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Igoryamba
3 years ago
12

Could anyone help with this question

Mathematics
1 answer:
AlexFokin [52]3 years ago
7 0

Answer:

k = 96

Step-by-step explanation:

f(x) = x\sqrt{(6 -x^{2}) } \\\\ = x(6 - x^{2})^{\frac{1}{2} }

V = \int\limits^2_ {-2}\pi (f(x))^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} (f(x))^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} (x(6 - x^{2})^{\frac{1}{2} })^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} x^{2}(6 - x^{2}) \, dx \\\\ = \pi \int\limits^2_{-2} 6x^{2} - x^{4}  \, dx \\\\ = \pi [\frac{6x^{3} }{3} -\frac{x^{5}}{5} ]\limits^2_{-2} \\\\ = \pi [(2(2)^{3}-\frac{(2)^{5}}{5})-(2(-2)^{3} - \frac{(-2)^{-5}}{5}) ] \\\\ = \pi[(16 - \frac{32}{5}) - (-16-(-\frac{32}{5}))] \\\\ = \pi[\frac{48}{5} - (-\frac{48}{5})]

= π[⁴⁸/₅ + ⁴⁸/₅]

= π(⁹⁶/₅)

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Step-by-step explanation:

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What is the equation of the following line written in general form? (The y-intercept is 7.)
Viktor [21]

Answer:

<h2>3x - y + 7 = 0</h2>

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept

Put the given y-intercept b = 7 and the coordinates of the point (-2, 1) to the equation:

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3=m\to m=3

We have the equation:

y=3x+7

Convert it to the general form Ax+By+C=0:

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4 0
4 years ago
Prove that (Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A
iVinArrow [24]

Answer:

The answer is below

Step-by-step explanation:

We need to prove that:

(Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A.

Firstly, 1 / cos A = sec A, 1 / sin A = cosec A and tanA = sinA / cosA.

Also, 1 + tan²A = sec²A; sec²A - 1 = tan²A

\frac{\sqrt{secA-1} }{\sqrt{secA+1} } +\frac{\sqrt{secA+1} }{\sqrt{secA-1} } =\frac{(\sqrt{secA-1)}(\sqrt{secA-1})+(\sqrt{secA+1)}(\sqrt{secA+1}) }{(\sqrt{secA+1})(\sqrt{secA-1}) } \\\\=\frac{secA-1+(secA+1)}{\sqrt{sec^2A-secA+secA-1} } \\\\=\frac{2secA}{\sqrt{sec^2A-1} } \\\\=\frac{2secA}{\sqrt{tan^2A} } \\\\=\frac{2secA}{tanA} \\\\=\frac{2*\frac{1}{cosA} }{\frac{sinA}{cosA} }\\\\= 2*\frac{1}{cosA}*\frac{cosA}{sinA}\\\\=2*\frac{1}{sinAA}\\\\=2cosecA

7 0
3 years ago
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