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2 years ago

Why can you use a model to check your answer for a division problem

1 answer:

7 0

If multiplication and retracing your track count as a model I believe it's good to see what you did wrong and to see what the answer really should bee

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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 baker mixes 8 3/4 cups of white flour with 2 1/2 cups of rye flour for a bread recipe. how many cups of white flour does the b

mr_godi [17]

Answer: 3.5 or 3 2/4 a cup of white flower for each cup of rye flower

Step-by-step explanation:

8 3/4 divided by 2 2/4

that's it

5 0

2 years ago

Read 2 more answers

Jim sells used drones for 70% of the original manufacturer's purchase price of a new drone. Jim also sells new drones for 15% mo

adell [148]

The function for the amount saved if they purchase a used drone rather than a new drone from Jim's store is f(x) = 0.45x

He sells used drones at 70% of the price (x).

So, the selling price of a used drone is:

$\mathbf{Used = 70\% \times x}$

Express percentage as decimal

$\mathbf{Used = 0.7 \times x}$

$\mathbf{Used = 0.7x}$

Also, he sells new drones at 15% more of the price (x).

So, the selling price of a new drone is:

$\mathbf{New= (1 + 15\%) \times x}$

Express percentage as decimal

$\mathbf{New= (1 + 0.15) \times x}$

$\mathbf{New= 1.15 \times x}$

$\mathbf{New= 1.15x}$

The amount saved is the difference between the prices of the drones.

So, we have:

$\mathbf{Saved =New - Old}$

This gives

$\mathbf{Saved =1.15x- 0.7x}$

Subtract

$\mathbf{Saved =0.45x}$

Express as a function

$\mathbf{f(x) = 0.45x}$

Hence, the function for the amount saved is f(x) = 0.45x

Read more about proportions at:

brainly.com/question/13114933

7 0

2 years ago

What are the lower, middle, and upper quartiles of this data?

Grace [21]

Answer:

71, 71, 75, 85, 98, 98, 104, 111, 114, 122, 164

The middle quartile is 98.

The lower quartile is 80

The upper quartile is 112.5

8 0

3 years ago

(20 pts)

irakobra [83]

A function can be represented by equations and tables

4 users are logged in by 9am
The domain is [3,23] and the range of the function is [3,4]

<h3>The number of users at 9am</h3>

The function is given as:

$g(x) = \frac14 \sqrt{x - 3} + 3$

At 9am, x = 9.

So, we have:

$g(x) = \frac14 \sqrt{9 - 3} + 3$

$g(x) = \frac14 \sqrt{6} + 3$

Simplify

$g(9) = 3.6$

Approximate

$g(9) = 4$

Hence, 4 users are logged in by 9am

<h3>The domain</h3>

Set the radical to 0

$x - 3 = 0$

Solve for x

$x = 3$

The maximum time after midnight is 23 hours.

So, the domain is [3,23]

<h3>The range</h3>

When x = 3, we have:

$g(x) = \frac14 \sqrt{x - 3} + 3$

$g(3) = \frac 14 * \sqrt{3 - 3} + 3 = 3$

When x = 23, we have:

$g(23) = \frac 14 * \sqrt{23 - 3} + 3 = 4$

So, the range of the function is [3,4]

Read more about domain and range at:

brainly.com/question/2264373

3 0

2 years ago