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diamong [38]
2 years ago
14

A clock has a diameter of 16 cm. How long is the metal band around it?

Mathematics
1 answer:
kramer2 years ago
6 0

Answer:

The length of  metal band around the given clock  is 50. 24 cm.

Step-by-step explanation:

Here, the diameter of given clock = 16 cm

Now, Diameter = 2 x Radius

So,  Radius  = D/2  = 16 cm/2  = 8 cm

⇒The radius of the clock = 8 cm

Now, The metal Band around it = The CIRCUMFERENCE of the watch

Circumference of the clock  = 2 π r

=  2 x ( 3.14) x ( 8)  = 50.24 cm

or, C = 50.24 cm

Hence, the length of  metal band around the given clock  is 50. 24 cm.

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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

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Taken mod 4, the last two terms vanish and we're left with

x\equiv63\equiv64-1\equiv-1\equiv3\pmod4

We have 3^2\equiv9\equiv1\pmod4, so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 7, the first and last terms vanish and we're left with

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x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 9, the first two terms vanish and we're left with

x\equiv140\equiv5\pmod9

so we don't need to make any adjustments here, and we end up with x=401.

By the Chinese remainder theorem, we find that any x such that

x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}

is a solution to this system, i.e. x=149+252n for any integer n, the smallest and positive of which is 149.

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