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3 years ago

2. Simplify the following expression 1 (16 (16-12)

Mathematics

2 answers:

meriva3 years ago

5 0

Answer:

The answer is 64.

Step-by-step explanation:

16-12=4.

4×16×1=64.

nikklg [1K]3 years ago

4 0

Answer:

The answer is 64.

16-12=4.

4×16×1=64.

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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

2 years ago

2. What if Janelle began by running, then slowed to a walk, stopped, and then began running

stealth61 [152]

I think it is A
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7 0

3 years ago

A square pyramid is sliced parallel to the base, as shown.

jeka94

There are 2 triangles once u slice in half so triangles is the right answer

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2 years ago

Point P is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of P A is 2

Orlov [11]

Answer:

C. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.

Step-by-step explanation:

Dilation is the process in which the size i.e dimensions of a given figure is either increased or decreased by a scale factor, without changing the shape of the figure.

Given that: PA = 2, PB = 3, A $A^{I}$ = 4, B $B^{I}$ = 5.

So that: P $A^{I}$ = 6, P $B^{I}$ = 8.

Therefore, triangle A'B'C' is not an exact dilation of triangle ABC. So that the correct option is; No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.

5 0

3 years ago

Read 2 more answers

Help me with this yes im lazy 2 pages thats it.

valentinak56 [21]

Answer:

2.) $\frac{1}{4}/3=\frac{1}{4}*\frac{1}{3}=\frac{1}{12}$ s yes she is correct