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3 years ago

Find the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches.

1 answer:

6 0

Surface area of a ball:
S=4πr^2=4*π*5^2=100π

Volume of a circle:
V=4/3*π*r^3=4/3*π*125=(500/3)*π=165π

The approximate surface-area-to-volume ratio would be 1:1,5

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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

Which number would make this statement true

Alinara [238K]

3.3 is greater than 3.01

Hope this helps!

8 0

3 years ago

What is the interquartile range of the following data set?3,8,14,19,22,29,33,37,43,49

Vaselesa [24]

Q1: 14
Q3: 37
Interquartile: 37-14 = 23

THE ANSWER IS 23

(Brainliest please?)

4 0

3 years ago

B) 5(2x - 4)<br> Expand the following

jeka94

Answer:

10x-20

Step-by-step explanation:

(5×2x)-(5×4)

10x-20

8 0

3 years ago

Hello there!

otez555 [7]

Answer:

24 Domain: s>=2 or s<=-2

25. 3x^2 +14x +10

26. x^2 -2x+5

Step-by-step explanation:

24. Domain is the input or s values

square roots must be greater than or equal to zero

s^2-4 >=0

Add 4 to each side

s^2 >=4

Take the square root

s>=2 or s<=-2

25. f(g(x)) stick g(x) into f(u) every place you see a u

f(u) = 3u^2 +2u-6

g(x) = x+2

f(g(x) = 3(x+2)^2 +2(x+2) -6

Foil the squared term

= 3(x^2 +4x+4) +2x+4-6

Distribute

= 3x^2 +12x+12 +2x+4-6

Combine like terms

=3x^2 +14x +10

26 f(g(x)) stick g(x) into f(u) every place you see a u

f(u) = u^2+4

g(x) = x-1

f(g(x) = (x-1)^2 +4

Foil the squared term

= (x^2 -2x+1) +4

= x^2 -2x+5

7 0

3 years ago