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Diano4ka-milaya [45]

2 years ago

9

The art teacher has 7 bottles of glue that are each 2/5 full. He combines them so he will have fewer bottles. How many bottles o

f glue does he have after he combines them?

1 answer:

Katen [24]2 years ago

7 0

Teacher will have 3 bottles of glue after he combines

<em><u>Solution:</u></em>

Given that,

The art teacher has 7 bottles of glue that are each 2/5 full

He combines them so he will have fewer bottles

<em><u>To find: bottles of glue does he have after he combines them</u></em>

From given,

Total bottles = 7

Each is 2/5 full

Therefore, multiply 7 with 2/5 to get total bottles of glues he will have after combining

$Number\ of\ bottles\ of\ glues = 7 \times \frac{2}{5}\\\\Number\ of\ bottles\ of\ glues = \frac{14}{5} = 2.8 \approx 3$

Thus teacher will have 3 bottles of glue after he combines

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$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

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