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2 years ago

Express 2x2 – 3x – 5 as the product of two binomial factors.

Mathematics

1 answer:

sergeinik [125]2 years ago

6 0

Answer:

Step-by-step explanation:

Express 2x2 – 3x – 5 as the product of two binomial factors.

factorize the given expression

2x^2 – 3x – 5

2x^2 – 5x+2x – 5

x(2x-5)+ 1 (2x-5)

(2x-5) (x+1)

Hence the expression as the product of two binomial is (2x-5) (x+1)

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Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
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Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
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Now,

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$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

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3 years ago

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Brrunno [24]

Answer:

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Step-by-step explanation:

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Answer:

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Fittoniya [83]

Let events
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