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Elan Coil [88]
3 years ago
5

Find the Laplace transform of the given function; a and b are real constants. f(t) = eat sinh bt Your answer should be an expres

sion in terms of a, b and s. L{f(t)}(s) = F(s) =
Mathematics
1 answer:
erik [133]3 years ago
6 0

Laplace transform of f(t) is  

L[f(t)] = \frac{1}{s-(a+b)}-\frac{1}{s-(a-b)}

Step-by-step explanation:

Given that f(t) = e^{at} sinh bt

Also, sinhx=\frac{e^{x}-e^{-x} }{2}

Simplyfing,

f(t) = e^{at} \frac{e^{bt}-e^{-bt} }{2}

f(t) = \frac{e^{bt+at}-e^{-bt+at} }{2}

f(t) = \frac{e^{(a+b)t}-e^{(a-b)t} }{2}

Now, we know

L(e^{at}) = \frac{1}{s-a}

Therefore,

L[f(t)] =L[ \frac{e^{(a+b)t}}{2}- \frac{e^{(a-b)t}}{2} ]

L[f(t)] = \frac{1}{s-(a+b)}-\frac{1}{s-(a-b)}

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Answer:

0.5,1.2,23,-34,-73

Step-by-step explanation:

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vitfil [10]
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(Another Question from meh since Imma dum kid) How do you know when you can stop looking for factors of a number?
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3 years ago
An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the d
nignag [31]

Solution:

Step 1:

We will calculate the volume of ice cream in the single scoop

The volume of the ice cream will be

\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}

By substituting the values, we will have

\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}

Step 2:

We will use the formula below to calculate the volume of the two scoops of ic cream

\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}

Step 3:

We will use the formula below to calculate the volume of the three scoops of ic cream

\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}

For the first ice cream with one scoop

\begin{gathered} 1in^3=\frac{3.50}{11.79} \\ 1in^3=\text{ \$}0.30 \end{gathered}

For the second ice cream with two scoops

\begin{gathered} 1in^3=\frac{4.50}{18.86} \\ 1in^3=\text{ \$}0.24 \end{gathered}

For the third ice cream with three scoops

\begin{gathered} 1in^3=\frac{5.50}{25.93} \\ 1in^3=\text{ \$}0.21 \end{gathered}

Hence,

The final answer is

The triple sold at $5.50 has the best value because it has the lowest price of $0.21 per cubic inch of the ice cream

3 0
1 year ago
Check Register Balance $526.13 Bank Statement Balance $531.38 Outstanding Checks $62.45 and $18.75 Service Charges $75.95 What i
mrs_skeptik [129]
WOULD IT BE THE FIRST ONE ($526.13)

7 0
3 years ago
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