BasimaElaskri
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Jonas has 1728 copies of a 1 × 1 × 1 cube with the net
shown, where c is a positive integer and c < 100. Using
these 1728 cubes, Jonas builds a large 12×12×12 cube in
such a way that the sum of the numbers on the exterior
faces is as large as possible. For some values of c, the sum
of the numbers on the exterior faces is between 80 000 and
85 000. The number of such values of c is
(A) 39 (B) 38 (C) 37
(D) 36 (E) 35

Sagot :

Answer:

37 :))

Step-by-step explanation:

Look thorugh the photo B)

Sorry its diagonal

View image YeahBoi134

The number of such values of c is 37, whose sum

of the numbers on the exterior faces is between 80 000 and

85 000.

The correct option is (C)

What is inequality?

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

1. Top or Bottom

  • Corners: (2c+100) x 8
  • Non- corners: 10(c+100) x 4 x2
  • 10 x 10x 100 x 2 =20000

2. Middle Layers:

  • Corners: (c+100)x 4 x 10
  • Non- Corners: 100 x 10 x 4 x 10 =40000

So,

(2c+100) x 8 + 10(c+100) x 4 x2 +  (c+100)x 4 x 10 + 20000 + 40000

16c + 800 + 80c + 8000 + 40c + 400 + 60000

136c + 72800

As per the condition:

  • 136c + 72800≤ 85000
  • 136c≤85000-72800

c≤89

and, 136c≥80000-72800

 c≥53

c= 89-53 =37

Hence, the number of such values of c is 37

Learn more about inequality here:

https://brainly.com/question/20383699

#SPJ2

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