Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −
1 1 s2 − 720 s7
1 answer:
When it comes to laplace equations, there are transformation equations to follow. Generally, when you want to transform a laplace equation, you change the equation from f(t) to F(s). If you do the reverse, it is called the reverse laplace equation.
Based on the given, the useful transformation equation is shown in the attached picture.
When the term is s^2, that must mean that the equation is 1!/s^(1+1) to yield 1/s^2. This means that n=1. Taking the reciprocal s^2 must be equal to 1/t. Thus, for the first term, -11s^2 is equal to -11/t. For the second term, n must be equal to 6 so that 6!/s^(6+1) would yield 720/s^7. Thus, 720s^7 is equal to 1/t^6.
Hence, the transformed equation is -11/t - 1/t^6
Based on the given, the useful transformation equation is shown in the attached picture.
When the term is s^2, that must mean that the equation is 1!/s^(1+1) to yield 1/s^2. This means that n=1. Taking the reciprocal s^2 must be equal to 1/t. Thus, for the first term, -11s^2 is equal to -11/t. For the second term, n must be equal to 6 so that 6!/s^(6+1) would yield 720/s^7. Thus, 720s^7 is equal to 1/t^6.
Hence, the transformed equation is -11/t - 1/t^6
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now i see half of a cylinder and rectangle:)
but first lets find the volume of the rectangle...
In order to find the Volume of a rectangle we need to use this formula...
Length x width x height
in this case...
length = 10in
width = 6 in
height = 8in
lets solve:)
10 x 6 x 8 = 480
or we write it like this
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now time to find the volume of the half cylinder:)
But first lets remember the volume for a cylinder
Volume =
So lets find our measurements
= 3.14
r² = 5² or 25
h = 6
so lets plug in our values just like our formula said:)
3.14 x 25 x 6
now lets easily solve
<span>3.14 x 25 x 6 = 471
</span>now since we found an entire cylinder and we only want half of a cylinder lets divide our answer in half
471 ÷ 2 = 235.5
so we write it like this 235.5units³
But we have to add both of our multiples together so lets do that
Volume of rectangle = <span>480in³
</span>volume of half sphere = 235.5units³
480 + 235.5 = 715.5
answer = 715.5units³
I hope this helped and everyone learned something new
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now i see half of a cylinder and rectangle:)
but first lets find the volume of the rectangle...
In order to find the Volume of a rectangle we need to use this formula...
Length x width x height
in this case...
length = 10in
width = 6 in
height = 8in
lets solve:)
10 x 6 x 8 = 480
or we write it like this
480in³
now time to find the volume of the half cylinder:)
But first lets remember the volume for a cylinder
Volume =
So lets find our measurements
r² = 5² or 25
h = 6
so lets plug in our values just like our formula said:)
3.14 x 25 x 6
now lets easily solve
<span>3.14 x 25 x 6 = 471
</span>now since we found an entire cylinder and we only want half of a cylinder lets divide our answer in half
471 ÷ 2 = 235.5
so we write it like this 235.5units³
But we have to add both of our multiples together so lets do that
Volume of rectangle = <span>480in³
</span>volume of half sphere = 235.5units³
480 + 235.5 = 715.5
answer = 715.5units³
I hope this helped and everyone learned something new
anyways don't forget to
MARK ME BRAINLIEST! :D
Given:
A prism with height 5 cm and equilateral triangular base with side 2 cm.
To find:
The total surface area of the prism.
Solution:
Area of an equilateral triangle is:
Where, a is the side length.
Putting , we get
The base and top of the prism are congruent so their area must be equal.
The lateral surface area of the prism is:
Where, P is the perimeter of the base and h is the height of the prism.
The lateral surface area of the prism is:
Now, the total surface area is the sum of areas of bases and lateral surface area.
Therefore, the total surface area is 33.46 cm².