Question

if x and y respectively denote the number of sexagecimal and centesimal seconds in any angle then show that 250x=81y

Answer 1

It is proved that 250x = 81y

Step-by-step explanation:

Given that,

x represents the number of sexagesimal

y  represents the number of centesimal

To prove,

250x = 81y

Procedure:

In the case of sexagesimal,

1 right angle = 90°

1° = 60 minutes

1 minute = 60 second

∵ 1 right angle = 90 * 60 * 60 seconds

In the case of centesimal,

1 right angle = 100 g

100 g = 100 minutes

1 minute = 100 seconds

∵ 1 right angle = 100 * 100 * 100 seconds

According to this,

x in sexagesimal unit = 90 * 60 * 60 seconds

y in centesimal unit = 100 * 100 * 100 seconds

so,

x/y = (90 * 60 * 60)/(100 * 100 * 100)

x/y = (9 * 36)/1000

x/y = 81/250

∵ 250x = 81y

Hence proved.

Learn more: Prove that

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