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3 years ago

6

Which statement best describes the expression 3 + 2 ÷ y? (1 point) The quotient of y and the sum of 3 and 2 The quotient of the

sum of 3 and 2 and y The sum of 3 and the quotient of 2 and y The sum of 3 and the quotient of y and 2

1 answer:

Gelneren [198K]3 years ago

4 0

Answer:

The sum of 3 and the quotient of y and 2.

Step-by-step explanation:

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ValentinkaMS [17]

1) substitute 10x in for the equation.

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3 years ago

What is the sum of the infinite geometric series 9−6+4−83+...9-6+4-83+...??

vivado [14]

Successive terms have a common factor of $-\dfrac23$ , which means the $n$ th partial sum of the series can be written as

$S_n=9-6+4-\dfrac83+\cdots+9\left(-\dfrac23\right)^{n-1}$
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$\implies-\dfrac23S_n=9\left(\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\left(-\dfrac23\right)^4+\cdots+\left(-\dfrac23\right)^n\right)$

$\implies S_n-\left(-\dfrac23\right)S_n=9\left(1-\left(-\dfrac23\right)^n\right)$
$\dfrac53S_n=9\left(1-\left(-\dfrac23\right)^n\right)$
$S_n=\dfrac{27}5\left(1-\left(-\dfrac23\right)^n\right)$

As $n\to\infty$ , the geometric term vanishes, leaving you with

$S=\displaystyle\lim_{n\to\infty}S_n=\dfrac{27}5$

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Required area of shaded portion

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