What is the total number of digits used when the first 2002 positive even integers are written?

Mathematics

1 answer:

Luda [366]2 years ago

7 0

The total number of digits used when the first 2002 positive even integers are written is 4 digits

<h3>How to find the number of sequence?</h3>

Using arithmetic sequence,

nth term = a + (n - 1)d

where

a = first term
d = common difference
n = number of terms

a = 2

d = 2

nth term = 2 + (2002 - 1)2

nth term = 2 + 4002

nth term = 4004

learn more on sequence here: brainly.com/question/15456604

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What value of cc will complete the square below and make the expression a perfect square trinomial?

Sav [38]

Question: What value of c will complete the square below ( $x^{2} +30x+c$ ) and make the expression a perfect square trinomial?

Answer: c = 225

Step-by-step explanation:

Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)². In the presented trinomial, we can immediately identify that a = x, and b² = c, but we need to find the numerical value of $c$ .

To do this, note that the middle term, or 2ab, corresponds with (is equal to) 30x. We know that a = x, and thus, 2ab = 2bx. Now, 2bx and 30x are corresponding terms; thus, 2bx = 30x.

Dividing by $2x$ on both sides gives us b = 15. Therefore, c = b² = 15² = 225. (As a squared binomial, this would be (x + 15)² as a = x and b = 15.)