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3 years ago

Use the reverse tabular method to solve division problem: (x^3+2x^2+2x+1)/(x+1)

Mathematics

1 answer:

belka [17]3 years ago

7 0

Answer:

x^2+x+1

Step-by-step explanation:

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Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2

LUCKY_DIMON [66]

Make a change of coordinates:

$u(x,y)=xy$
$v(x,y)=\dfrac xy$

The Jacobian for this transformation is

$\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}$

and has a determinant of

$\det\mathbf J=-\dfrac{2x}y$

Note that we need to use the Jacobian in the other direction; that is, we've computed

$\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}$

but we need the Jacobian determinant for the reverse transformation (from $(x,y)$ to $(u,v)$ . To do this, notice that

$\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}$

we need to take the reciprocal of the Jacobian above.

The integral then changes to

$\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv$
$=\displaystyle\frac12\int_{v=}^{v=}\int_{u=}^{u=}\frac{e^u}v\,\mathrm du\,\mathrm dv=\frac{(e^4-e)\ln2}2$

8 0

3 years ago

A production manager tests 10 batteries and finds that their mean lifetime is 468 hours. She then designs a sales package for th

Usimov [2.4K]

iits probalty like based analyse

6 0

4 years ago

Read 2 more answers

Finding angle measures using triangles

S_A_V [24]

Because HI and JK are parallel, that makes their angles congruent. So angle K equals angle I
So the interior angles of a triangle add up to 180°
So, Angle I + angle H + angle x =180°
60°+56°+x°=180°
116°+x°=180°
X=180-116
X=64°

6 0

3 years ago

The slope of the the tangent line to a curve at a point. Calc derivative help

pickupchik [31]

Answer:

y = 108x + 216

Step-by-step explanation:

given

y = 4x³ then $\frac{dy}{dx}$ = 12x² = $m_{tgt}$

x = 3 ⇒ m = 12(- 3)² = 108

equation of tangent in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept ), hence

y = 108x + b

To find b substitute (- 3, - 108) into the equation

- 108 = -324 + b ⇒ b = - 108 + 324 = 216

y = 108x + 216 ← equation of tangent

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3 years ago

Crisps <br> normal price £1.43 <br> three for the price of two<br> what is the total of 6 packets

Anettt [7]

Answer:

3 packs equal the price of two, therefore 1.43•2= 2.86

and 6 packs equal the price of 4, so 2.86•2= 5.72

7 0

3 years ago