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3 years ago

8

Estimate and then find the product of 12×5.2

1 answer:

ozzi3 years ago

8 0

12 x 5.2

Estimate:
since 5.2 is about 5, we can estimate this to:
12 x 5 = 60

Find the Product:

12
<u> x 5.2
</u> 2 4
<u> + 6 0 0
</u> 6 2 4

now add the decimal back in. In the original problem there is one decimal place (the .2 in 5.2) so we move the decimal place one over in our product

624 becomes 62.4

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and subtracting this from $S_n$ gives

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$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

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$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

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and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

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r-5r

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