Physiology. In a study on the speed of muscle contraction in frogs under various loads, researchers found that the speed of contraction decreases with increasing loads. More precisely, they found that the relationship between speed of contraction, S (in centimeters per second), and load w , (in grams), is given approximately by S ( w ) = 26 + 0.06 w w w ≥ 5 Graph S .
Physiology. In a study on the speed of muscle contraction in frogs under various loads, researchers found that the speed of contraction decreases with increasing loads. More precisely, they found that the relationship between speed of contraction, S (in centimeters per second), and load w , (in grams), is given approximately by S ( w ) = 26 + 0.06 w w w ≥ 5 Graph S .
Solution Summary: The author analyzes the graph of the function S(w)=26+0.06w
Physiology. In a study on the speed of muscle contraction in frogs under various loads, researchers found that the speed of contraction decreases with increasing loads. More precisely, they found that the relationship between speed of contraction, S (in centimeters per second), and load w, (in grams), is given approximately by
M = log
The formula
determines the magnitude of an earthquake,
where / is the intensity of the earthquake and S is the intensity of
a "standard earthquake." How many times stronger is an
earthquake with a magnitude of 8 than an earthquake with a
magnitude of 6? Show your work.
Now consider equations of the form ×-a=v
= √bx + c, where a, b, and c
are all positive integers and b>1.
(f) Create an equation of this form that has 7 as a solution and
an extraneous solution. Give the extraneous solution.
(g)
What must be true about the value of bx + c to ensure that
there is a real number solution to the equation? Explain.
The equation ×+ 2 = √3x+10 is of the form ×+ a = √bx + c, where a, b, and
c are all positive integers and b > 1. Using this equation as a
model, create your own equation that has extraneous solutions.
(d) Using trial and error with numbers for a, b, and c, create an
equation of the form x + a = √bx + c, where a, b, and c are all
positive integers and b>1 such that 7 is a solution and there
is an extraneous solution. (Hint: Substitute 7 for x, and
choose a value for a. Then square both sides so you can
choose a, b, and c that will make the equation true.)
(e) Solve the equation you created in Part 2a.
Chapter 4 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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