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2 years ago

Restrictions must be indicated for rational functions involving a denominator because__________

Mathematics

1 answer:

Svetradugi [14.3K]2 years ago

5 0

Answer:

rational expressions

hope I helped! :)

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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

2 years ago

What is the slope of the line?

lutik1710 [3]

Answer:

todavía no me la sé pero al rato te mando la respuesta

7 0

2 years ago

From the airport hanger H, an areoplane A is 18km away on the bearing of 115° while another aeroplane B is 29km away on a bearin

maks197457 [2]

The difference in distance between Aero plane A and B is; 34.67 km

<h3>How to calculate bearing?</h3>

To get the bearing;

∠H = (115 - 90) + (270 - 203)

∠H = 92°

Then, we will use cosine rule to get the distance between both Planes A and B.

d_ab = √(18² + 29² - 2(18 * 29) * cos 92)

d_ab = √(324 + 841 + 36.435)

d_ab = 34.67 km

Read more about bearing at; brainly.com/question/22518031

#SPJ1

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1 year ago

What is two methods to 92/9 as a decmal

DENIUS [597]

10.2 is the decimal of it

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2 years ago

What is the least common denominator (LCD)

Romashka [77]

The least common denominator is 15. The equivalent fractions would be 10/15 and 12/15.

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2 years ago