Prob. 63RECh. 7 - During a penalty kick, a soccer ball is kicked at...Ch. 7 - A small plane travels 120mph on a bearing of N40E...Ch. 7 - Prob. 66RECh. 7 - For Exercises 66-68, find the indicated value. a...Ch. 7 - For Exercises 66-68, find the indicated value. a....Ch. 7 - For Exercises 69-72 use the dot product to...Ch. 7 - Prob. 70RECh. 7 - Prob. 71RECh. 7 - Prob. 72RECh. 7 - Given v=i+3j and w=2ij a. Find projwv . b. Find...Ch. 7 - Given v=10j and w=9i+12j a. Find projwv . b. Find...Ch. 7 - A van weighing 2200lb is parked on a street with...Ch. 7 - Prob. 76RECh. 7 - Prob. 77RECh. 7 - Prob. 78RECh. 7 - Prob. 79RECh. 7 - Prob. 80RECh. 7 - Convert 5,54 in polar coordinates to rectangular...Ch. 7 - Convert 63,6 in rectangular coordinates to polar...Ch. 7 - Prob. 3TCh. 7 - For Exercises 3-4, write an equivalent equation...Ch. 7 - For Exercises 5-6, write an equivalent equation...Ch. 7 - For Exercises 5-6, write an equivalent equation...Ch. 7 - For Exercises 7-10, graph the polar equation and...Ch. 7 - For Exercises 7-10, graph the polar equation and...Ch. 7 - For Exercises 7-10, graph the polar equation and...Ch. 7 - For Exercises 7-10, graph the polar equation and...Ch. 7 - For Exercises 11-12, determine whether the tests...Ch. 7 - For Exercises 11-12, determine whether the tests...Ch. 7 - Find the modulus of 55i and write the number in...Ch. 7 - Convert 24cos43+isin43 from polar form to...Ch. 7 - Find 12cos143+isin1438cos220+isin220 and write the...Ch. 7 - Find 18cos100+isin10016cos55+isin55 and write the...Ch. 7 - Prob. 17TCh. 7 - Find the cube roots of 8cos56+isin56 .Ch. 7 - For Exercises 19-24, perform the indicated...Ch. 7 - For Exercises 19-24, perform the indicated...Ch. 7 - For Exercises 19-24, perform the indicated...Ch. 7 - For Exercises 19-24, perform the indicated...Ch. 7 - For Exercises 19-24, perform the indicated...Ch. 7 - For Exercises 19-24, perform the indicated...Ch. 7 - Given v=3,10 , a. Find v2 . b. Find vv . c. How...Ch. 7 - Find a unit vector in the direction of v=8i+6j .Ch. 7 - Prob. 27TCh. 7 - Find the magnitude and direction angle 0360 for...Ch. 7 - Prob. 29TCh. 7 - Prob. 30TCh. 7 - The forces F1=6ij,F2=7i2j and F3=9i+3j act on an...Ch. 7 - Given v=7,5 and w=10,12 , Find projwv .Ch. 7 - A plane heading S21E with an an air speed of...Ch. 7 - Prob. 34TCh. 7 - Prob. 35TCh. 7 - Prob. 36TCh. 7 - Find the amount of work done if an object is...Ch. 7 - For Exercises 1-7, solve for y. Write solutions to...Ch. 7 - For Exercises 1-7, solve for y. Write solutions to...Ch. 7 - For Exercises 1-7, solve for y. Write solutions to...Ch. 7 - For Exercises 1-7, solve for y. Write solutions to...Ch. 7 - For Exercises 1-7, solve for y. Write solutions to...Ch. 7 - For Exercises 1-7, solve for y. Write solutions to...Ch. 7 - For Exercises 1-7, solve for y. Write solutions to...Ch. 7 - Prob. 8CRECh. 7 - Prob. 9CRECh. 7 - Write an equation of a line in slope-intercept...Ch. 7 - Write an equation of a line in polar coordinates...Ch. 7 - For Exercises 12-14, solve each triangle. Round to...Ch. 7 - For Exercises 12-14, solve each triangle. Round to...Ch. 7 - For Exercises 12-14, solve each triangle. Round to...Ch. 7 - Evaluate the difference quotient fx+hf(x)h for...Ch. 7 - Give the domain and range of fx=3x .Ch. 7 - Find the period and phase shift of each function....Ch. 7 - The height h (in feet) of a swing above ground...Ch. 7 - Given v=8,3 and w=12,4 , find vector projection of...Ch. 7 - Prob. 20CRE

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Polar Coordinates Basic Introduction, Conversion to Rectangular, How to Plot Points, Negative R Valu; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=aSdaT62ndYE;License: Standard YouTube License, CC-BY