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3 years ago

(g + a)2 g = -5 and a = 25 Evaluate expression:

Mathematics

2 answers:

CaHeK987 [17]3 years ago

6 0

Answer:

25+625-250

650-250

400

agasfer [191]3 years ago

5 0

-5+25 is (20) and it’s in the parenthesis so it’s still connected by multiplication. your answer is 40.

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Use the laplace transform to solve the given initial-value problem. y' 5y = e4t, y(0) = 2

Basile [38]

The Laplace transform of the given initial-value problem

$y' 5y = e^{4t}, y(0) = 2$ is mathematically given as

$y(t)=\frac{1}{9} e^{4 t}+\frac{17}{9} e^{-5 t}$

<h3>What is the Laplace transform of the given initial-value problem? y' 5y = e4t, y(0) = 2?</h3>

Generally, the equation for the problem is mathematically given as

$&\text { Sol:- } \quad y^{\prime}+s y=e^{4 t}, y(0)=2 \\\\&\text { Taking Laplace transform of (1) } \\\\&\quad L\left[y^{\prime}+5 y\right]=\left[\left[e^{4 t}\right]\right. \\\\&\Rightarrow \quad L\left[y^{\prime}\right]+5 L[y]=\frac{1}{s-4} \\\\&\Rightarrow \quad s y(s)-y(0)+5 y(s)=\frac{1}{s-4} \\\\&\Rightarrow \quad(s+5) y(s)=\frac{1}{s-4}+2 \\\\&\Rightarrow \quad y(s)=\frac{1}{s+5}\left[\frac{1}{s-4}+2\right]=\frac{2 s-7}{(s+5)(s-4)}\end{aligned}$

$\begin{aligned}&\text { Let } \frac{2 s-7}{(s+5)(s-4)}=\frac{a_{0}}{s-4}+\frac{a_{1}}{s+5} \\&\Rightarrow 2 s-7=a_{0}(s+s)+a_{1}(s-4)\end{aligned}$

$put $s=-s \Rightarrow a_{1}=\frac{17}{9}$$

$\begin{aligned}\text { put } s &=4 \Rightarrow a_{0}=\frac{1}{9} \\\Rightarrow \quad y(s) &=\frac{1}{9(s-4)}+\frac{17}{9(s+s)}\end{aligned}$

In conclusion, Taking inverse Laplace tranoform

$L^{-1}[y(s)]=\frac{1}{9} L^{-1}\left[\frac{1}{s-4}\right]+\frac{17}{9} L^{-1}\left[\frac{1}{s+5}\right]$ \\\\$

$y(t)=\frac{1}{9} e^{4 t}+\frac{17}{9} e^{-5 t}$

Read more about Laplace tranoform

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6 0

2 years ago

Plzzzzz help asappppppp

wariber [46]

The measure of angle 7 is 61 degrees by the Alternate interior angles theorem.

The alternate interior angles theorem states that, the alternate interior angles are congruent when the transversal intersects two parallel lines. Hence, it is proved. Alternate interior angles can be calculated by using properties of the parallel lines.

3 0

3 years ago

What is the sum of 52 and its additive inverse?

Lisa [10]

Hello there!

The additive inverse of any number just means to flip it's value.

For example;

The number "3" would have an additive inverse of "-3".
The number "-15" would have an additive inverse of "15".

Since we have "52", we can flip the value sign of it.
We now have -52 and 52.

Since the question asked us to sum our numbers, we need to add them.

-52 + 52 = 0

The sum of 52 and its additive inverse is 0.

I hope this helps!

5 0

3 years ago

The sum of 5 consecutive odd integers is 2,555. What is the sum of the first, third, and last integer?

Lilit [14]

Answer:

The sum of the first, third, and last integer is 1533.

Step-by-step explanation:

<u><em>Step 1: You need to create a equation first:</em></u>

n + n + 2 + n + 4 + n + 6 + n + 8 = 2555

<u><em>How did I make the equation?</em></u>

If n is odd number, n + 2 must be the consecutive odd number

5 , 5 + 2 , 5 + 4 , 5 + 6 , 5 + 8

5, 7, 9, 11, 13 ALL CONSECUTIVE ODD NUMBERS

<u><em>Step 2: Simplifying the equation</em></u>

n + n + 2 + n + 4 + n + 6 + n + 8 = 2555

5n + 20 = 2555

<u><em>Step 3: Solving the equation, with explanation</em></u>

5n + 20 = 2555 Subtract 20 on both sides

5n = 2535 Isolate the variable by dividing 5 on both sides

n = 507

<u><em>Step 4: Plug in the value</em></u>

n + n + 2 + n + 4 + n + 6 + n + 8

507, 507 + 2 , 507 + 4 , 507 + 6 , 507 + 8

507, 509, 511, 513, 515

<u><em>Step 5: Solve the sum of the first, third, and last integer</em></u>

507 + 511 + 515 = 1533

<u><em>Step 6: THE ANSWER</em></u>

1533

<h3><u><em>Hope this helps!!! </em></u></h3><h3><u><em>Please mark this as brainliest!!! </em></u></h3><h3><u><em>Thank You!!! </em></u></h3><h3><u><em>:)</em></u></h3>

8 0

3 years ago

I will give Brainliest !

Sidana [21]

Answer:i believe it’s A

Step-by-step explanation:

4,5,3 are almost the same and almost the same rotation just letters are different

3 0

3 years ago