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inna [77]
3 years ago
10

Please help me with this question

Mathematics
1 answer:
azamat3 years ago
7 0
It is 90 your welcome
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Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).
lutik1710 [3]

Answer:

The arc length is \dfrac{21}{16}

Step-by-step explanation:

Given that,

The given curve between the specified points is

x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}

The points from (\dfrac{9}{16},1) to (\dfrac{9}{8},2)

We need to calculate the value of \dfrac{dx}{dy}

Using given equation

x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}

On differentiating w.r.to y

\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})

\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})

\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})

\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}

We need to calculate the arc length

Using formula of arc length

L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}

Put the value into the formula

L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}

L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}

L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}

L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}

L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}

L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}

L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}

L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}

Put the limits

L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})

L=\dfrac{21}{16}

Hence, The arc length is \dfrac{21}{16}

6 0
3 years ago
HELP PLZZZ I NEED ANSWERS
asambeis [7]

Answer:

D.

Step-by-step explanation:

y = (x - 5)^2 + 16

= x^2 - 5x - 5x + 25 + 16

= x^2 - 10x + 41

That corresponds with answer choice D.

Hope this helps!

3 0
3 years ago
an athlete completes a race in 55.72 seconds how many times greater is the digit in the tens place than the digit in the ones pl
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7 is 5 greater than the 2
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Can I please get some help on this question ?
FrozenT [24]

Answer:

Step-by-step explanation:

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7 0
2 years ago
arrange the expressions in the correct sequence to rationalize the denominator of the expression -(2)/(\sqrt(x+y-2)-\sqrt(x+y+2)
cupoosta [38]
We have to rationalize the denominator:
\frac{-2}{ \sqrt{x+y-2} - \sqrt{x+y+2} } = \\  \frac{-2}{ \sqrt{x+y-2} -  \sqrt{x+y+2} }* \frac{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2})  }{x+y-2-(x+y+2)}= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2})  }{x+y-2-x-y-2}= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2}  }{-4}= \\  \frac{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }{2}
6 0
3 years ago
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