Answer:
The area of the floor of the shed is <u>1500 square feet.</u>
Step-by-step explanation:
Given:
The vertices of the floor of a shed are: (20,80), (50,60), (50,20) and (20,20)
Let us plot the given vertices on a graph.
From the graph, it is clear that the given figure is a trapezium with opposite parallel sides being parallel to the y axis. The height of the trapezium is the side that is parallel to x axis.
The area of the trapezium ABCD is given as:
From the graph, AB = 60 ft, CD = 40 ft, AD = 30 ft
Therefore, the area is given as:
Therefore, the area of the floor of the shed is 1500 square feet.
Answer:
Step-by-step explanation:
let's start by separating the fraction into two new smaller fractions
.
First,<em> s(s^2+s+1)</em> must be factorized the most, and it is already. Every factor will become the denominator of a new fraction.
Where <em>A</em>, <em>B</em> and <em>C</em> are unknown constants. The numerator of <em>s</em> is a constant <em>A</em>, because <em>s</em> is linear, the numerator of <em>s^2+s+1</em> is a linear expression <em>Bs+C</em> because <em>s^2+s+1</em> is a quadratic expression.
Multiply both sides by the complete denominator:
![[{s(s^{2} + s +1)]\frac{s+1}{s(s^{2} + s +1)}=[\frac{A}{s}+\frac{Bs+C}{s^{2}+s+1}][{s(s^{2} + s +1)]](https://tex.z-dn.net/?f=%5B%7Bs%28s%5E%7B2%7D%20%2B%20s%20%2B1%29%5D%5Cfrac%7Bs%2B1%7D%7Bs%28s%5E%7B2%7D%20%2B%20s%20%2B1%29%7D%3D%5B%5Cfrac%7BA%7D%7Bs%7D%2B%5Cfrac%7BBs%2BC%7D%7Bs%5E%7B2%7D%2Bs%2B1%7D%5D%5B%7Bs%28s%5E%7B2%7D%20%2B%20s%20%2B1%29%5D)
Simplify, reorganize and compare every coefficient both sides:
Solving the system, we find <em>A=1</em>, <em>B=-1</em>, <em>C=0</em>. Now:
Then, we can solve the inverse Laplace transform with simplified expressions:
The first inverse Laplace transform has the formula:
For:
We have the formulas:
We have to factorize the denominator:
It means that:
So <em>a=-1/2</em> and <em>b=(√3)/2</em>. Then:
![\mathcal{L}^{-1}\{-\frac{s+1/2}{(s+1/2)^{2}+3/4}\}=e^{-\frac{t}{2}}[cos\frac{\sqrt{3}t }{2}]\\\\\\\frac{1}{2}[\frac{2}{\sqrt{3} } ]\mathcal{L}^{-1}\{\frac{\sqrt{3}/2 }{(s+1/2)^{2}+3/4}\}=\frac{1}{\sqrt{3} } e^{-\frac{t}{2}}[sin\frac{\sqrt{3}t }{2}]](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5C%7B-%5Cfrac%7Bs%2B1%2F2%7D%7B%28s%2B1%2F2%29%5E%7B2%7D%2B3%2F4%7D%5C%7D%3De%5E%7B-%5Cfrac%7Bt%7D%7B2%7D%7D%5Bcos%5Cfrac%7B%5Csqrt%7B3%7Dt%20%7D%7B2%7D%5D%5C%5C%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2%7D%5B%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%20%7D%20%5D%5Cmathcal%7BL%7D%5E%7B-1%7D%5C%7B%5Cfrac%7B%5Csqrt%7B3%7D%2F2%20%7D%7B%28s%2B1%2F2%29%5E%7B2%7D%2B3%2F4%7D%5C%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%20e%5E%7B-%5Cfrac%7Bt%7D%7B2%7D%7D%5Bsin%5Cfrac%7B%5Csqrt%7B3%7Dt%20%7D%7B2%7D%5D)
Finally:
Answer:
36 I think!
Step-by-step explanation:
Answer:
a = -6, b = 48
Step-by-step explanation:
a(3x - 8) = b - 18x --> 3ax - 8a = b - 18x, then comparing two sides for the x part, only 3ax and -18x has x, so there are equivalent 3ax = -18x, solve for a = -6, then the part left is -8a = b, let a = -6 into the equation, get -8 * -6 = b = 48.
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