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Fudgin [204]
3 years ago
12

Horses are to race over a certain english meadow for a distance of 6.7 furlongs. what is the race distance in units of (a) rods

and (b) chains? (1 furlong = 201.168 m, 1 rod = 5.0292 m, and 1 chain = 20.117 m.)
Mathematics
1 answer:
Law Incorporation [45]3 years ago
7 0

we are given

distance=6.7 furlongs

(a) In rods

we know that

1 furlong=40.0001 rod

we can multiply both sides by 6.7

6.7*1 furlong=6.7*40.0001 rod

6.7furlong=268.00067 rods..............Answer

(b) In chains

we know that

1 furlong=10 chains

we can multiply both sides by 6.7

6.7*1 furlong=6.7*10 chains

6.7furlong=67 chains..............Answer


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Let u = 4x then:

\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}

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\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}

Convert u-term back to 4x:

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\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

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\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

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