 3.10.1: If is the volume of a cube with edge length and the cube expands as...
 3.10.2: (a) If is the area of a circle with radius and the circle expands a...
 3.10.3: If y x dx dt 5 dy dt x 2 3 2x 1 and , find when .
 3.10.4: If x dy dt 6 dx dt y 4 2 y2 25 y and , find when .
 3.10.5: If , , and , find when and .
 3.10.6: A particle moves along the curve . As it reaches the point , the c...
 3.10.7: (a) What quantities are given in the problem? (b) What is the unkno...
 3.10.8: (a) What quantities are given in the problem? (b) What is the unkno...
 3.10.9: (a) What quantities are given in the problem? (b) What is the unkno...
 3.10.10: (a) What quantities are given in the problem? (b) What is the unkno...
 3.10.11: Two cars start moving from the same point. One travels south at 60 ...
 3.10.12: A spotlight on the ground shines on a wall 12 m away. If a man 2 m ...
 3.10.13: A man starts walking north at 4 ft s from a point . Five minutes la...
 3.10.14: A baseball diamond is a square with side 90 ft. A batter hits the b...
 3.10.15: The altitude of a triangle is increasing at a rate of 1 cm min whil...
 3.10.16: A boat is pulled into a dock by a rope attached to the bow of the b...
 3.10.17: At noon, ship A is 100 km west of ship B. Ship A is sailing south a...
 3.10.18: A particle is moving along the curve . As the particle passes throu...
 3.10.19: Water is leaking out of an inverted conical tank at a rate of 10,00...
 3.10.20: A trough is 10 ft long and its ends have the shape of isosceles tri...
 3.10.21: A water trough is 10 m long and a crosssection has the shape of an...
 3.10.22: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow...
 3.10.23: Gravel is being dumped from a conveyor belt at a rate of 30 , and i...
 3.10.24: A kite 100 ft above the ground moves horizontally at a speed of 8 f...
 3.10.25: Two sides of a triangle are 4 m and 5 m in length and the angle bet...
 3.10.26: Two sides of a triangle have lengths 12 m and 15 m. The angle betwe...
 3.10.27: Boyles Law states that when a sample of gas is compressed at a cons...
 3.10.28: When air expands adiabatically (without gaining or losing heat), it...
 3.10.29: If two resistors with resistances and are connected in parallel, as...
 3.10.30: Brain weight as a function of body weight in fish has been modeled ...
 3.10.31: A ladder 10 ft long rests against a vertical wall. If the bottom of...
 3.10.32: Two carts, A and B, are connected by a rope 39 ft long that passes ...
 3.10.33: A television camera is positioned 4000 ft from the base of a rocket...
 3.10.34: A lighthouse is located on a small island 3 km away from the neares...
 3.10.35: A plane flying with a constant speed of 300 kmh passes over a groun...
 3.10.36: Two people start from the same point. One walks east at 3 mih and t...
 3.10.37: A runner sprints around a circular track of radius 100 m at a const...
 3.10.38: The minute hand on a watch is 8 mm long and the hour hand is 4 mm l...
Solutions for Chapter 3.10: Related Rates
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 3.10: Related Rates
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus,, edition: 5. Since 38 problems in chapter 3.10: Related Rates have been answered, more than 48025 students have viewed full stepbystep solutions from this chapter. Calculus, was written by and is associated to the ISBN: 9780534393397. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.10: Related Rates includes 38 full stepbystep solutions.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Differentiable at x = a
ƒ'(a) exists

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Equivalent vectors
Vectors with the same magnitude and direction.

Extracting square roots
A method for solving equations in the form x 2 = k.

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Frequency table (in statistics)
A table showing frequencies.

Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Modified boxplot
A boxplot with the outliers removed.

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Parallel lines
Two lines that are both vertical or have equal slopes.

Parameter
See Parametric equations.

Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

Real axis
See Complex plane.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Relation
A set of ordered pairs of real numbers.

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Solve by substitution
Method for solving systems of linear equations.

Triangular form
A special form for a system of linear equations that facilitates finding the solution.