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jenyasd209 [6]
3 years ago
14

Which number is a rational number?

Mathematics
1 answer:
Nikitich [7]3 years ago
6 0

Answer:sq rt of 49

Step-by-step explanation:

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5. A soccer ball is kicked from the ground level with an upward velocity of 60 feet per second. The
elixir [45]

Answer:

-16(1)^2+60(1)= -16+60=44

Step-by-step explanation:

6 0
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

brainly.com/question/14487937

#SPJ4

6 0
1 year ago
What is the solution set of 4x^2+3=4x+2​
jeka94

Answer:

1

— = X

12

Step-by-step explanation:

4 0
3 years ago
Determine whether y varies directly with x. If so, find the constant of variation k.
kumpel [21]
Direct variation is y=kx, inverse variation is y=k/x....

-5y=-2x divide both sides by -5

y=2.5x

So this is a direct variation with a constant of 2.5
5 0
3 years ago
. An elevator starts at the 6th floor. It goes up 7 floors twice, and then it goes
Anettt [7]

Well let's see what floor each one lands on and figure out which one is higher.

Something to note:

down = subtracting

up = adding

if something says it's doing something more than once, add it the number of times it's doing that thing. (You can also multiply it by that number but the adding way is a bit easier to understand and explain)

<u>Elevator 1:</u>

6 + 7 + 7 - 10 = 10

<u>Elevator 2:</u>

20 - 5 - 5 - 5 + 12 = 17

Elevator 2 ends on a higher floor (reasoning above)

4 0
3 years ago
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