In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y = f ( x ) to represent a function, an applied problem might use C = C ( q ) to represent the cost C of manufacturing q units of a good. Because of this, the inverse notation f − 1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C = C ( q ) will be q = q ( C ) . So C = C ( q ) is a function that represents the cost C as a function of the number q of units manufactured, and q = q ( C ) is a function that represents the number q as a function of the cost C . Problems 91-94 illustrate this idea. Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function W ( h ) = 50 + 2.3 ( h − 60 ) (a) What is the ideal weight of a 6-foot male? (b) Express the height h as a function of weight W . (c) Verify that h = h ( W ) is the inverse of W = W ( h ) by showing that h ( W ( h ) ) = h and W ( h ( W ) ) = W . (d) What is the height of a male who is at his ideal weight of 80 kilograms? [ Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given by W ( h ) = 45.5 + 2.3 ( h − 60 ) .
In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y = f ( x ) to represent a function, an applied problem might use C = C ( q ) to represent the cost C of manufacturing q units of a good. Because of this, the inverse notation f − 1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C = C ( q ) will be q = q ( C ) . So C = C ( q ) is a function that represents the cost C as a function of the number q of units manufactured, and q = q ( C ) is a function that represents the number q as a function of the cost C . Problems 91-94 illustrate this idea. Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function W ( h ) = 50 + 2.3 ( h − 60 ) (a) What is the ideal weight of a 6-foot male? (b) Express the height h as a function of weight W . (c) Verify that h = h ( W ) is the inverse of W = W ( h ) by showing that h ( W ( h ) ) = h and W ( h ( W ) ) = W . (d) What is the height of a male who is at his ideal weight of 80 kilograms? [ Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given by W ( h ) = 45.5 + 2.3 ( h − 60 ) .
Solution Summary: The author explains the ideal body weight W for men as a function of height h (in inches).
In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using
to represent a function, an applied problem might use
to represent the cost
of manufacturing q units of a good. Because of this, the inverse notation
used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as
will be
. So
is a function that represents the cost
as a function of the number
of units manufactured, and
is a function that represents the number
as a function of the cost
. Problems 91-94 illustrate this idea.
Ideal Body Weight One model for the ideal body weight
for men (in kilograms) as a function of height
(in inches) is given by the function
(a) What is the ideal weight of a 6-foot male?
(b) Express the height
as a function of weight
.
(c) Verify that
is the inverse of
by showing that
and
.
(d) What is the height of a male who is at his ideal weight of 80 kilograms?
[Note: The ideal body weight
for women (in kilograms) as a function of height
(in inches) is given by
.
Exercise 1
Given are the following planes:
plane 1:
3x4y+z = 1
0
plane 2:
(s, t) =
( 2 ) + (
-2
5 s+
0
(
3 t
2
-2
a) Find for both planes the Hessian normal form and for plane 1 in addition the parameter form.
b) Use the cross product of the two normal vectors to show that the planes intersect in a line.
c) Calculate the intersection line.
d) Calculate the intersection angle of the planes. Make a sketch to indicate which angle you are
calculating.
Only 100% sure experts solve it correct complete solutions ok
rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
Chapter 5 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY