Muscle contraction. In a study of the speed of muscle contraction in frogs under various loads, British biophysicist A. W. Hill determined that the weight w in grams placed on the muscle and the speed of contraction v in centimeters per second are approximately related by an equation of the form w + a v + b = c where a , b , and c are constants. Suppose that for a certain muscle, a = 15 , b = 1 , and c = 90. Express v as a function of w . Find the speed of contraction if a weight of 16 g is placed on the muscle.
Muscle contraction. In a study of the speed of muscle contraction in frogs under various loads, British biophysicist A. W. Hill determined that the weight w in grams placed on the muscle and the speed of contraction v in centimeters per second are approximately related by an equation of the form w + a v + b = c where a , b , and c are constants. Suppose that for a certain muscle, a = 15 , b = 1 , and c = 90. Express v as a function of w . Find the speed of contraction if a weight of 16 g is placed on the muscle.
Solution Summary: The author calculates the speed of contraction vin centimeter per second if a weight is placed on the muscle.
Muscle contraction. In a study of the speed of muscle contraction in frogs under various loads, British biophysicist A. W. Hill determined that the weight
w
in grams
placed on the muscle and the speed of contraction
v
in centimeters per
second
are approximately related by an equation of the form
w
+
a
v
+
b
=
c
where
a
,
b
,
and
c
are constants. Suppose that for a certain muscle,
a
=
15
,
b
=
1
,
and
c
=
90.
Express
v
as a function of
w
. Find the speed of contraction if a weight of
16
g
is placed on the muscle.
Refer to page 100 for problems on graph theory and linear algebra.
Instructions:
•
Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors.
• Interpret the eigenvalues in the context of graph properties like connectivity or clustering.
Discuss applications of spectral graph theory in network analysis.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]
Refer to page 110 for problems on optimization.
Instructions:
Given a loss function, analyze its critical points to identify minima and maxima.
• Discuss the role of gradient descent in finding the optimal solution.
.
Compare convex and non-convex functions and their implications for optimization.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]
Refer to page 140 for problems on infinite sets.
Instructions:
• Compare the cardinalities of given sets and classify them as finite, countable, or uncountable.
•
Prove or disprove the equivalence of two sets using bijections.
• Discuss the implications of Cantor's theorem on real-world computation.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
Chapter 2 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY