 2.5.1: In your own words, explain what is meant by each term.(a) Perimeter...
 2.5.2: In parts (a)(c), choose one of the following words to make the stat...
 2.5.3: The measure of a straight angle is . Vertical angleshave measures.(...
 2.5.4: If a formula has exactly five variables, how many values would youn...
 2.5.5: Decide whether perimeter or area would be used to solve a problem c...
 2.5.6: Decide whether perimeter or area would be used to solve a problem c...
 2.5.7: Decide whether perimeter or area would be used to solve a problem c...
 2.5.8: Decide whether perimeter or area would be used to solve a problem c...
 2.5.9: Decide whether perimeter or area would be used to solve a problem c...
 2.5.10: Decide whether perimeter or area would be used to solve a problem c...
 2.5.11: Decide whether perimeter or area would be used to solve a problem c...
 2.5.12: Decide whether perimeter or area would be used to solve a problem c...
 2.5.13: A formula is given along with the values of all but one of the vari...
 2.5.14: A formula is given along with the values of all but one of the vari...
 2.5.15: A formula is given along with the values of all but one of the vari...
 2.5.16: A formula is given along with the values of all but one of the vari...
 2.5.17: A formula is given along with the values of all but one of the vari...
 2.5.18: A formula is given along with the values of all but one of the vari...
 2.5.19: A formula is given along with the values of all but one of the vari...
 2.5.20: A formula is given along with the values of all but one of the vari...
 2.5.21: A formula is given along with the values of all but one of the vari...
 2.5.22: A formula is given along with the values of all but one of the vari...
 2.5.23: A formula is given along with the values of all but one of the vari...
 2.5.24: A formula is given along with the values of all but one of the vari...
 2.5.25: C = 16.328 (circumference of a circle);C = 2pr
 2.5.26: C = 2pr C = 8.164
 2.5.27: C = 2pr C = 20p
 2.5.28: C = 2pr C = 100p
 2.5.29: a = pr (area of a circle); r = 4
 2.5.30: a = pr r = 12
 2.5.31: S = 2prh; S = 120p, h = 10
 2.5.32: S = 2prh; S = 720p, h = 30
 2.5.33: The volume of a threedimensional object is a measure of the space ...
 2.5.34: The volume of a threedimensional object is a measure of the space ...
 2.5.35: The volume of a threedimensional object is a measure of the space ...
 2.5.36: The volume of a threedimensional object is a measure of the space ...
 2.5.37: The volume of a threedimensional object is a measure of the space ...
 2.5.38: The volume of a threedimensional object is a measure of the space ...
 2.5.39: The length of a rectangle is 9 in. more than the width. The perimet...
 2.5.40: The width of a rectangle is 3 ft less than the length. The perimete...
 2.5.41: The perimeter of a rectangle is 36 m. The length is 2 m more than t...
 2.5.42: The perimeter of a rectangle is 36 yd. The width is 18 yd less than...
 2.5.43: The longest side of a triangle is 3 in. longer than the shortest si...
 2.5.44: The perimeter of a triangle is 28 ft. The medium side is 4 ft longe...
 2.5.45: Two sides of a triangle have the same length. The third side measur...
 2.5.46: A triangle is such that its medium side is twice as long as its sho...
 2.5.47: Use a formula to solve each problem. (Use 3.14 as an approximation ...
 2.5.48: Use a formula to solve each problem. (Use 3.14 as an approximation ...
 2.5.49: The largest fashion catalogue in the world was published in Hamburg...
 2.5.50: The worlds largest sand painting was created by Buddhist monks in t...
 2.5.51: The area of a triangular road sign is If the base of the sign measu...
 2.5.52: The area of a triangular advertising banner is 96 . If the height o...
 2.5.53: The largest drum ever constructed was made from Japanese cedar and ...
 2.5.54: A drum played at the Royal Festival Hall in London had diameter 13 ...
 2.5.55: The survey plat depicted here shows two lots that form a trapezoid....
 2.5.56: . Lot A in the survey plat is in the shape of a trapezoid. The para...
 2.5.57: The U.S. Postal Service requires that any box sent by Priority Mail...
 2.5.58: The worlds largest sandwich, made by Wild Woodys Chill and Grill in...
 2.5.59: Find the measure of each marked angle. See Example 5.(x + 1) (4x 56)
 2.5.60: Find the measure of each marked angle. See Example 5.(10x + 7) (7x ...
 2.5.61: Find the measure of each marked angle. See Example 5.(8x 2 1)(5x)
 2.5.62: Find the measure of each marked angle. See Example 5.3x 13)(4
 2.5.63: Find the measure of each marked angle. See Example 5.(5x 129) (2x 21)
 2.5.64: Find the measure of each marked angle. See Example 5. (3x + 45) (7x...
 2.5.65: Find the measure of each marked angle. See Example 5.(10x + 15) (12...
 2.5.66: Find the measure of each marked angle. See Example 5.(11x 37)(7x + 27)
 2.5.67: Solve each formula for the specified variable. See Examples 69.d = ...
 2.5.68: Solve each formula for the specified variable. See Examples 69.d = ...
 2.5.69: Solve each formula for the specified variable. See Examples 69.a = ...
 2.5.70: Solve each formula for the specified variable. See Examples 69.a = ...
 2.5.71: Solve each formula for the specified variable. See Examples 69.C = ...
 2.5.72: Solve each formula for the specified variable. See Examples 69.P = ...
 2.5.73: Solve each formula for the specified variable. See Examples 69.V = ...
 2.5.74: Solve each formula for the specified variable. See Examples 69.V = ...
 2.5.75: Solve each formula for the specified variable. See Examples 69.I = ...
 2.5.76: Solve each formula for the specified variable. See Examples 69.I = ...
 2.5.77: Solve each formula for the specified variable. See Examples 69.a = ...
 2.5.78: Solve each formula for the specified variable. See Examples 69.a = ...
 2.5.79: Solve each formula for the specified variable. See Examples 69.V = ...
 2.5.80: Solve each formula for the specified variable. See Examples 69.V = ...
 2.5.81: Solve each formula for the specified variable. See Examples 69.P = ...
 2.5.82: Solve each formula for the specified variable. See Examples 69.P = ...
 2.5.83: Solve each formula for the specified variable. See Examples 69.P = ...
 2.5.84: Solve each formula for the specified variable. See Examples 69.A = ...
 2.5.85: Solve each formula for the specified variable. See Examples 69.y = ...
 2.5.86: Solve each formula for the specified variable. See Examples 69.y = ...
 2.5.87: Solve each formula for the specified variable. See Examples 69.Ax +...
 2.5.88: Solve each formula for the specified variable. See Examples 69.Ax +...
 2.5.89: Solve each formula for the specified variable. See Examples 69.M = ...
 2.5.90: Solve each formula for the specified variable. See Examples 69.C = ...
 2.5.91: Solve each formula for the specified variable. See Examples 69.P = ...
 2.5.92: Solve each formula for the specified variable. See Examples 69.P = ...
 2.5.93: Solve each equation. See Section 2.2.0.06x = 300
 2.5.94: Solve each equation. See Section 2.2.0.4x = 80
 2.5.95: Solve each equation. See Section 2.2.34 = 21
 2.5.96: Solve each equation. See Section 2.2.56x = 30
 2.5.97: Solve each equation. See Section 2.2.3x = 14
 2.5.98: Solve each equation. See Section 2.2.4x = 13
Solutions for Chapter 2.5: Formulas and Additional Applications from Geometry
Full solutions for Beginning Algebra  11th Edition
ISBN: 9780321673480
Solutions for Chapter 2.5: Formulas and Additional Applications from Geometry
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Beginning Algebra was written by and is associated to the ISBN: 9780321673480. Since 98 problems in chapter 2.5: Formulas and Additional Applications from Geometry have been answered, more than 36031 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Beginning Algebra, edition: 11. Chapter 2.5: Formulas and Additional Applications from Geometry includes 98 full stepbystep solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Column space C (A) =
space of all combinations of the columns of A.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Iterative method.
A sequence of steps intended to approach the desired solution.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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 ().

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).