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3 years ago

Which expressions show how 8 • 54 can be rewritten using the distributive property? Choose all answers that are correct.

Mathematics

1 answer:

irga5000 [103]3 years ago

6 0

Answer choice B is using the distributive property.

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Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note

Viktor [21]

a. Recall that

$\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C$

For $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

By integrating both sides, we get

$\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

If $x=0$ , then

$\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0$

so that

$\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

We can shift the index to simplify the sum slightly.

$\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n$

b. The power series for $x\ln(1-x)$ can be obtained simply by multiplying both sides of the series above by $x$ .

$\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n$

c. We have

$\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)$

$\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}$

4 0

3 years ago

The equation of a line is y = {x+5.

Mariulka [41]

Answer:

Sorry I did not know your answer

4 0

3 years ago

1.) Use a property to write an equivalent expression for 12*(100-5). Which property did you use?

Jlenok [28]

1. 12*100 - 12*5

You would use the distributive property to get this equation (it is equivalent to the original one)

2. Um... There's no actual story for this problem; sorry I can't solve this problem

3 0

3 years ago

Read 2 more answers

Please help me with number 1 please help ???

stira [4]

Answer:

mean: 26

median: 28

mode: 28

range:19

Step-by-step explanation:

hipe this helped hun

3 0

3 years ago

Six items purchased at a grocery store weigh 11 kilograms one of the items is detergent weighing 556 grams what is the total wei

slavikrds [6]

$556 \: g \times \frac{1 \: kg}{1000g} = 0.556 \: kg$

$11 \: kg - 0.556 \: kg = 10.444 \: kg$

The total weight of the other five items are 10.444 kg

<em>(round as you wish)</em>

7 0

3 years ago