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4 years ago

What is the name of the angle formed by BA and BC', given that the two rays share a common endpoint?

Mathematics

1 answer:

sattari [20]4 years ago

5 0

Answer:

B. ∠ABC

Step-by-step explanation:

When naming an angle using three points, the points should be given in order, with the vertex of the angle in the middle. B is the only option that has the letters in the right order.

∠CBA would also be a valid name for the angle, but that's not one of the options.

The diagram below shows what the problem is describing.

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2 years ago

Written as a simplified polynomial in standard form, what is the result when (2x - 7) ^ 2 is subtracted from 1?

zaharov [31]

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Step-by-step explanation:

as per question

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8 0

3 years ago

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Dimas [21]

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3 years ago

Read 2 more answers

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

Winston owns a coffe cart. He charges $1.50 for a cup of coffe , and it costs him $0.50 to make each cup of coffe plus $100 a da

Artist 52 [7]

100 + 0.50c = 1.50c <== ur equation
100 = 1.50c - 0.50c
100 = c....so he would have to sell 100 cups of coffee to break even

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3 years ago