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Veseljchak [2.6K]
3 years ago
15

A beverage manufacturer performs a taste-test and discovers that people like their fizzy beverages best when the radius of the b

ubbles is about 0.3 mm. According to the formula below, what would be the volume of one of these bubbles?
Mathematics
2 answers:
adell [148]3 years ago
5 0
Okay, can we all just agree that this is sillier then the man who bought 27 watermelons? The volume for one of the bubbles is about 0.11mm. 
ohaa [14]3 years ago
4 0

Answer: About 0.11 cubic mm.

Step-by-step explanation:

We assume the shape of bubbles is spherical.

The volume of sphere is given by :-

\text{Volume}=\dfrac{4}{3}\pi r^3

Given : The radius of bubbles is about 0.3 mm.

Then , the volume of one bubble will be :-

\text{Volume}=\dfrac{4}{3}(3.14) (0.3)^3=0.11304\approx0.11

Hence, the volume of one of these bubbles = 0.11 cubic mm.

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Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0
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The power series for given function g(x)=\frac{4x}{(x-1)(x+3)} is g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)

For given question,

We have been given a function g(x) = 4x / (x² + 2x - 3)

We need to find a power series for the function, centered at c, for c = 0.

First we factorize the denominator of function g(x), we have:

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We can write g(x) as,

\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\

We know that, \frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n} if |x| < 1

and \frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n  if |\frac{x}{6}| < 1

\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\     if |x| < 1 and  if |\frac{x}{6}| < 1

\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n) if |x| < 1

Therefore, the power series for given function g(x)=\frac{4x}{(x-1)(x+3)} is g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)

Learn more about the power series here:

brainly.com/question/11606956

#SPJ4

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ExtremeBDS [4]

Answer:

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Step-by-step explanation:

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