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3 years ago

6

WRITE AN EQUATION 331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students we

re in each bus?

1 answer:

Molodets [167]3 years ago

3 0

Answer:

probably 331-7=6x

Step-by-step explanation:

cause you take away 7 and have 324, then divide by 6 and end up with 54 soooo

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James is setting up a fish tank. He is buying a breed of goldfish that typically grows to be 12 inches long . It's recommended t

ASHA 777 [7]

12:12 is the ratio because each fish can grow up to be 12 inches long so 12 gallons would be in the tank per fish.

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3 years ago

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

1 year ago

Mackenzie has a bag that contains 6 red marbles, 4 blue marbles, and 14 yellow marbles. If she chooses one marble from the bag,

NeX [460]

10 of the 24 marbles in the bag are not yellow.

$\frac{10}{24} \: is \: approximately \: equal \: to \: 41.67\%$

6 0

3 years ago

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James and Cameron are watching a film. They pause it with one fifth left to watch. What is the ratio of how much they have watch

goldenfox [79]

Answer:

The ratio of how much they have watched to how much they have left to see is 4 : 1.

Step-by-step explanation:

Consider that the total duration of the film is, 1.

It is provided that James and Cameron paused when there is one-fifth left to watch.

That is, they have already watched, $1-\frac{1}{5}=\frac{4}{5}$ th of the film.

Compute the ratio of how much they have watched to how much they have left to see as follows:

$\frac{\text{Duration Watched}}{\text{Duration Left}}=\frac{4/5}{1/5}=\frac{4}{1}=4:1$

Thus, the ratio of how much they have watched to how much they have left to see is 4 : 1.

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3 years ago

22) Use the expression 5x + 3 + 2y + x

Katena32 [7]

A. 5x and 2y
B. 3 and x
C. 5x and x
D. 4

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3 years ago

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