An envelope measures 5 inches by 12 inches. A pencil is placed in the envelope at a diagonal. What is the maximum possible lenght of the pencil?

the maximum possible length of the pencil is 13 inches

Step-by-step explanation:

Here we have , An envelope measures 5 inches by 12 inches. A pencil is placed in the envelope at a diagonal. We need to find What is the maximum possible length of the pencil . Let's find out:

We know that maximum length which can be fitted in envelope will be the length of diagonal of envelope . So

By Pythagoras theorem

⇒

⇒

⇒

⇒

⇒

⇒

Therefore,  the maximum possible length of the pencil is 13 inches .

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

step by step explanation: when u removing the parentheses and combined them that would be : x+3y-x-y=2y