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Zielflug [23.3K]
2 years ago
15

Alex stayed up 20 a week How many hours did Alex stay up in 12 weeks?

Mathematics
1 answer:
Simora [160]2 years ago
3 0

Answer:

240 hours

Step-by-step explanation:

1 week = 20 hours

12 weeks = 20 × 12

= 240 hours

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I need help with the answer
solmaris [256]

Answer:

Its the last option

y = 1488.33x + 23800 ; $172,600.

Step-by-step explanation:

The slope of the trend line = (median value for 2000 - median value for 1940) / 60

= 89300 / 60

= 1488.33.

So the equation is 1488.33x + 23,800

Estimate for 2040

is 1483.33* 100 + 23800

= 172,600.

5 0
3 years ago
Which number belongs to the solution set of the equation below?
ollegr [7]
The correct answer would be: C. 44
Explanation: If you're trying to find out x's value, you have to do the inverse operation which means if it's subtraction, you add. So to find x's value, you'd add 36 + 8 = x. And 36 + 8 = 44. So therefore, x = 44. That means the answer is C.
5 0
3 years ago
(10 points) Consider the initial value problem y′+3y=9t,y(0)=7. Take the Laplace transform of both sides of the given differenti
Rashid [163]

Answer:

The solution

Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Consider the initial value problem y′+3 y=9 t,y(0)=7

<em>Step(i)</em>:-

Given differential problem

                           y′+3 y=9 t

<em>Take the Laplace transform of both sides of the differential equation</em>

                L( y′+3 y) = L(9 t)

 <em>Using Formula Transform of derivatives</em>

<em>                 L(y¹(t)) = s y⁻(s)-y(0)</em>

  <em>  By using Laplace transform formula</em>

<em>               </em>L(t) = \frac{1}{S^{2} }<em> </em>

<em>Step(ii):-</em>

Given

             L( y′(t)) + 3 L (y(t)) = 9 L( t)

            s y^{-} (s) - y(0) +  3y^{-}(s) = \frac{9}{s^{2} }

            s y^{-} (s) - 7 +  3y^{-}(s) = \frac{9}{s^{2} }

Taking common y⁻(s) and simplification, we get

             ( s +  3)y^{-}(s) = \frac{9}{s^{2} }+7

             y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}

<em>Step(iii</em>):-

<em>By using partial fractions , we get</em>

\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}

  \frac{9}{s^{2} (s+3} =  \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}

 On simplification we get

  9 = A s(s+3) +B(s+3) +C(s²) ...(i)

 Put s =0 in equation(i)

   9 = B(0+3)

 <em>  B = 9/3 = 3</em>

  Put s = -3 in equation(i)

  9 = C(-3)²

  <em>C = 1</em>

 Given Equation  9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Comparing 'S²' coefficient on both sides, we get

  9 = A s²+3 A s +B(s)+3 B +C(s²)

 <em> 0 = A + C</em>

<em>put C=1 , becomes A = -1</em>

\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}

<u><em>Step(iv):-</em></u>

y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}

y^{-}(s)  =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}

Applying inverse Laplace transform on both sides

L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})

<em>By using inverse Laplace transform</em>

<em></em>L^{-1} (\frac{1}{s} ) =1<em></em>

L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}

L^{-1} (\frac{1}{s+a} ) =e^{-at}

<u><em>Final answer</em></u>:-

<em>Now the solution , we get</em>

Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}

           

           

5 0
3 years ago
if the area of a rectangle is expressed as x^4 - 9y^2, then the product of the length and the width of the rectangle could be ex
kvasek [131]

Answer:the product of the length and the width of the rectangle could be expressed as

(x^2 - 3y)(x^2 + 3y)

Step-by-step explanation:

If the area of a rectangle is expressed as x^4 - 9y^2, we would determine the dimensions by simplifying the given expression. The simplified expression becomes

(x^2 - 3y)(x^2 + 3y)

Let us check by multiplying each term in one parenthesis by each term in the other parenthesis to get the given expression. It becomes

(x^2 - 3y)(x^2 + 3y) = x^4 + 3x^2y - 3x^2y - 9y^2 = x^4 - 9y^2

6 0
3 years ago
PLS HELP!!!!!!!!!!!!!!!!<br> I got all the way to 4 x <img src="https://tex.z-dn.net/?f=%5Csqrt%7B6250" id="TexFormula1" title="
crimeas [40]

Answer:

No its not right :(

The correct answer should be 100 root 10, or around 316.23

3 0
1 year ago
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