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Alla [95]
3 years ago
11

18 ➗ (-4 1/2) with explanation​

Mathematics
1 answer:
slamgirl [31]3 years ago
8 0

Answer:

-4

Step-by-step explanation:

If anything the first thing you would want to do is covert your fraction so a decimal. (-4 1/2) as a decimal is -4.50. From there it would be easier to divide. to get an answer of -4

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Please help with last 2 domain and range
Strike441 [17]

Answer:

See below for answers and explanations

Step-by-step explanation:

Top left: Since y can't be greater than 0 but is equal to 0, then the range is (-∞,0] and the domain is (-∞,∞) since there are no domain restrictions

Top right: Since both x and y have no restrictions, then the domain is (-∞,∞) and the range is (-∞,∞)

Bottom left: Since y cannot be less than 2 but equal to it, and x holds no domain restrictions, then the domain is (-∞,∞) and the range is [2,∞)

Bottom right: Since both x and y have no restrictions, then the domain is (-∞,∞) and the range is (-∞,∞)

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Ruby has a loss of $45 in her business. How will she enter the loss in her account book?
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512, 256, 128, 64, __, __, __, ...​
Cerrena [4.2K]

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I do this pattern in my head literally all the time!

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3 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
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