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egoroff_w [7]
3 years ago
15

Please help me Determine the value of base b if (152)b = 0x6A. Please show all steps.

Mathematics
1 answer:
egoroff_w [7]3 years ago
5 0

Answer:

The value of b is, 8

Step-by-step explanation:

To determine the value of b:

Given:

(152)_b = 0x6A               ....[1]

Since, 0x6A represents the hexadecimal form.

To convert this hexadecimal form into decimal form:

(6A)_{16}= (6 \times 16^1)+(A \times 16^0)=(6 \times 16)+(10 \times 1) =96+10 = 106

⇒0x6A=106(decimal form)

Now we have to convert this decimal form into octal

8  |  106

8   |  13   | 2

    |   1    |  5

        1

Then, the octal form we get, (152)_8

Substitute this in [1] we have;

(152)_b = (152)_8

On comparing both sides we have;

b = 8

Therefore, the value of b is, 8

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Answer:

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Step-by-step explanation:

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P₁ = 96 cm = 2l₁ + 2a₁  (1)  

Como sabemos el margen superior, inferior, izquierdo y derecho podemos encontrar la relación entre el largo y ancho del rectángulo interno (región impresa) con el largo (l) y ancho (a) del rectángulo externo (hoja de papel):      

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a_{2} = a_{1} - (m_{d} + m_{iz}) = a_{1} - (2 cm + 5 cm) = a_{1} - 7 cm   (3)    

El perímetro del rectángulo interno es:

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Introduciendo la ecuación (2) y (3) en (4):

P_{2} = 2l_{2} + 2a_{2} = 2(l_{1} - 5 cm) + 2(a_{1} - 7 cm) = 2l_{1} + 2a_{1} - 10 cm - 14 cm = 96 cm - 24 cm = 72 cm  

Por lo tanto el perímetro del rectángulo interno (región impresa) es 72 cm.

 

2. Ahora para encontrar el área rectángulo interno debemos encontrar el largo y ancho del mismo, sabiendo que:

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Introduciendo (5) en (4):

P_{2} = 2l_{2} + 2a_{2} = 2*2a_{2} + 2a_{2} = 6a_{2}

a_{2} = \frac{P_{2}}{6} = \frac{72 cm}{6} = 12 cm

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Entonces el área es:

A_{2} = l_{2}*a_{2} = 12 cm*24 cm = 288 cm^{2}

Por lo tanto el área del rectágulo interno (región impresa) es 288 cm².      

Espero que te sea de utilidad!  

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