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Let’s check out your problem:
=
2
π
V
∗
1
+
(
e
−
J
2
)
=
=2\pi V*1+\left(\frac{e^{-J}}{2}\right)=
=
2
πV
∗
1
+
(
2
e
−
J
)
=
View step-by-step help
Home
Math Problems
Algebra 2
Composition of linear and quadratic functions: find a value
Full solution
Q.
=
2
π
V
∗
1
+
(
e
−
J
2
)
=
=2\pi V*1+\left(\frac{e^{-J}}{2}\right)=
=
2
πV
∗
1
+
(
2
e
−
J
)
=
Plug in and simplify:
First, let's plug in the values we know and simplify the expression.
2
π
V
×
(
1
+
e
−
J
2
)
2\pi V \times \left(1 + \frac{e^{-J}}{2}\right)
2
πV
×
(
1
+
2
e
−
J
)
Distribute
2
π
V
2\pi V
2
πV
:
Now, we need to distribute
2
π
V
2\pi V
2
πV
across the terms inside the parentheses.
\newline
2
π
V
×
1
+
2
π
V
×
(
e
−
J
2
)
2\pi V \times 1 + 2\pi V \times \left(\frac{e^{-J}}{2}\right)
2
πV
×
1
+
2
πV
×
(
2
e
−
J
)
Simplify first term:
Simplify the first term by multiplying
2
π
V
2\pi V
2
πV
by
1
1
1
.
2
π
V
+
2
π
V
×
(
e
−
J
2
)
2\pi V + 2\pi V \times \left(\frac{e^{-J}}{2}\right)
2
πV
+
2
πV
×
(
2
e
−
J
)
Divide by
2
2
2
:
Next, divide
2
π
V
2\pi V
2
πV
by
2
2
2
to simplify the second term.
\newline
2
π
V
+
π
V
⋅
e
(
−
J
)
2\pi V + \pi V \cdot e^{(-J)}
2
πV
+
πV
⋅
e
(
−
J
)
Combine terms:
Combine the terms to get the final expression.
2
π
V
+
π
V
⋅
e
−
J
2\pi V + \pi V \cdot e^{-J}
2
πV
+
πV
⋅
e
−
J
is the simplified form of the original expression.
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