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Kipish [7]
3 years ago
5

Shoe sales for a certain company were $25.9 billion. Sales are expected to increase by 20% in the next year. Find the projected

amount of shoe sales next year.

Mathematics
1 answer:
ololo11 [35]3 years ago
7 0
I believe the projected amount is 129.5 billion.
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Polygons QRST and Q′R′S′T′ are shown on the following coordinate grid:
Rudik [331]
ANSWER : QR is the answer
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3 years ago
Find the radius of convergence, then determine the interval of convergence
galben [10]

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.  

<h3>Find the radius of convergence R and the interval of convergence:</h3>

Ratio test is the test that is used to find the convergence of the given power series.  

First aₙ is noted and then aₙ₊₁ is noted.

For  ∑ aₙ,  aₙ and aₙ₊₁ is noted.

\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }| = β

  • If β < 1, then the series converges
  • If β > 1, then the series diverges
  • If β = 1, then the series inconclusive

Here a_{k} = \frac{(x+2)^{k}}{\sqrt{k} }  and  a_{k+1} = \frac{(x+2)^{k+1}}{\sqrt{k+1} }

   

Now limit is taken,

\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }| = \lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|

= \lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|

= \lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|

= |{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}

= |{x+2 }| < 1

- 1 < {x+2 } < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

 

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

Learn more about radius of convergence here:

brainly.com/question/14394994

#SPJ1

5 0
1 year ago
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Which of the following may fall outside a triangle? Check all that apply.?
Luda [366]
Circumcenter is the one among the following choices given in the question that may fall outside a triangle. The correct option among all the options that are given in the question is the first option or option "A". I hope that this is the answer you were looking for and it has come to your help.
5 0
3 years ago
Best answer gets the brainliest!<br> Find $a/b$ when $2\log{(a -2b)} = \log{a} + \log{b}$.
andrey2020 [161]

By some properties of logarithms, rewrite the equation as

2\log(a-2b) = \log(a) + \log(b) \\\\ \log(a-2b)^2 = \log(ab)

so that

(<em>a</em> - 2<em>b</em>)² = <em>ab</em>

Expand the left side:

<em>a</em> ² - 4<em>ab</em> + 4<em>b</em> ² = <em>ab</em>

Rearrange terms to get a quadratic equation in <em>a</em>/<em>b</em> :

<em>a</em> ² - 5<em>ab</em> + 4<em>b</em> ² = 0

<em>b</em> must be greater than 0, otherwise log(<em>b</em>) doesn't exist, and the same goes for <em>a</em>. So we can divide by <em>b</em> ² to get

<em>a</em> ²/<em>b</em> ² - 5<em>a</em>/<em>b</em> + 4 = 0

Factorize and solve for <em>a</em>/<em>b</em> :

(<em>a</em>/<em>b</em> - 4) (<em>a</em>/<em>b</em> - 1) = 0

==>   <em>a</em>/<em>b</em> = 4   or   <em>a</em>/<em>b</em> = 1

However, if <em>a</em>/<em>b</em> = 1, then <em>a</em> = <em>b</em> makes <em>a</em> - 2<em>b</em> = -<em>b</em>. But we must have <em>b</em> > 0, so we omit the second solution and end up with

<em>a</em>/<em>b</em> = 4

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What is the perimeter of triangle with side lengths of 29, 15, and 4xy?
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The perimeter of any polygon is equal to the sum of the length of all sides of this polygon.

Therefore:

<h3>P = 29 + 15 + 4xy = 44 + 4xy</h3>
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3 years ago
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