For Exercises 79-80, the formula L = 10 log I I 0 gives the loudness of sound L (in dB) based on the intensity of sound I in W/m 2 . The value I 0 = 10 − 12 W/m 2 is the minimal threshold for hearing for midfrequency sounds. Hearing impairment measured according to the minimal sound level (in dB) detected by an individual for sounds at various frequencies. For one frequency, the table depicts the level of hearing impairment. Determine the range that represents the intensity of sound that can be heard by an individual with severe hearing impairment.
For Exercises 79-80, the formula L = 10 log I I 0 gives the loudness of sound L (in dB) based on the intensity of sound I in W/m 2 . The value I 0 = 10 − 12 W/m 2 is the minimal threshold for hearing for midfrequency sounds. Hearing impairment measured according to the minimal sound level (in dB) detected by an individual for sounds at various frequencies. For one frequency, the table depicts the level of hearing impairment. Determine the range that represents the intensity of sound that can be heard by an individual with severe hearing impairment.
Solution Summary: The author calculates the range of the loudness of sound that can be heard by an individual with a severe hearing impairment.
For Exercises 79-80, the formula
L
=
10
log
I
I
0
gives the loudness of sound L (in dB) based on the intensity of sound
I
in W/m
2
. The value
I
0
=
10
−
12
W/m
2
is the minimal threshold for hearing for midfrequency sounds. Hearing impairment measured according to the minimal sound level (in dB) detected by an individual for sounds at various frequencies. For one frequency, the table depicts the level of hearing impairment.
Determine the range that represents the intensity of sound that can be heard by an individual with severe hearing impairment.
4.
The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x².
a) Find the average rate of change of revenue when the production is increased from 1000 to 1001 units.
MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
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