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Katena32 [7]
3 years ago
5

Convert the hexadecimal numeral to Hindu-Arabic 4A9EDsixteen 8

Mathematics
1 answer:
IceJOKER [234]3 years ago
5 0

9514 1404 393

Answer:

  305,645 base 10

  1124755 base 8

Step-by-step explanation:

In expanded form, the number is ...

  4×16^4 +10×16^3 +9×16^2 +14×16^1 +13

  = (((4×16 +10)×16 +9)×16 +14)×16 +13 = ((74×16 +9)×16 +14)×16 +13

  = (1193×16 +14)×16 +13 = 19102×16 +13 = 305,645 base 10

_____

If you want to convert this to base 8, that is easily done by writing the binary equivalents of the hex digits, then regrouping them by 3s.

  4A9ED₁₆ = 0100 1010 1001 1110 1101₂ = 01 001 010 100 111 101 101₂

  = 1124755₈

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According to the remainder theorem, if a binomial x-a is a factor of a polynomial p(x), then p(a)=0.

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p(1)=a \times 1^4+b \times 1^3 + c \times 1^2+ d \times 1+e \\
p(-1)=a \times (-1)^4 + b \times (-1)^3 + c \times (-1)^2 + d \times (-1)+e \\ \\
p(1)=a+b+c+d+e \\
p(-1)=a-b+c-d+e \\ \\
p(1)=0 \\
p(-1)=0 \\ \\ \hbox{add both equations:} \\
a+b+c+d+e=0 \\
\underline{a-b+c-d+e=0} \\
2a+2c+2e=0 \\
2(a+c+e)=0 \\
a+c+e=0 \\ \\
\hbox{substitute 0 for a+c+e in the first equation:} \\
a+b+c+d+e=0 \\
(a+c+e)+b+d=0 \\
0+b+d=0 \\
b+d=0 \\ \\
\boxed{a+c+e=b+d=0} \\
\hbox{proved } \checkmark
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Answer:

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2. 150- 30= 120

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