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Novosadov [1.4K]
3 years ago
12

What fraction of a day is 24 seconds? PLS HELP WITH THIS QUESTION

Mathematics
1 answer:
MrRissso [65]3 years ago
4 0
1/3,600 [explanation: (24 hours(60 mins))60 seconds)= 86,400 seconds -> 24/86,400 -> (24/86,400)/24 -> 1/3,600{
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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

brainly.com/question/14487937

#SPJ4

6 0
1 year ago
3. Bryce mows lawns to make some extra money. He charges $15 per lawn. Bryce will
anyanavicka [17]

The domain and range of a function is the set of input and output values, the function can take.

  • <em>The domain is [0,6]</em>
  • <em>The range is [0,90]</em>

<em />

From the question, we have:

\mathbf{Rate = \$15}

<u>The domain</u>

He cannot mow more than 6 yards a day.

This means that the domain is: 0 to 6

<em>This is properly represented as: [0,6]</em>

<u></u>

<u>The range</u>

When he mows 0 yards, his earnings is:

\mathbf{Earnings = 0 \times \$15 = \$ 0}

When he mows 6 yards, his earnings is:

\mathbf{Earnings = 6 \times \$15 = \$ 90}

This means that the range is: 0 to 90

<em>This is properly represented as: [0,90]</em>

Read more about domain and range at:

brainly.com/question/4767962

5 0
2 years ago
Are the following polygons similar explain
ra1l [238]
<h3>Answer: No, they are not similar.</h3>

Technically, we don't have enough info so it could go either way.

==========================================================

Explanation:

We can see that the sides are proportional to each other, but we don't know anything about the angles. We need to know if the angles are the same. If they are, then the hexagons are similar. If the angles are different, then the figures are not similar.

Right now we simply don't have enough info. So they could be similar, or they may not be. The best answer (in my opinion) is "not enough info". However, your teacher likely wants you to pick one side or the other. We can't pick "similar" so it's best to go with "not similar" until more info comes along the way.

4 0
2 years ago
At a farmers market, oranges sell for $5 per bag and apples sell for $3 per
dimulka [17.4K]

Answer:

A. 3 bags of oranges, 4 bags of apples

Step-by-step explanation:

If O is number of bags of oranges and A is number of bags of apples:

O + A = 7

5O + 3A = 27

We can solve this system of equations with either substitution or elimination.  I like to use substitution, but you can use whichever you prefer.

O = 7 − A

5 (7 − A) + 3A = 27

35 − 5A + 3A = 27

35 − 2A = 27

8 = 2A

A = 4

O = 7 − A

O = 3

Teresa bought 3 bags of oranges and 4 bags of apples.

4 0
3 years ago
What is the area of the figure below?
Mashutka [201]
The answer to your question is 67
4 0
2 years ago
Read 2 more answers
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