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3 years ago

What is the fractional form of?

Mathematics

2 answers:

Tomtit [17]3 years ago

7 0

Answer:

Step-by-step explanation:

You can memorize the patterns of fractions of ninths.

0/9 = 0

1/9 = 0.1111111111111111111111

2/9 = 0.222222222222

3/9 = 0.3333333333333

4/9 = 0.4444444444444

5/9 = 0.5555555555556

6/9 = 0.6666666666667

7/9 = 0.777777777777778

8/9 = 0.88888888888889

9/9 = 1

Hope this helps!

SashulF [63]3 years ago

7 0

Answer:

C. 8/9

Step-by-step explanation:

Well .8 repeating is not 8/10.

Though many would choose that.

If you do 8 ÷ 10 you get .8 not .8 repeating meaning 8/10 is not correct.

To get .8 repeating we would divide 8 by 9.

Because all natural numbers below 9 can be divided by 9 to create a .repeating itself.

For example 8 ÷ 9 = .8 repeating,

4÷9 = .4 repeating.

Thus,

C. is the correct answer.

Hope this helps :)

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(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:

Explanation:-

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

Step(i):-

Given differential problem

y′+3 y=9 t

Take the Laplace transform of both sides of the differential equation

L( y′+3 y) = L(9 t)

Using Formula Transform of derivatives

L(y¹(t)) = s y⁻(s)-y(0)

By using Laplace transform formula

$L(t) = \frac{1}{S^{2} }$

Step(ii):-

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

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

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

Step(iii):-

By using partial fractions , we get

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

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

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)

B = 9/3 = 3

Put s = -3 in equation(i)

9 = C(-3)²

C = 1

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)

0 = A + C

put C=1 , becomes A = -1

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

Step(iv):-

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

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

Applying inverse Laplace transform on both sides

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

By using inverse Laplace transform

$L^{-1} (\frac{1}{s} ) =1$

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

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

Final answer:-

Now the solution , we get

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

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-3x -4y = 20 x - 10y =16 if (x, y) is the solution to the system of equations above what is the value of x?

balu736 [363]

Multiply first equation by -5 and 2nd by 2, add them

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2x-20y=32 +
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17x=-68
divide both sides by 17
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the x value is -4

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Derive the equation of motion of the spring-mass system given below. Please show and MARK your derivation step by step. Missing

Arte-miy333 [17]

Answer:

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Step-by-step explanation:

Use the FBD attached:

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Using small angle approximations:

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Ö = angular acceleration.

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