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3 years ago

Can someone please help me with these couple questions I don’t really understand how to read this graph

Mathematics

1 answer:

galben [10]3 years ago

6 0

Answer:

1. 7.5 hours

2. TV

3. Computer

4. All electronic usage except for the heater would decrease because summer is usually when people go outside and don't really stay indoors. While in winter, most people stay inside their houses.

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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

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

4 0

3 years ago

Which quadratic function has a wider graph than y=2x^2?

ioda

so all those quadratics have their parent y = x², which has the graph of a "bowl".

and depending on the coefficient, the bowl is wider or not.

the larger the coefficient, the narrower the bowl, the smaller the coefficient, the wider the bowl.

well, 1/2 is smaller then 2, thus y = (1/2)x² is wider than y = 2x².

7 0

3 years ago

If the first three Fibonacci numbers are given as <img src="https://tex.z-dn.net/?f=x_%7B1%7D%20%3D1" id="TexFormula1" title="x_

vazorg [7]

Answer:

n = 8

Step-by-step explanation:

Continuing the sequence using

$x_{n}$ + $x_{n+1}$

x₄ = x₂ + x₃ =1 + 2 = 3

x₅ = x₃ + x₄ = 2 + 3 = 5

x₆ = x₄ + x₅ = 3 + 5 = 8

x₇ = x₅ + x₆ = 5 + 8 = 13

x₈ = x₆ + x₇ = 8 + 13 = 21

x₉ = x₇ + x₈ = 13 + 21 = 34

x₁₀ = x₈ + x₉ = 21 + 34 = 55 ← with n = 8

6 0

2 years ago

Read 2 more answers

Point D is located on MN at (2,43). What ratio relates MD to DN?

Eva8 [605]

The ratio of MD to DN is equal to 2.

<h3>How to find the partition ratio for a line segment</h3>

In accordance with the image set aside, the locations of the points M and N are M(x, y) = (- 6, - 4) and N(x, y) = (6, 4), respectively. Now we determine the vectors associated to line segments MD and DN by vector sum:

<u>MD</u> = D(x, y) - M(x, y)

<u>MD</u> = (2, 4 / 3) - (- 6, - 4)

<u>MD</u> = (8, 16 / 3)

<u>DN</u> = N(x, y) - D(x, y)

<u>DN</u> = (6, 4) - (2, 4 / 3)

<u>DN</u> = (4, 8 / 3)

Lastly, we find the length of each line segment by Pythagorean theorem:

MD = √[8² + (16 / 3)²]

MD = (8 / 3)√13

DN = √[4² + (8 / 3)²]

DN = (4 / 3)√13

And the ratio of MD to DN is:

MD / DN = [(8 / 3)√13] / [(4 / 3)√13]

MD / DN = 2

The ratio of MD to DN is equal to 2.

<h3>Remark</h3>

The statement presents typing mistakes, we kindly present the correct form below:

<em>Point D is located on line segment MN at (2, 4 / 3). What ratio relates MD to DN?</em>

To learn more on line ratios: brainly.com/question/3148758

#SPJ1

4 0

1 year ago

You have 8 songs, 10 podcasts, and 12 audio books on your iCloud. How many ways can you choose 1 of each to download to your iPh

Fofino [41]

Answer:

960 ways

Step-by-step explanation:

Multiplication Principle: if there are n ways to do one thing and m ways to do another, then there are m x n ways to do both.

That can expand to include three things (or more).

8 x 10 x 12 = 960

4 0

3 years ago