- 4.8.115: In Exercises 115118, solve the right triangle shown in the fi gure....
- 4.8.116: In Exercises 115118, solve the right triangle shown in the fi gure....
- 4.8.117: In Exercises 115118, solve the right triangle shown in the fi gure....
- 4.8.118: In Exercises 115118, solve the right triangle shown in the fi gure....
- 4.8.119: From a point on level ground 80 feet from the base of a building, t...
- 4.8.120: Two buildings with fl at roofs are 60 yards apart. The height of th...
- 4.8.121: You want to measure the height of an antenna on the top of a 125-fo...
- 4.8.122: In Exercises 122123, use the fi gures shown to fi nd the bearing fr...
- 4.8.123: In Exercises 122123, use the fi gures shown to fi nd the bearing fr...
- 4.8.124: A ship is due west of a lighthouse. A second ship is 12 miles south...
- 4.8.125: From city A to city B, a plane fl ies 850 miles at a bearing of N 5...
- 4.8.126: In Exercises 126127, an object moves in simple harmonic motion desc...
- 4.8.127: In Exercises 126127, an object moves in simple harmonic motion desc...
- 4.8.128: In Exercises 128129, an object is attached to a coiled spring. In E...
- 4.8.129: In Exercises 128129, an object is attached to a coiled spring. In E...
Solutions for Chapter 4.8: Precalculus 5th Edition
Full solutions for Precalculus | 5th Edition
See Inverse cotangent function.
Average rate of change of ƒ over [a, b]
The number ƒ(b) - ƒ(a) b - a, provided a ? b.
Axis of symmetry
See Line of symmetry.
Conic section (or conic)
A curve obtained by intersecting a double-napped right circular cone with a plane
A variable that affects a response variable.
See Component form of a vector.
Inverse composition rule
The composition of a one-toone function with its inverse results in the identity function.
Length of an arrow
See Magnitude of an arrow.
Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0
A system of linear equations
Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)
NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx
Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)
A function that assigns real-number values to the outcomes in a sample space.
Real number line
A horizontal line that represents the set of real numbers.
Zeros of a function that are real numbers.
Removable discontinuity at x = a
lim x:a- ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined
Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.