 10.4.1: A coast artillery gun can fire at any angle of elevation between an...
 10.4.2: In Exercises 1 and 2, approximate the coordinates of the points.
 10.4.3: In Exercises 1 and 2, approximate the coordinates of the points.
 10.4.4: In Exercises 36, plot the points on the same threedimensional coor...
 10.4.5: In Exercises 36, plot the points on the same threedimensional coor...
 10.4.6: In Exercises 36, plot the points on the same threedimensional coor...
 10.4.7: In Exercises 36, plot the points on the same threedimensional coor...
 10.4.8: In Exercises 710, find the coordinates of the point.The point is lo...
 10.4.9: In Exercises 710, find the coordinates of the point.The point is lo...
 10.4.10: In Exercises 710, find the coordinates of the point.The point is lo...
 10.4.11: In Exercises 710, find the coordinates of the point.The point is lo...
 10.4.12: Think About It What is the coordinate of any point in the plane?
 10.4.13: Think About It What is the coordinate of any point in the plane?
 10.4.14: In Exercises 1324, determine the location of a point that satisfies...
 10.4.15: In Exercises 1324, determine the location of a point that satisfies...
 10.4.16: In Exercises 1324, determine the location of a point that satisfies...
 10.4.17: In Exercises 1324, determine the location of a point that satisfies...
 10.4.18: In Exercises 1324, determine the location of a point that satisfies...
 10.4.19: In Exercises 1324, determine the location of a point that satisfies...
 10.4.20: In Exercises 1324, determine the location of a point that satisfies...
 10.4.21: In Exercises 1324, determine the location of a point that satisfies...
 10.4.22: In Exercises 1324, determine the location of a point that satisfies...
 10.4.23: In Exercises 1324, determine the location of a point that satisfies...
 10.4.24: In Exercises 1324, determine the location of a point that satisfies...
 10.4.25: In Exercises 1324, determine the location of a point that satisfies...
 10.4.26: In Exercises 2528, find the distance between the points.0, 0, 0, 4,...
 10.4.27: In Exercises 2528, find the distance between the points.2, 3, 2, 2,...
 10.4.28: In Exercises 2528, find the distance between the points.1, 2, 4, 6,...
 10.4.29: In Exercises 2528, find the distance between the points.2, 2, 3, 4,...
 10.4.30: In Exercises 2932, find the lengths of the sides of the triangle wi...
 10.4.31: In Exercises 2932, find the lengths of the sides of the triangle wi...
 10.4.32: In Exercises 2932, find the lengths of the sides of the triangle wi...
 10.4.33: In Exercises 2932, find the lengths of the sides of the triangle wi...
 10.4.34: Think About It The triangle in Exercise 29 is translated five units...
 10.4.35: Think About It The triangle in Exercise 30 is translated three unit...
 10.4.36: In Exercises 35 and 36, find the coordinates of the midpoint of the...
 10.4.37: In Exercises 35 and 36, find the coordinates of the midpoint of the...
 10.4.38: In Exercises 37 40, find the standard equation of the sphere.
 10.4.39: In Exercises 37 40, find the standard equation of the sphere.
 10.4.40: In Exercises 37 40, find the standard equation of the sphere.Endpoi...
 10.4.41: In Exercises 37 40, find the standard equation of the sphere.
 10.4.42: In Exercises 41 44, complete the square to write the equation of th...
 10.4.43: In Exercises 41 44, complete the square to write the equation of th...
 10.4.44: In Exercises 41 44, complete the square to write the equation of th...
 10.4.45: In Exercises 41 44, complete the square to write the equation of th...
 10.4.46: In Exercises 4548, describe the solid satisfying the condition.
 10.4.47: In Exercises 4548, describe the solid satisfying the condition.
 10.4.48: In Exercises 4548, describe the solid satisfying the condition.
 10.4.49: In Exercises 4548, describe the solid satisfying the condition.
 10.4.50: In Exercises 4952, (a) find the component form of the vector v, (b)...
 10.4.51: In Exercises 4952, (a) find the component form of the vector v, (b)...
 10.4.52: In Exercises 4952, (a) find the component form of the vector v, (b)...
 10.4.53: In Exercises 4952, (a) find the component form of the vector v, (b)...
 10.4.54: In Exercises 5356, find the component form and magnitude of the vec...
 10.4.55: In Exercises 5356, find the component form and magnitude of the vec...
 10.4.56: In Exercises 5356, find the component form and magnitude of the vec...
 10.4.57: In Exercises 5356, find the component form and magnitude of the vec...
 10.4.58: In Exercises 57 and 58, the initial and terminal points of a vector...
 10.4.59: In Exercises 57 and 58, the initial and terminal points of a vector...
 10.4.60: In Exercises 59 and 60, the vector and its initial point are given....
 10.4.61: In Exercises 59 and 60, the vector and its initial point are given....
 10.4.62: In Exercises 61 and 62, find each scalar multiple of and sketch its...
 10.4.63: In Exercises 61 and 62, find each scalar multiple of and sketch its...
 10.4.64: In Exercises 63 68, find the vector given that and w 4, 0, 4.
 10.4.65: In Exercises 63 68, find the vector given that and w 4, 0, 4.
 10.4.66: In Exercises 63 68, find the vector given that and w 4, 0, 4.
 10.4.67: In Exercises 63 68, find the vector given that and w 4, 0, 4.
 10.4.68: In Exercises 63 68, find the vector given that and w 4, 0, 4.
 10.4.69: In Exercises 63 68, find the vector given that and w 4, 0, 4.
 10.4.70: In Exercises 6972, determine which of the vectors is (are) parallel...
 10.4.71: In Exercises 6972, determine which of the vectors is (are) parallel...
 10.4.72: In Exercises 6972, determine which of the vectors is (are) parallel...
 10.4.73: In Exercises 6972, determine which of the vectors is (are) parallel...
 10.4.74: In Exercises 7376, use vectors to determine whether the points are ...
 10.4.75: In Exercises 7376, use vectors to determine whether the points are ...
 10.4.76: In Exercises 7376, use vectors to determine whether the points are ...
 10.4.77: In Exercises 7376, use vectors to determine whether the points are ...
 10.4.78: In Exercises 77 and 78, use vectors to show that the points form th...
 10.4.79: In Exercises 77 and 78, use vectors to show that the points form th...
 10.4.80: In Exercises 7984, find the magnitude of v
 10.4.81: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.82: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.83: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.84: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.85: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.86: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.87: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.88: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.89: In Exercises 85 88, find a unit vector (a) in the direction of v an...
 10.4.90: Programming You are given the component forms of the vectors and Wr...
 10.4.91: Consider the two nonzero vectors and and let and be real numbers. D...
 10.4.92: In Exercises 91 and 92, determine the values of that satisfy the eq...
 10.4.93: In Exercises 91 and 92, determine the values of that satisfy the eq...
 10.4.94: In Exercises 9396, find the vector with the given magnitude and dir...
 10.4.95: In Exercises 9396, find the vector with the given magnitude and dir...
 10.4.96: In Exercises 9396, find the vector with the given magnitude and dir...
 10.4.97: In Exercises 9396, find the vector with the given magnitude and dir...
 10.4.98: In Exercises 97 and 98, sketch the vector and write its component f...
 10.4.99: In Exercises 97 and 98, sketch the vector and write its component f...
 10.4.100: In Exercises 99 and 100, use vectors to find the point that lies tw...
 10.4.101: In Exercises 99 and 100, use vectors to find the point that lies tw...
 10.4.102: Let and (a) Sketch and (b) If show that and must both be zero. (c) ...
 10.4.103: Writing The initial and terminal points of the vector are and Descr...
 10.4.104: A point in the threedimensional coordinate system has coordinates ...
 10.4.105: Give the formula for the distance between the points x . 1, y1, z1
 10.4.106: Give the standard equation of a sphere of radius centered at x0, y0...
 10.4.107: State the definition of parallel vectors.
 10.4.108: Let and be vertices of a triangle. Find AB\ BC\ CA\A, B, C .
 10.4.109: Let and Describe the set of all points such that r r0 x, y, z 2.
 10.4.110: Numerical, Graphical, and Analytic Analysis The lights in an audito...
 10.4.111: Think About It Suppose the length of each cable in Exercise 109 has...
 10.4.112: Diagonal of a Cube Find the component form of the unit vector in th...
 10.4.113: Tower Guy Wire The guy wire supporting a 100foot tower has a tensi...
 10.4.114: Load Supports Find the tension in each of the supporting cables in ...
 10.4.115: Construction A precast concrete wall is temporarily kept in its ver...
 10.4.116: Write an equation whose graph consists of the set of points that ar...
 10.4.117: In Exercises 18, find (a) (b) (c) (d) and (e) u 2vu 3, 4, v 1, 5 u
 10.4.118: In Exercises 18, find (a) (b) (c) (d) and (e) u 2v
 10.4.119: In Exercises 18, find (a) (b) (c) (d) and (e) u 2v
 10.4.120: In Exercises 18, find (a) (b) (c) (d) and (e) u 2vu 4, 8, v 7, 5u
 10.4.121: In Exercises 18, find (a) (b) (c) (d) and (e) u 2vu 2, 3, 4, v 0, 6...
 10.4.122: In Exercises 18, find (a) (b) (c) (d) and (e) u 2vu i, v i
Solutions for Chapter 10.4: Polar Coordinates and Polar Graphs
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 10.4: Polar Coordinates and Polar Graphs
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9. Since 122 problems in chapter 10.4: Polar Coordinates and Polar Graphs have been answered, more than 61052 students have viewed full stepbystep solutions from this chapter. Calculus was written by and is associated to the ISBN: 9780547167022. Chapter 10.4: Polar Coordinates and Polar Graphs includes 122 full stepbystep solutions.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Bar chart
A rectangular graphical display of categorical data.

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

Index of summation
See Summation notation.

Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Multiplication property of equality
If u = v and w = z, then uw = vz

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Rational zeros
Zeros of a function that are rational numbers.

Reciprocal function
The function ƒ(x) = 1x

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Solve a system
To find all solutions of a system.

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Translation
See Horizontal translation, Vertical translation.

Vertical translation
A shift of a graph up or down.