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LUCKY_DIMON [66]

3 years ago

12

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the e

ntire lake, how long would it take for the patch to cover half of the lake?

2 answers:

ArbitrLikvidat [17]3 years ago

7 0

See the plants grow in airthemetic progression.
day 1 its is 1 and day 2 it is 2, day 3 it is 4.......
so,
1,2,4,6,8,......
so it take 48 days to fill the pond..
total plants = 48/2(2*1+(48-1)*2)
total plants= 2304
so half the plants is 1152
so,
1152=n/2(2*1+(n-1)2)
n=47
it so 47 days to complete half the pond.

alisha [4.7K]3 years ago

5 0

The day before it is full it will be half full ( bacuse it doubles in size every day)

So the answer is 47 days

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3 years ago

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Using the rules for special cases, what is the result of?

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Answer:

C) 4x^2 -8x +4[/tex]

Step-by-step explanation:

(-2x+2)^2

we apply (a+b)^2 formula

$(a+b)^2 = a^2 + 2ab +b^2$

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How do you simplify this problem?

Yuri [45]

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3 years ago

Please help very urgent

Alik [6]

Answer:

32, <u>16</u>, <u>8</u>, <u>4</u>, <u>2</u>, 1

Explanation:

The geometric mean can be represented by $\sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}$ .

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

$a_{n} = a_{1} • r^{n-1}$

Where $a_{n}$ is the nth term, $a_{1}$ is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, $a_{1}$ will simply be 32.

Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

$\sqrt[5]{\frac{a_{6}}{a_{1}}}$ =

$\sqrt[5]{\frac{1}{32}}$ =

$\frac{1}{2}$ .

Therefore: $r = \frac{1}{2}$ .

Using all the information we have, we can find the explicit rule:

$a_{n} = a_{1} • r^{n-1}$

$a_{1}$ = 32
$r = \frac{1}{2}$

$a_{n} = a_{1} • r^{n-1}$ →

$\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}$

________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

$a_{1} = 32 • (\frac{1}{2})^{1-1}$

$a_{1} = 32 • (\frac{1}{2})^{0}$

$a_{1} = 32 • 1$

$a_{1} = 32$

$a_{6} = 32 • (\frac{1}{2})^{6-1}$

$a_{6} = 32 • (\frac{1}{2})^{5}$

$a_{6} = 32 • \frac{1}{32}$

$a_{6} = 1$

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