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3 years ago

Please help right away.

Mathematics

1 answer:

Travka [436]3 years ago

8 0

$\sum\limits_{k=1}^{\infty}420\left(\dfrac{1}{6}\right)^{k-1}$

The infinite geometric series is converges if |r| < 1.

We have r=1/6 < 1, therefore our infinite geometric series is converges.

The sum S of an infinite geometric series with |r| < 1 is given by the formula :

$S=\dfrac{a_1}{1-r}$

We have:

$a_1=420\left(\dfrac{1}{6}\right)^{1-1}=420\left(\dfrac{1}{6}\right)^0=420\\\\r=\dfrac{1}{6}$

substitute:

$S=\dfrac{420}{1-\frac{1}{6}}=\dfrac{420}{\frac{5}{6}}=420\cdot\dfrac{6}{5}=84\cdot6=504$

Answer: d. Converges, 504.

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Answer:

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2 years ago

Please solve this, will rate 5 stars and mark as STAR!

Nina [5.8K]

Answer:

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Step-by-step explanation:

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Once

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We have

$5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5}$

We can proceed considering the common base of exponentials

$\sqrt[3]{2} \cdot \sqrt[6]{2} = 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} }=\sqrt{2}$

Therefore,

$5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5} = 5 \cdot \sqrt{2} \cdot \sqrt[6]{5}$

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3 years ago

If Keira spends $45 on petrol, 1/ 9 of the money on other items and 1 /5 of the money on clothes. How much money does she spend

gogolik [260]

Answer:

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Step-by-step explanation:

Total money spent by Keira = $45

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2. Food

3. Other items

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Money spent of on Food = Money spent - (Money spent on clothing + other items)

Money spent on food = 45 - (9+5)

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