- 2.8.1: In Exercises 14, use the given values to find andEquation Find Given
- 2.8.2: In Exercises 14, use the given values to find andEquation Find Given
- 2.8.3: In Exercises 14, use the given values to find andEquation Find Given
- 2.8.4: In Exercises 14, use the given values to find andEquation Find Given
- 2.8.5: Area The radius of a circle is increasing at a rate of 3 inches per...
- 2.8.6: Volume The radius of a sphere is increasing at a rate of 3 inches p...
- 2.8.7: Area Let be the area of a circle of radius that is changing with re...
- 2.8.8: Volume Let be the volume of a sphere of radius that is changing wit...
- 2.8.9: Volume A spherical balloon is inflated with gas at a rate of 10 cub...
- 2.8.10: Volume The radius rof a right circular cone is increasing at a rate...
- 2.8.11: Cost, Revenue, and Profit A company that manufactures sport supplem...
- 2.8.12: Cost, Revenue, and Profit A company that manufactures pet toys calc...
- 2.8.13: Volume All edges of a cube are expanding at a rate of 3 centimeters...
- 2.8.14: Surface Area All edges of a cube are expanding at a rate of 3 centi...
- 2.8.15: Moving Point A point is moving along the graph of such that is 2 ce...
- 2.8.16: Moving Point A point is moving along the graph of such that is 2 ce...
- 2.8.17: Moving Ladder A 25-foot ladder is leaning against a house (see figu...
- 2.8.18: Boating A boat is pulled by a winch on a dock, and the winch is 12 ...
- 2.8.19: Air Traffic Control An air traffic controller spots two airplanes a...
- 2.8.20: Air Traffic Control An airplane flying at an altitude of 6 miles pa...
- 2.8.21: Baseball A (square) baseball diamond has sides that are 90 feet lon...
- 2.8.22: Advertising Costs A retail sporting goods store estimates that week...
- 2.8.23: Environment An accident at an oil drilling platform is causing a ci...
- 2.8.24: Profit A company is increasing the production of a product at the r...
- 2.8.25: Sales The profit for a product is increasing at a rate of $5600 per...
- 2.8.26: Cost The annual cost (in millions of dollars) for a government agen...
Solutions for Chapter 2.8: Related Rates
Full solutions for Calculus: An Applied Approach | 8th Edition
Addition principle of probability.
P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)
Boxplot (or box-and-whisker plot)
A graph that displays a five-number summary
A degree 3 polynomial function
A statement of equality between two expressions.
equation of a hyperbola
(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1
Variable representing the domain value of a function (usually x).
Inequality symbol or
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative
A function viewed as a mapping of the elements of the domain onto the elements of the range
Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.
Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2- ba2 + b2 i
nth root of a complex number z
A complex number v such that vn = z
A function in which each element of the range corresponds to exactly one element in the domain
One-to-one rule of logarithms
x = y if and only if logb x = logb y.
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)
Position vector of the point (a, b)
The vector <a,b>.
Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02
If a polynomial f(x) is divided by x - c , the remainder is ƒ(c)
Root of a number
See Principal nth root.
A matrix A = [aij] with the property aij = aji for all i and j