(5x-3y,3x-y)=(16,12)

a family pass to the amusement park costs $54.using the distributive property , write an expression that can be used to find the

Mandarinka [93]

9 x 6 = 54 is this right I'll do distributive property next time

4 0

2 years ago

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J^2 over 2j times 2j over 3g

Serhud [2]

Answer:

D

Step-by-step explanation:

given $\frac{j^2}{2j}$ × $\frac{2j}{3g}$

the 2j on the denominator of the first fraction cancels with the 2j on the numerator of the second fraction, leaving the expression in simplified form as

= $\frac{j^2}{3g}$ → D

5 0

2 years ago

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

If the ratio of similarity between two similar polygons is 4:3.2, this ratio converts to

Liula [17]

Answer:

Step-by-step explanation:

7 0

2 years ago

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1) 5x-2y=4. 2) 3x-5y=13 x-2y=5<br>3x+y=9

Natali [406]

$\left\{\begin{array}{ccc}5x-2y=4\\3x+y=9&/\cdot2\end{array}\right\\+\left\{\begin{array}{ccc}5x-2y=4\\6x+2y=18\end{array}\right\\----------\\.\ \ \ \ \ 11x=22\ \ \ \ /:11\\.\ \ \ \ \ \ \ x=2\\\\3\cdot2+y=9\\6+y=9\\y=9-6\\y=3\\\\Answer:x=2;\ y=3$

$\left\{\begin{array}{ccc}3x-5y=13\\x-2y=5\end{array}\right\\\left\{\begin{array}{ccc}3x-5y=13\\x=2y+5\end{array}\right\\\\substitute:\\\\3(2y+5)-5y=13\\6y+15-5y=13\\y=13-15\\y=-2\\\\x=2\cdot(-2)+5=-4+5=1\\\\Answer:x=1;\ y=-2.$

5 0

2 years ago

(5x-3y,3x-y)=(16,12)​

(5x-3y,3x-y)=(16,12)