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2 years ago

I Need to know a or b is the answer to this question

Mathematics

1 answer:

grandymaker [24]2 years ago

3 0

Answer:

Step-by-step explanation:

in option B, you are adding the 3 pound plastic box to each cardboard box

in option A, you have 5 separate carboard packages, and one 3 pound plastic box

This [option a] is the diagram that matches the scenario given.

Think of the x's as normal numbers. Let's say the weight of each "x" is 1. [it's not I'm aware that this question is different]

if you have 5 x's, you have

1 1 1 1 1 3

not 1+3 ; 1+3 ; 1+3 ; 1+3 ; 1+3

you would only have this if you were to add a 3 pound plastic box to each individual package

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I found the interval of convergence, but I am not sure how to do the second part, finding the sum of the series as a function of

antiseptic1488 [7]

The given series is geometric with common ratio $6^x - 9$ , which converges if $|6^x - 9|$ (i.e. the interval of convergence). We have the well-known result

$\displaystyle |r| < 1 \implies \sum_{n=0}^\infty ar^n = \frac{a}{1-r}$

If you're not familiar with that result, it's easy to reproduce.

Let $S_N$ be the $N$ -th partial sum of the infinite series,

$\displaystyle S_N = \sum_{n=0}^N \left(6^x - 9\right)^n = 1 + \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \cdots + \left(6^x - 9\right)^N$

Multiply both sides by the ratio.

$\left(6^x - 9\right) S_N = \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \left(6^x - 9\right)^3 + \cdots + \left(6^x - 9\right)^{N+1}$

Subtract this from $S_N$ to eliminate all the powers of the ratio between 0 and $N+1$ .

$\left(1 - \left(6^x - 9\right)\right) S_N = 1 - \left(6^x - 9\right)^{N+1}$

Solve for $S_N$ .

$S_N = \dfrac{1 - \left(6^x - 9\right)^{N+1}}{10-6^x}$

Now as $N\to\infty$ , the exponential term converges to 0 and we're left with

$\displaystyle \sum_{n=0}^\infty \left(6^x-9\right)^n = \lim_{N\to\infty} S_N = \boxed{\frac1{10-6^x}}$

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2 years ago

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elixir [45]

Answer:

Step-by-step explanation:

use the exponent rule of division: you just subtract the exponents if the base is the same, so 4-8=-4

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3 years ago

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