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4 years ago

5

What is the radius of the circle who’s equation is x^2 + y^2 = 9

1 answer:

Svetllana [295]4 years ago

8 0

Answer:

r=3

Step-by-step explanation:

The equation of a circumference is $(x-a)^2+(y-b)^2=r^2$ .
Then , in this case $r^2=9$ , and then to know the value of r we just simply have to calculate the square root of 9, which is 3.

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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

Choose the equation of the horizontle lime that passes through the point (-8,-7)

adoni [48]

The horizontal line has an equation: y = a, where a is any real number.

We know, the line passes through the point (-8, -7) → x = -8, y = -7.

<h3>Answer: y = -7</h3>

7 0

3 years ago

Make n the subject of the formula: M=3n

natta225 [31]

Divide each side by 3. ----- n=M/3 .

4 0

4 years ago

Deandre wants to earn at least $30 trimming trees. He charges $7 per hour and pays $5 in equipment fees. What are the possible n

exis [7]

8 hours for the possible numbers of house

5 0

3 years ago

7. Fred had 85 marbles. After a few games, he had 120% of his original number. How many

Gnoma [55]

Answer:

102 marbles

Step-by-step explanation:

100% of 85 is 85.

20% of 85 = 17

85 + 17 = 102

Hope that helps!

4 0

3 years ago