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4 years ago

IF:

Mathematics

1 answer:

castortr0y [4]4 years ago

4 0

So they go up and first they double then triple etc do the answer would be 3050

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What number sentence is true?

meriva

D would be true because if you think about it in percentage wise
2/8= 25%
2/3=66.66%
2/3 is automatically greater than 2/8
Hope this helps :)

5 0

3 years ago

Simplify the following (1 1/2) ^-2

Serjik [45]

Answer:

1/2.25 or 4/9

Step-by-step explanation:

6 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:

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

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

5 0

3 years ago

Forty gallons of a 60% acid solution is obtained by mixing a 75% solution with a 50% solution. How many gallons of each solution

Novay_Z [31]

Sry but I don’t know the answer I just have two answer 2 questions so I don’t have to watch a video

7 0

3 years ago

Simplify : (√x + √y ) (√x − √y) (x + y)(x2 + y2)

Ivan

$Solution, \mathrm{Expand}\::\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)\left(x+y\right)\left(x^2+y^2\right):\quad :x^4-:y^4$

$Steps:$

$\mathrm{Expand}\:\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right):\quad x-y, =\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)$

$\mathrm{Expand}\:\left(x-y\right)\left(x+y\right):\quad x^2-y^2, =:\left(x^2-y^2\right)\left(x^2+y^2\right)$

$\mathrm{Expand}\:\left(x^2-y^2\right)\left(x^2+y^2\right):\quad x^4-y^4, =:\left(x^4-y^4\right)$

$\mathrm{Expand}\::\left(x^4-y^4\right):\quad :x^4-:y^4, =:x^4-:y^4$

The correct answer is $x^4-y^4$

Hope this helps!!!

4 0

3 years ago