Answer:
y(t)= 11/3 e^(-t) - 5/2 e^(-2t) -1/6 e^(-4t)
Step-by-step explanation:
We know that 
, so we have
By using the method of partial fraction we have:
Now we have:
](https://tex.z-dn.net/?f=%20y%28t%29%3DL%5E%7B-1%7D%5BY%28s%29%5D%28t%29%20)
Using linearity of inverse transform we get:
 -L^{-1}[\frac{5}{2(s+2)}](t) -L^{-1}[\frac{1}{6(s+4)}](t)](https://tex.z-dn.net/?f=%20y%28t%29%3DL%5E%7B-1%7D%5B%5Cfrac%7B11%7D%7B3%28s%2B1%29%7D%5D%28t%29%20-L%5E%7B-1%7D%5B%5Cfrac%7B5%7D%7B2%28s%2B2%29%7D%5D%28t%29%20-L%5E%7B-1%7D%5B%5Cfrac%7B1%7D%7B6%28s%2B4%29%7D%5D%28t%29%20)
Using the inverse transforms
![L^{-1}[c\frac{1}{s-a}]=ce^{at}](https://tex.z-dn.net/?f=%20L%5E%7B-1%7D%5Bc%5Cfrac%7B1%7D%7Bs-a%7D%5D%3Dce%5E%7Bat%7D%20)
we have:
Let's solve your equation step-by-step.<span><span>
6<span>(<span>x−1</span>)</span></span>=<span>9<span>(<span>x+2</span>)</span></span></span>
Step 1: Simplify both sides of the equation.<span><span>
6<span>(<span>x−1</span>)</span></span>=<span>9<span>(<span>x+2</span>)</span></span></span><span>
Simplify:</span><span><span><span><span>
(6)</span><span>(x)</span></span>+<span><span>(6)</span><span>(<span>−1</span>)</span></span></span>=<span><span><span>(9)</span><span>(x)</span></span>+<span><span>(9)</span><span>(2)</span></span></span></span>(Distribute)<span><span><span><span>
6x</span>+</span>−6</span>=<span><span>9x</span>+18</span></span><span><span><span>
6x</span>−6</span>=<span><span>9x</span>+18</span></span>
Step 2: Subtract 9x from both sides.<span><span><span><span>
6x</span>−6</span>−<span>9x</span></span>=<span><span><span>9x</span>+18</span>−<span>9x</span></span></span><span><span><span>
−<span>3x</span></span>−6</span>=18</span>
Step 3: Add 6 to both sides.<span><span><span><span>
−<span>3x</span></span>−6</span>+6</span>=<span>18+6</span></span><span><span>
−<span>3x</span></span>=24</span>
Step 4: Divide both sides by -3.<span><span><span>
−<span>3x</span></span><span>−3</span></span>=<span>24<span>−3</span></span></span><span>
x=<span>−8</span></span><span>
Answer: x= -8
-Hope I helped.</span>
The ratio of AB to AC and the ratio of AD to DC is 1 : 2 each respectively. They are equivalent ratios.
<h3>Ratios and proportions</h3><h3 />
A ratio means a comparison of two different quantities while proportion is an equality of two ratios.
- AB = 5 in
- AC = 10 in
- AD = 4 in
- DC = 8 in
Ratio of AB to AC = 5 in : 10 in
= 5 / 10
= 1 / 2
= 1 : 2
Ratio of AD to DC = 4 in : 8 in
= 4 / 8
= 1 / 2
= 1 : 2
Therefore, the ratio of AB to AC and the ratio of AD to DC is 1 : 2 each respectively. They are equivalent ratios.
Learn more about ratios and proportions:
brainly.com/question/12024093
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