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son4ous [18]
3 years ago
10

Find the exact length of the curve. x = 9 + 9t2, y = 6 + 6t3, 0 ≤ t ≤ 4

Mathematics
1 answer:
andrew11 [14]3 years ago
3 0

ANSWER

=102 \sqrt{ 17}

EXPLANATION

The equation of the curve is:

x = 9 + 9 {t}^{2}

y = 6 + 6 {t}^{3}

We differentiate to obtain:

\frac{dx}{dt}  = 18t

\frac{dy}{dt}  = 18t

The length of the arc

l =  \int _0 ^{4}  \sqrt{  {( \frac{dx}{dt} )}^{2} + {( \frac{dy}{dt} )}^{2} } dt

This implies that:

=  \int _0 ^{4}  \sqrt{  {( 18t )}^{2} + {(  {18 {t}^{2} } )}^{2} } dt

= \int _0 ^{4} 18t \sqrt{  1+ { {18 {t}^{2} } }} dt

=102 \sqrt{ 17}

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Use the given qualitative data to construct the relative frequency distribution.
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Category                         Relative Frequency

male survivors                           17.3%

males who died                          63.7 %

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Step-by-step explanation:

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Given : Total people on ship = 2274

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⇒ Relative Frequency of male ​survivors =\dfrac{394}{2274}

In percent , \dfrac{394}{2274}\times100\approx17.3\%

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⇒ Relative Frequency of male ​who​ died =\dfrac{1449}{2274}

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Number of female​ survivors =344

⇒ Relative Frequency of female​ survivors =\dfrac{344}{2274}

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Category                         Relative Frequency

male survivors                           17.3%

males who died                          63.7 %

Female survivors                        15.1 %

Females who died                       3.8%

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