Step-by-step explanation:
Area of parallelogram = base x height
Step-by-step explanation:
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Answer:
Step-by-step explanation:
<h3>
Algebraic Identities:</h3>
Identity used: (a +b)³ = a³ + b³ + 3ab(a +b)
p + q = -2 ------------------(I)
Both sides take cube,
(p +q)³ = (-2)³
a = p and b =q
p³ + q³ + 3pq(p +q) = -8
p³ + q³ + 3pq*(-2) = - 8 {From (I)}
p³ + q³ - 6pq = -8
p³ + q³ = -8 + 6pq
p³ + q³ + 8 = 6pq
Hence, proved.
To help solve this, we need to use the slope formula.
(y2 - y1) / (x2 - x1). We get these values by picking two points on a line.
We will use points (-3, 1) and (-17, 2).
y1 = 1
y2 = 2
x1 = -3
x2 = -17
Let's plug these into our formula.
(2) - (1) / (-17) - (-3) = 1 / - 14
The slope is 1 / -14
Answer:
x(t)=
Step-by-step explanation:
The function x(s) = (2)/(s(s+1)^2) can be expressed as partial fractions:
X(s)=
2=A·(s+1)²+B·s·(s+1)+C·s
2=A·(s²+2s+1)+B·(s²+s)+C·s
2=A·s²+2sA+A+B·s²+Bs+C·s
2=s²(A+B)+s(2A+B+C)+A
So we can find the values of A, B and C by solving these equations:
A+B=0 ⇒ 2+B=0 ⇒ B= -2
2A+B+C=0 ⇒ 2·2+(-2)+C=0 ⇒ C= -2
A=2
So X(s) is expressed as:
X(s)=
Using the inverse laplace transform tables we obtain x(t):
ℒ⁻¹{X(s)}=ℒ⁻¹{}
ℒ⁻¹{X(s)}=ℒ⁻¹{}+ℒ⁻¹{}+ℒ⁻¹{}
x(t)=