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3 years ago

Which of the following best defines an angle?

Mathematics

1 answer:

scoray [572]3 years ago

8 0

Answer:

Third option

Step-by-step explanation:

The first definition is not as broad as it should be, therefore, while an angle does meet that criteria, it's not a general definition, hence, it is incorrect. The second one is incorrect as well because a parabola has a vertex, and it is certainly not an angle. This definition is not specific enough, so it will be eliminated. The last one is again, too specific. The third one is the best answer because it is broad enough while still being specific.

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Ede4ka [16]

Answer:

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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densk [106]

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Step-by-step explanation:

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3 years ago

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guajiro [1.7K]

Answer:

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Step-by-step explanation:

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3 years ago

Find the length of the curve y = integral from 1 to x of sqrt(t^3-1)

Arlecino [84]

$y=\displaystyle\int_1^x\sqrt{t^3-1}\,\mathrm dt$

By the fundamental theorem of calculus,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm d}{\mathrm dx}\displaystyle\int_1^x\sqrt{t^3-1}\,\mathrm dt=\sqrt{x^3-1}$

Now the arc length over an arbitrary interval $(a,b)$ is

$\displaystyle\int_a^b\sqrt{1+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx=\int_a^b\sqrt{1+x^3-1}\,\mathrm dx=\int_a^bx^{3/2}\,\mathrm dx$

But before we compute the integral, first we need to make sure the integrand exists over it. $x^{3/2}$ is undefined if $x$ , so we assume $a\ge0$ and for convenience that $a$ . Then

$\displaystyle\int_a^bx^{3/2}\,\mathrm dx=\frac25x^{5/2}\bigg|_{x=a}^{x=b}=\frac25\left(b^{5/2}-a^{5/2}\right)$

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3 years ago