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Darya [45]
4 years ago
9

A particular fraction is equivalent to 2/3. The sum of its numerator and denominator is 105. What is the numerator of the fracti

on?
Mathematics
1 answer:
Sphinxa [80]4 years ago
3 0
3x = 2(105-x)
3x = 210-2x
5x=21x = 42 the numerator. 105-42=63
So 63 is the denominator
42/63 = 2/3
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Ayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the value of the expression was 8.5. Select all the statem
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Jayden's solution is incorrect.

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Jayden substituted the wrong value for a.

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3 years ago
A square has vertices T(1,2), U(4,2), V(4,5), W(1,5). If the square is rotated clockwise 90 degrees around (0,0), what are the c
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6 0
3 years ago
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Licemer1 [7]

We're looking for a solution of the form F(x,y)=C. By the chain rule, this solution should have total differential

\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0

and the equation is exact if the mixed second-order partial derivatives of Fare equal, i.e. \frac{\partial^2F}{\partial x\partial y}=\dfrac{\partial^2F}{\partial y\partial x}.

The given ODE is exact, since

\dfrac{\partial(2xy^3+\cos x)}{\partial y}=6xy^2

\dfrac{\partial(3x^2y^2-\sin y)}{\partial x}=6xy^2

Then

\dfrac{\partial F}{\partial x}=2xy^3+\cos x\implies F(x,y)=x^2y^3+\sin x+f(y)

\dfrac{\partial F}{\partial y}=3x^2y^2-\sin y=3x^2y^2+\dfrac{\mathrm df}{\mathrm dy}

\dfrac{\mathrm df}{\mathrm dy}=-\sin y\implies f(y)=\cos y+C

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With y(0)=\pi, we get

\cos\pi=C\implies C=-1

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6 0
3 years ago
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