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3 years ago

3. Simplify log3 20 - log3 5

Mathematics

1 answer:

aalyn [17]3 years ago

5 0

$\log_320-\log_35=\log_3\dfrac{20}{5}=\log_34$

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A rectangular prism has a length of 4 cm a width of 6 cm and a height of 3 cm what is it’s volume

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Answer: 72

Step-by-step explanation:

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3 years ago

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Maggie's brother is 3 years younger than four times her age. The sum of their ages is 62. How old is Maggie? Maggie is years old

Nadusha1986 [10]

Answer:

Maggie is 13 years old.

Step-by-step explanation:

1M + 1B = 62

rearrange to get:

1B = 62 - 1M

4M - 3 = 1B

substitute B with 62 - 1M so there is only one variable. this gives:

4M - 3 = 62 - 1M

Get all the variables on one side:

4M + 1M - 3 = 62

Get all non variables on the other side:

4M + 1M = 62 + 3

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Divide both sides by 5 to get the M by itself:

M = 13.

BONUS:

M + B = 62

B = 49

So her brother is 49 years old.

Maggie is 13 years old.

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3 years ago

How many names are for square

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3 years ago

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The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i

kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.

Recall the formula for the sum of consecutive positive integers,

$\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2$

Now,

$1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016$

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

$\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224$

numbers, and their sum is

$\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400$

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of $1+9\times2=19$ .

So, the sum of the first 1234 terms in the sequence is 2419.

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2 years ago

C Campus Student

Alla [95]

52 is your answer

Hope this helps

4 0

3 years ago