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daser333 [38]
3 years ago
10

Ayana works at Eastern Community College as a math teacher. She will

Mathematics
1 answer:
AveGali [126]3 years ago
8 0

Answer:

  a.  $2622.00

Step-by-step explanation:

After taking out federal health insurance taxes, Ayana's pay for the year will be ...

  $45000 × (1 - 0.224) = $45000 × 0.776 = $34,920

On a monthly basis, that is ...

  $34,920/12 months = $2910 per month

Then, additional deductions of $3 + 85 + 200 = $288 are made, so her pay will be ...

  $2910 -288 = $2622 per month

_____

<em>Comment on federal taxes</em>

Federal income taxes are not accounted for in the problem statement. If Ayana can claim "head of household" status (and is not married), she will have federal income tax on the order of $121 per month deducted from the above amount, assuming her retirement plan deduction is "before tax."

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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

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6 0
1 year ago
15. What's the sum of 3/8 and 1/16?<br> 1/6 7/16 4/24 1/4
allsm [11]

Answer:

7/16

Step-by-step explanation:

1. you have to have the same denominator

7 0
3 years ago
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Write an equation of the line, in slope intercept form.
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Answer:

y = -3x + 6

Step-by-step explanation:

Slope-intercept form:

y = mx + b

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3n + 6n -4 = 2n + 2 + 5n​
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Answer:

3n +6n-4=2n+2+5n

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2 years ago
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Answer:

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a/b =2/3

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a/b = 2/3

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a = 2 and b = 3

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