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bogdanovich [222]
3 years ago
9

Isaac wrote the integers from 1 through 104, inclusive. How many digits did he write?

Mathematics
1 answer:
Lilit [14]3 years ago
6 0

We know that Isaac wrote the integers from 1 to 104, and we need to determine how many digits did he write

Let's look at single digit, double digit and triple digit numbers separately:

Single Digit Numbers' Range: 1-9

Total Single Digit Numbers = Ending Number - Beginning Number + 1

⇒ Total Single Digit Numbers = 9 - 1 + 1 = 9

Number of digits written in single digit numbers = 9 × 1 = 9 ......... (i)

Double Digit Numbers' Range: 10-99

Total Double Digit Numbers = Ending Number - Beginning Number + 1

⇒ Total Double Digit Numbers = 99 - 10 + 1 = 90

Number of digits written in double digit numbers = 90 × 2 = 180 ....... (ii)

Triple Digit Numbers' Range: 100-104

Total Triple Digit Numbers = Ending Number - Beginning Number + 1

⇒ Total Triple Digit Numbers = 104 - 100 + 1 = 5

Number of digits written in triple digit numbers = 5 × 3 = 15 .......... (iii)

Adding (i), (ii) and (iii)

Total number of digits written from 1-104 = 9 + 180 + 15

⇒ Total number of digits written from 1-104 = 204

Hence, while writing the integers from 1-104, we use 204 digits.

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Option D.

Step-by-step explanation:

  • First, the you need ti understand that the triangle is an isosceles right angled triangle. In other words, the base and height are equal in length. The third side is the slide. This is the longest side.
  • Next, we know that the formula for calculating the area of a right angled triangle is given by:

        A = 1/2 (base × perpendicular height)

  • The perpendicular height is equal to the base. Let's say the base is <em>x</em>. It means that the height is also x, since height = base.
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       A = 1/2 (x.x)

           =1/2 (x²)

      32 = 1/2 (x²)

     Multiplying both sides by 2 gives:

     32×2 = x²

     64  = x²

       8   = x

To find the third side, we use the Pythagoras theorem:

    C² = A² + B²

         = 8² + 8²

         = 128

   C = √128

       = 8√2

However, the answer will not be exact, so we  multiply the length of the base and height by 2. This gives x = 16 (Length of base = length of height)

Repeating the steps above gives C = √ (16)² + (16)²

                                                           = √256

This corresponds to option D.

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[PICTURE ATTACHED] HEEELLPPP
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The answer to this question would be 8,4,4
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