 3.9.1: If is the volume of a cube with edge length and the cube expands as...
 3.9.2: . (a) If is the area of a circle with radius and the circle expands...
 3.9.3: Each side of a square is increasing at a rate of . At what rate is ...
 3.9.4: The length of a rectangle is increasing at a rate of and its width ...
 3.9.5: A cylindrical tank with radius 5 m is being filled with water at a ...
 3.9.6: The radius of a sphere is increasing at a rate of . How fast is the...
 3.9.7: . Suppose , where and are functions of . (a) If , find when . (b) I...
 3.9.8: Suppose , where and are functions of . (a) If , find when and . (b)...
 3.9.9: x dxdt 5 dydt 4 dzdt 2 y 2 z 2 9 y 2
 3.9.10: A particle is moving along a hyperbola . As it reaches the point , ...
 3.9.11: 1114 (a) What quantities are given in the problem? (b) What is the ...
 3.9.12: 1114 (a) What quantities are given in the problem? (b) What is the ...
 3.9.13: 1114 (a) What quantities are given in the problem? (b) What is the ...
 3.9.14: 1114 (a) What quantities are given in the problem? (b) What is the ...
 3.9.15: Two cars start moving from the same point. One travels south at 60 ...
 3.9.16: A spotlight on the ground shines on a wall 12 m away. If a man 2 m ...
 3.9.17: A man starts walking north at 4 fts from a point . Five minutes lat...
 3.9.18: A baseball diamond is a square with side 90 ft. A batter hits the b...
 3.9.19: The altitude of a triangle is increasing at a rate of 1 cmmin while...
 3.9.20: 0. A boat is pulled into a dock by a rope attached to the bow of th...
 3.9.21: At noon, ship A is 100 km west of ship B. Ship A is sailing south a...
 3.9.22: A particle moves along the curve . As the particle passes through t...
 3.9.23: Water is leaking out of an inverted conical tank at a rate of 10,00...
 3.9.24: A trough is 10 ft long and its ends have the shape of isosceles tri...
 3.9.25: A water trough is 10 m long and a crosssection has the shape of an...
 3.9.26: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow...
 3.9.27: Gravel is being dumped from a conveyor belt at a rate of 30 , and i...
 3.9.28: A kite 100 ft above the ground moves horizontally at a speed of 8 f...
 3.9.29: Two sides of a triangle are 4 m and 5 m in length and the angle bet...
 3.9.30: How fast is the angle between the ladder and the ground changing in...
 3.9.31: The top of a ladder slides down a vertical wall at a rate of . At t...
 3.9.32: A faucet is filling a hemispherical basin of diameter 60 cm with wa...
 3.9.33: . Boyles Law states that when a sample of gas is compressed at a co...
 3.9.34: When air expands adiabatically (without gaining or losing heat), it...
 3.9.35: If two resistors with resistances and are connected in parallel, as...
 3.9.36: Brain weight as a function of body weight in fish has been modeled ...
 3.9.37: Two sides of a triangle have lengths 12 m and 15 m. The angle betwe...
 3.9.38: Two carts, A and B, are connected by a rope 39 ft long that passes ...
 3.9.39: A television camera is positioned 4000 ft from the base of a rocket...
 3.9.40: A lighthouse is located on a small island 3 km away from the neares...
 3.9.41: A plane flies horizontally at an altitude of and passes directly ov...
 3.9.42: A Ferris wheel with a radius of is rotating at a rate of one revolu...
 3.9.43: A plane flying with a constant speed of 300 kmh passes over a groun...
 3.9.44: Two people start from the same point. One walks east at 3 mih and t...
 3.9.45: A runner sprints around a circular track of radius 100 m at a const...
 3.9.46: The minute hand on a watch is 8 mm long and the hour hand is 4 mm l...
Solutions for Chapter 3.9: RELATED RATES
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 3.9: RELATED RATES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. Chapter 3.9: RELATED RATES includes 46 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Since 46 problems in chapter 3.9: RELATED RATES have been answered, more than 29414 students have viewed full stepbystep solutions from this chapter.

Base
See Exponential function, Logarithmic function, nth power of a.

Circle graph
A circular graphical display of categorical data

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

Finite series
Sum of a finite number of terms.

Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers

Logarithmic form
An equation written with logarithms instead of exponents

Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.

Phase shift
See Sinusoid.

Polar equation
An equation in r and ?.

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Random behavior
Behavior that is determined only by the laws of probability.

Reciprocal function
The function ƒ(x) = 1x

Secant line of ƒ
A line joining two points of the graph of ƒ.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Standard deviation
A measure of how a data set is spread

Standard representation of a vector
A representative arrow with its initial point at the origin

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Vertical stretch or shrink
See Stretch, Shrink.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.