119. Current in an RL Circuit The equation governing the amount of current I (in amperes) after time t (in seconds) in a single RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys), and an electromotive force E (in voles) is I = E R [ 1 − e − ( R / L ) t ] (a) If E = 120 volts, R = 10 ohms, and L = 5 henrys, how much current I 1 is flowing after 0.3 second? After 0.5 second? After 1 second? (b) What is the maximum current? (c) Graph this function I = I 1 (t), measuring I along the y -axis and t along the x -axis . (d) If E = 120 volts, R = 5 ohms, and L = 10 henrys, how much current I 2 is flowing after 0.3 second? After 0.5 second? After 1 second? (e) What is the maximum current? (f) Graph the function I = I 2 ( t ) on the same coordinate axes as I 1 ( t ) .
119. Current in an RL Circuit The equation governing the amount of current I (in amperes) after time t (in seconds) in a single RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys), and an electromotive force E (in voles) is I = E R [ 1 − e − ( R / L ) t ] (a) If E = 120 volts, R = 10 ohms, and L = 5 henrys, how much current I 1 is flowing after 0.3 second? After 0.5 second? After 1 second? (b) What is the maximum current? (c) Graph this function I = I 1 (t), measuring I along the y -axis and t along the x -axis . (d) If E = 120 volts, R = 5 ohms, and L = 10 henrys, how much current I 2 is flowing after 0.3 second? After 0.5 second? After 1 second? (e) What is the maximum current? (f) Graph the function I = I 2 ( t ) on the same coordinate axes as I 1 ( t ) .
Solution Summary: The author calculates how much current I 1 is flowing after 0.3 second, 7.5855, and 10.3760, respectively, when time approaches infinity.
119. Current in an RL Circuit The equation governing the amount of current I (in amperes) after time t (in seconds) in a single RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys), and an electromotive force E (in voles) is
(a) If
volts,
ohms, and
henrys, how much current I1 is flowing after 0.3 second? After 0.5 second? After 1 second?
(b) What is the maximum current?
(c) Graph this function
(t), measuring I along the
and t along the
.
(d) If
volts,
ohms, and
henrys, how much current I2 is flowing after 0.3 second? After 0.5 second? After 1 second?
(e) What is the maximum current?
(f) Graph the function
on the same coordinate axes as
.
Let h(x, y, z)
=
—
In (x) — z
y7-4z
-
y4
+ 3x²z — e²xy ln(z) + 10y²z.
(a) Holding all other variables constant, take the partial derivative of h(x, y, z) with
respect to x, 2 h(x, y, z).
მ
(b) Holding all other variables constant, take the partial derivative of h(x, y, z) with
respect to y, 2 h(x, y, z).
ints) A common representation of data uses matrices and vectors, so it is helpful
to familiarize ourselves with linear algebra notation, as well as some simple operations.
Define a vector ♬ to be a column vector. Then, the following properties hold:
• cu with c some constant, is equal to a new vector where every element in cv is equal
to the corresponding element in & multiplied by c. For example, 2
2
=
● √₁ + √2 is equal to a new vector with elements equal to the elementwise addition of
₁ and 2. For example,
問
2+4-6
=
The above properties form our definition for a linear combination of vectors. √3 is a
linear combination of √₁ and √2 if √3 = a√₁ + b√2, where a and b are some constants.
Oftentimes, we stack column vectors to form a matrix. Define the column rank of
a matrix A to be equal to the maximal number of linearly independent columns in
A. A set of columns is linearly independent if no column can be written as a linear
combination of any other column(s) within the set. If all…
The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 3.
Select all that apply:
7
-6-
5
4
3
2
1-
-7-6-5-4-3-2-1 1 2 3 4 5 6 7
+1
-2·
3.
-4
-6-
f(x) is not continuous at a
=
3 because it is not defined at x = 3.
☐
f(x) is not continuous at a
=
- 3 because lim f(x) does not exist.
2-3
f(x) is not continuous at x = 3 because lim f(x) ‡ ƒ(3).
→3
O f(x) is continuous at a = 3.
Chapter 5 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
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