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3 years ago

How do you identify the necessary information that is missing from a problem?

Mathematics

1 answer:

alexdok [17]3 years ago

6 0

Answer:

It depends

Step-by-step explanation:

Identifying what is <em>not there</em> is always difficult. In the general case, the range of possibilities is infinite.

For relatively simple math problems, the problem statement usually gives a context and asks a question. The context will generally tell you the nature of the relationships that apply. The question will generally be answered by making use of the relationships to relate given information to requested information.

If a relationship involves 4 items, one is "unknown" (that you're asked to find), and only 2 are given, then you know the missing information is the remaining item in the relationship.

Often, you can work a problem a number of ways, so the information that is missing depends on the method you choose for working the problem.

___

In complicated multi-step problems, relationships may need to be developed, theorems proved, massive amounts of data examined, and more. In some cases, whole new areas of mathematics may need to be invented.

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A radioactive substance decreases in the amount of grams by one-third each year. If the starting amount of the

katovenus [111]

Answer:

The sequence is geometric. The recursive formula is $a_{n}=2/3a_{n-1}$

Step-by-step explanation:

In order to solve this problem, you have to calculate the amount of the substance left after the end of each year to obtain a sequence and then you have to determine if the sequence is arithmetic or geometric.

The substance decreases by one-third each year, therefore:

After 1 year:

$1452-\frac{1}{3}(1452)$

Using 1452 as a common factor and solving the fraction:

$1452(1-\frac{1}{3})=1452(\frac{2}{3})=968$

You can notice that in general, after each year the amount of grams is the initial amount of the year multiplied by 2/3

After 2 years:

$968(\frac{2}{3})=\frac{1936}{3}$

After 3 years:

$\frac{1936}{3}(\frac{2}{3})=\frac{3872}{9}$

The sequence is:

1452,968,1936/3,3872/9....

In order to determine if the sequence is geometric, you have to calculate the ratio of two consecutive terms and see if the ratio is the same for all two consecutive terms. The ratio is obtained by dividing a term by the previous term.

The sequence is arithmetic if the difference of two consecutive terms is the same for all two consecutive terms.

-Calculating the ratio:

For the first and second terms:

968/1452=2/3

For the second and third terms:

1936/3 ÷ 968 = 2/3

In conclussion, the sequence is geometric because the ratio is common.

The recursive formula of a geometric sequence is given by:

$a_{n}=ra_{n-1}$

where an is the nth term, r is the common ratio and an-1 is the previous term.

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3 years ago

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timurjin [86]

Answer:

a = 9

Step-by-step explanation:

2(a + 7) = 5a - 13

We want to bring a to one side, I will choose to bring it to the right

First, expand the bracket by multiplying 2 with a + 7

2a + 14 = 5a - 13

Bring the -13 to the left by adding 13 to both sides

2a + 14 + 13 = 5a - 13 + 13

Simplify

2a + 27 = 5a

Bring the 2a to the right by subtracting 2a from both sides

2a - 2a + 27 = 5a - 2a

Simplify

27 = 5a - 2a

27 = 3a

Bring the 3 to the left by dividing both sides by 3

27÷3 = a

Simplify

a = 9

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Answer:

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