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3 years ago

11

I need help on my corrections! Can someone help me please if u do know!!

1 answer:

Harlamova29_29 [7]3 years ago

8 0

Looks good for high school math make sure the teacher sees you're work clearly and know what the numbers are overall you should be good

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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

The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2

romanna [79]

Answer:

Perimeter is irrational

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Step-by-step explanation:

<em>The attachment is missing but the question is still answerable</em>

Given

$Area = 24200 yd^2$

Required

Determine if the Perimeter is rational or not

First, we need to determine the sides of the square;

$Area = Length * Length$

Substitute $Area = 24200 yd^2$

$24200 = Length * Length$

$24200 = Length^2$

Take Square root of both sides

$\sqrt{24200} = Length$

$Length = 155.563492$

The perimeter of a square is calculated as:

$Perimeter = 4 * Length$

$Perimeter = 4 * 155.563492$

$Perimeter = 622.253968$

<em>Because the value of </em><em>perimeter </em><em>can't be gotten by dividing two integers, then </em><em>perimeter is irrational</em>

4 0

3 years ago

Suppose a line parallel to side BC of triangle ABC intersects AB and AC at point D and E, respectively. Find the length of AE if

MrRissso [65]

Answer: AE=13

Step-by-step explanation: took test

4 0

3 years ago

Really help me please

Ivanshal [37]

144 x 3= (D) 432

Hope this can help! :)

6 0

3 years ago

Are cracks in rock mechanical or chemical weathering

guajiro [1.7K]

Answer: Chemical weathering
its the breakdown of rocks by chemical reactions that change the rocks' makeup, or composition.

3 0

3 years ago