 1.5.1: To complete the square of x2 + 10x, you would (add/ subtract) the n...
 1.5.2: Use the Square Root Method to solve the equation 1x  222 = 9. (p. ...
 1.5.3: Every equation of the form x2 + y2 + ax + by + c = 0 has a circle a...
 1.5.4: For a circle, the ______ is the distance from the center to any poi...
 1.5.5: The radius of the circle x2 + y2 = 9 is 3.
 1.5.6: The center of the circle 1x + 322 + 1y  222 = 13 is (3, 2).
 1.5.7: In 710, find the center and radius of each circle. Write the standa...
 1.5.8: In 710, find the center and radius of each circle. Write the standa...
 1.5.9: In 710, find the center and radius of each circle. Write the standa...
 1.5.10: In 710, find the center and radius of each circle. Write the standa...
 1.5.11: In 1120,r = 2; 1h, k2 = 10, 02
 1.5.12: In 1120,r = 3; 1h, k2 = 10, 02
 1.5.13: In 1120,r = 2; 1h, k2 = 10, 22
 1.5.14: In 1120,r = 3; 1h, k2 = 11, 02
 1.5.15: In 1120,r = 5; 1h, k2 = 14, 32
 1.5.16: In 1120,r = 4; 1h, k2 = 12, 32
 1.5.17: In 1120,r = 4; 1h, k2 = 1 2, 12
 1.5.18: In 1120,r = 7; 1h, k2 = 15, 22
 1.5.19: In 1120,= 12; 1h, k2 = a120b
 1.5.20: In 1120,r = 12; 1h, k2 = a0,  12
 1.5.21: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.22: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.23: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.24: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.25: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.26: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.27: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.28: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.29: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.30: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.31: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.32: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.33: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.34: In 2134, (a) find the center 1h, k2 and radius r of each circle; (b...
 1.5.35: Center at the origin and containing the point 1 2, 32
 1.5.36: Center 11, 02 and containing the point 1 3, 22
 1.5.37: Center 12, 32 and tangent to the xaxis
 1.5.38: Center 1 3, 12 and tangent to the yaxis
 1.5.39: With endpoints of a diameter at 11, 42 and 1 3, 22
 1.5.40: With endpoints of a diameter at 14, 32 and 10, 12
 1.5.41: Center 1 1, 32 and tangent to the line y = 2
 1.5.42: Center 14, 22 and tangent to the line x = 1
 1.5.43: In 4346, match each graph with the correct equation.
 1.5.44: In 4346, match each graph with the correct equation.
 1.5.45: In 4346, match each graph with the correct equation.
 1.5.46: In 4346, match each graph with the correct equation.
 1.5.47: Find the area of the square in the figure.
 1.5.48: Find the area of the blue shaded region in the figure, assuming the...
 1.5.49: The original Ferris wheel was built in 1893 by Pittsburgh, Pennsylv...
 1.5.50: In 2008, the Singapore Flyer opened as the worlds largest Ferris wh...
 1.5.51: Earth is represented on a map of a portion of the solar system so t...
 1.5.52: The tangent line to a circle may be defined as the line that inters...
 1.5.53: The Greek method for finding the equation of the tangent line to a ...
 1.5.54: Use the Greek method described in to find an equation of the tangen...
 1.5.55: Refer to 52. The line x  2y + 4 = 0 is tangent to a circle at 10, ...
 1.5.56: Find an equation of the line containing the centers of the two circ...
 1.5.57: If a circle of radius 2 is made to roll along the xaxis, what is a...
 1.5.58: If the circumference of a circle is 6p, what is its radius?
 1.5.59: Which of the following equations might have the graph shown? (More ...
 1.5.60: Which of the following equations might have the graph shown? (More ...
 1.5.61: Explain how the center and radius of a circle can be used to graph ...
 1.5.62: A student stated that the center and radius of the graph whose equa...
 1.5.63: Open the Circle: the role of the center applet. Place the cursor on...
 1.5.64: Open the Circle: the role of the radiusapplet. Place the cursor on ...
Solutions for Chapter 1.5: Circles
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 1.5: Circles
Get Full SolutionsSince 64 problems in chapter 1.5: Circles have been answered, more than 52911 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. Chapter 1.5: Circles includes 64 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.