Solve the equation for a. 55a – 44a = 11
2 answers:
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The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.
According to the statement
we have to find the inverse of the Laplace theorem with the help pf the given theorem in the statement.
So, For this purpose, we know that the
Laplace transformation is a transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.
Now, We assume you want to find the inverse transform of
This can be written in partial fraction form as
which can be found in a table of transforms to be the transform of
There are a number of ways to determine the partial fractions. They all start with factoring the denominator.
After that, you can postulate the final form and determine the values of the coefficients that make it so.
For example:
This gives rise to two equations:
(A+B) = 1
(4B-A) = 0.
So, The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.
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Question:
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ−1 s s2 + 3s − 4.
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Answer: 54 cm²
Step-by-step explanation: In this problem, we're asked to find the area of the trapezoid shown. A trapezoid is a quadrilateral with one pair of parallel sides.
The formula for the area of a trapezoid is shown below.
The <em>b's</em> represent the bases which are the parallel sides and <em>h</em> is the height.
So in the trapezoid shown, the bases are 6 cm and 12 cm and the height is 6 cm. Plugging this information into the formula, we have .
Next, the order of operations tell us that we must simplify inside the parentheses first. 6 cm + 12 cm is 18 cm and we have .
is 9 cm and we have 9 cm · 6 cm of 54 cm²
So the area of the trapezoid shown is 54 cm².
so h = 7, k = -2, meaning the vertex is at (7, -2).
the squared variable is the "y", meaning is a horizontal parabola.
the "p" distance is negative, for a horizontal parabola that means, it's opening towards the left-hand-side.
we know the focus and directrix are "p" units away from the vertex, and we know the parabola is opening horizontally towards the left-hand-side.
the focus is towards it opens 1 unit away, at (6, -2).
the directrix is on the opposite direction, 1 unit away, at (8, -2), namely x = 8.
Answer:
Step-by-step explanation:
<h3>Given expression</h3>sin²5° + sin²10° + sin²15° +... sin²85° + sin²90°
<h3>Concept:</h3>sin²x + cos²x = 1
sin(x) = cos (90 - x)
<u />
<u>There are in total these terms:</u>
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90
<u>In total, there are 18 terms, and the first one matches with the second to the last one:</u>
5 -- 85
10 -- 80
.
.
.
40 -- 50
<u />
<u>There are 2 terms left over:</u>
sin²45 and sin²90
<h3>Convert the first half of the sine terms (sin²5 - sin²40) to the cosine terms</h3>sin²5 = cos² (90 - 5) = cos²85
sin²10 = cos² (90 - 10) = cos²80
.
.
.
sin²40 = cos² (90 - 40) = cos²50
<h3>Simplify the 16 grouped terms </h3><em>i.e. sin²85 and cos²85</em>
Using the concept of sin²x + cos²x = 1
sin²85 + cos²85 = 1
sin²80 + cos²80 = 1
.
.
.
sin²50 + cos²50 = 1
Total = (16/2) × 1 = 8 × 1 = 8
<h3>Evaluate the 2 terms that are left over</h3>sin²45 = (sin45) (sin45) = (√2 / 2) (√2 / 2) = 1/2
sin²90 = (sin90) (sin 90) = (1) (1) = 1
<h3>Add all the terms together</h3>Hope this helps!! :)
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