Sounds are produced when vibrating objects create pressure waves in some medium such as air. When these variations in pressure reach the human eardrum, it causes the eardrum to vibrate in a similar manner and the ear detects sound. The intensity of sound is measured as power per unit area. The threshold for hearing (minimum sound detectable by a young, healthy ear) is defined to be I 0 = 10 − 12 W / m 2 (watts per square meter). The sound level L , or “loudnessâ€� of sound, is measured in decibels (dB) as L = 10 log I I 0 , where I is the intensity of the given sound. Use this formula for Exercises 95-96. a. Find the sound level of a motorcycle if its intensity is 10 10 times I 0 . b. Find the sound level of a vacuum cleaner if its intensity is 10 7 times I 0 . c. How many times more intense is the sound of a motorcycle than a vacuum cleaner?
Sounds are produced when vibrating objects create pressure waves in some medium such as air. When these variations in pressure reach the human eardrum, it causes the eardrum to vibrate in a similar manner and the ear detects sound. The intensity of sound is measured as power per unit area. The threshold for hearing (minimum sound detectable by a young, healthy ear) is defined to be I 0 = 10 − 12 W / m 2 (watts per square meter). The sound level L , or “loudnessâ€� of sound, is measured in decibels (dB) as L = 10 log I I 0 , where I is the intensity of the given sound. Use this formula for Exercises 95-96. a. Find the sound level of a motorcycle if its intensity is 10 10 times I 0 . b. Find the sound level of a vacuum cleaner if its intensity is 10 7 times I 0 . c. How many times more intense is the sound of a motorcycle than a vacuum cleaner?
Sounds are produced when vibrating objects create pressure waves in some medium such as air. When these variations in pressure reach the human eardrum, it causes the eardrum to vibrate in a similar manner and the ear detects sound. The intensity of sound is measured as power per unit area. The threshold for hearing (minimum sound detectable by a young, healthy ear) is defined to be
I
0
=
10
−
12
W
/
m
2
(watts per square meter). The sound level
L
,
or “loudness� of sound, is measured in decibels (dB) as
L
=
10
log
I
I
0
,
where
I
is the intensity of the given sound. Use this formula for Exercises 95-96.
a. Find the sound level of a motorcycle if its intensity is
10
10
times
I
0
.
b. Find the sound level of a vacuum cleaner if its intensity is
10
7
times
I
0
.
c. How many times more intense is the sound of a motorcycle than a vacuum cleaner?
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY