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Morgarella [4.7K]

3 years ago

8

A train left Denver, Colorado at 12:00 going 250 kilometers per hour. How long will it take the train to get to Chicago, Illinoi

s if the train took a 2 hour stop every 250 kilometers?

1 answer:

Allushta [10]3 years ago

8 0

It will be about 12:55ish at night if the train starts in the day

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Sketch the domain D bounded by y = x^2, y = (1/2)x^2, and y=6x. Use a change of variables with the map x = uv, y = u^2 (for u ?

cluponka [151]

Under the given transformation, the Jacobian and its determinant are

$\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2$

so that

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv$

where $D'$ is the region $D$ transformed into the $u$ - $v$ plane. The remaining integral is the twice the area of $D'$ .

Now, the integral over $D$ is

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y$

but through the given transformation, the boundary of $D'$ is the set of equations,

$\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}$

We require that $u>0$ , and the last equation tells us that we would also need $v>0$ . This means $1\le v\le\sqrt2$ and $0$ , so that the integral over $D'$ is

$\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6$

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3 years ago

Please give a explanation :)<br> i will mark as brainliest!!

Fynjy0 [20]

Answer:

x=12 y=3

Step-by-step explanation:

Since the scale factor is 1:3, that means that the length and width of Q multiplied by 3 gives the corresponding length and width of P.

Similarly, the length and width of P divided by 3 gives the corresponding length and width of Q.

With this, 9/3=3, which is the value of y.

4*3=12, which is the value of x.

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3 years ago

If you shift the quadratic parent function, Flx) =x, down 9 units, what is the equation of the new function?

Mashutka [201]

Answer:

y = x-9

Step-by-step explanation:

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3 years ago

Please help, I will give brainliest to best answer

tester [92]

Answer:

060.28

Step-by-step explanation:

3 can't go into 1, but it goes into 18 six times with 0 left over. 3 goes into 0 zero times. 3 goes into 5 one time with 2 left over. 3 goes into 26 (because you pull the 6 down) 8 times with 2 left over.

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An experiment consists of rolling a die, flipping a coin, and spinning a spinner divided into 7 equal regions. The number of ele

oee [108]

Answer:

Option A.

<em>The number of elements in the sample space of this experiment is 84</em>

Step-by-step explanation:

The sample space for an experiment represents the number of possible results that may occur when conducting the experiment.

When throwing a die and observe the number obtained there are 6 possible results

When throwing a coin there are 2 possible results.

When spinning a wheel divided into 7 regions we have 7 possible outcomes.

If we combine these three experiments, then the sample space S is composed of the product of the possible results of each experiment.

$S = (6)(2)(7)\\\\S =84$

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