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3 years ago

I need help with this question ASAP!!!

Mathematics

1 answer:

alex41 [277]3 years ago

4 0

I’m not sure sorry also it past due

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Find the laplace transform of f(t) = cosh kt = (e kt + e −kt)/2

iren2701 [21]

Hello there, hope I can help!

I assume you mean $L\left\{\frac{ekt+e-kt}{2}\right\}$
With that, let's begin

$\frac{ekt+e-kt}{2}=\frac{ekt}{2}+\frac{e}{2}-\frac{kt}{2} \ \textgreater \ L\left\{\frac{ekt}{2}-\frac{kt}{2}+\frac{e}{2}\right\}$

$\mathrm{Use\:the\:linearity\:property\:of\:Laplace\:Transform}$
$\mathrm{For\:functions\:}f\left(t\right),\:g\left(t\right)\mathrm{\:and\:constants\:}a,\:b$
$L\left\{a\cdot f\left(t\right)+b\cdot g\left(t\right)\right\}=a\cdot L\left\{f\left(t\right)\right\}+b\cdot L\left\{g\left(t\right)\right\}$
$\frac{ek}{2}L\left\{t\right\}+L\left\{\frac{e}{2}\right\}-\frac{k}{2}L\left\{t\right\}$

$L\left\{t\right\} \ \textgreater \ \mathrm{Use\:Laplace\:Transform\:table}: \:L\left\{t\right\}=\frac{1}{s^2} \ \textgreater \ L\left\{t\right\}=\frac{1}{s^2}$

$L\left\{\frac{e}{2}\right\} \ \textgreater \ \mathrm{Use\:Laplace\:Transform\:table}: \:L\left\{a\right\}=\frac{a}{s} \ \textgreater \ L\left\{\frac{e}{2}\right\}=\frac{\frac{e}{2}}{s} \ \textgreater \ \frac{e}{2s}$

$\frac{ek}{2}\cdot \frac{1}{s^2}+\frac{e}{2s}-\frac{k}{2}\cdot \frac{1}{s^2}$

$\frac{ek}{2}\cdot \frac{1}{s^2} \ \textgreater \ \mathrm{Multiply\:fractions}: \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d} \ \textgreater \ \frac{ek\cdot \:1}{2s^2} \ \textgreater \ \mathrm{Apply\:rule}\:1\cdot \:a=a$
$\frac{ek}{2s^2}$

$\frac{k}{2}\cdot \frac{1}{s^2} \ \textgreater \ \mathrm{Multiply\:fractions}: \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d} \ \textgreater \ \frac{k\cdot \:1}{2s^2} \ \textgreater \ \mathrm{Apply\:rule}\:1\cdot \:a=a$
$\frac{k}{2s^2}$

$\frac{ek}{2s^2}+\frac{e}{2s}-\frac{k}{2s^2}$

Hope this helps!

3 0

3 years ago

Please help I will give 10 points

vazorg [7]

Answer:

x = 13.75

Step-by-step explanation:

a right-angled triangle.

so, we use Pythagoras

c² = a² + b²

where c is the Hypotenuse (the side opposite of the 90 degree angle).

so, in our case

17² = 10² + x²

289 = 100 + x²

189 = x²

x = 13.75

3 0

2 years ago

Does |-13 + 2| equal to |10 + 1|

lesya [120]

Yes, because |-13+2| is |-11| And |10+1| is |11|. Since it’s the absolute value, which is the distance it is from 0, they both are 11. So 11=11

8 0

3 years ago

Find the equation of the exponential function represented by the table below:

amm1812

Answer:

f(x) = 2^(2x+1)

Step-by-step explanation:

2 = 2¹

8 = 2³

32 = 2⁵

128 = 2⁷

1,3,5 and 7 are odd numbers.

Individual numbers in mathematics are represented as 2x + 1.

4 0

3 years ago

Find the Highest Common Factor (HCF) of 196 and 12

Norma-Jean [14]

Answer:

The greatest common factor is 4

Step-by-step explanation:

1.Find the prime factorization of 12

a) 12 = 2 × 2 × 3

2.Find the prime factorization of 196

a) 196 = 2 × 2 × 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

a)GCF=2x2

Therefore, GCF = 2 × 2

GCF = 4

7 0

3 years ago

Read 2 more answers