Answer:
given
Step-by-step explanation:
Answer:
17/24
Step-by-step explanation:
This expression simplifies to the following:
-7 15 1 1
---- * ----- - ----- + -----
18 -7 4 8
Reducing the product, we get
15 1
-------- - -----
18 8
and this simplifies further:
5 1
----- - -----
6 8
The LCD is 24. Thus, we have:
20 3 17
------ - ----- = -----
24 24 24
Step-by-step explanation:
Multiply 2/3 by (x-3) to get 2/3x -3.
Then subtract -1 on the y side to the right side compair like terms.
Answer:
c₁ = 1/2
c₂ = - e²/2
y = (1/2)*(eˣ - e²⁻ˣ)
Step-by-step explanation:
Given
y = c₁eˣ + c₂e⁻ˣ
y(1) = 0
y'(1) = e
We get y' :
y' = (c₁eˣ + c₂e⁻ˣ)' ⇒ y' = c₁eˣ - c₂e⁻ˣ
then we find y(1) :
y(1) = c₁e¹ + c₂e⁻¹ = 0
⇒ c₁ = - c₂/e² <em>(I)</em>
then we obtain y'(1):
y'(1) = c₁e¹ - c₂e⁻¹ = e <em>(II)</em>
⇒ (- c₂/e²)*e - c₂e⁻¹ = e
⇒ - c₂e⁻¹ - c₂e⁻¹ = - 2c₂e⁻¹ = e
⇒ c₂ = - e²/2
and
c₁ = - c₂/e² = - (- e²/2) / e²
⇒ c₁ = 1/2
Finally, the equation will be
y = (1/2)*eˣ - (e²/2)*e⁻ˣ = (1/2)*(eˣ - e²⁻ˣ)