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secondary 3 | A Maths
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Date Posted: 3 years ago
Views: 192
Altitude doubles means that the altitude is now 2h.
Original wind speed = 2 ln 100h
New wind speed
= 2 ln 100(2h)
= 2 ln 200h
Increase in wind speed
= 2 ln 200h - 2 ln 100h
= 2 (ln 200h - ln 100h)
= 2 ln (200h/100h)
= 2 ln 2
= ln 2²
= ln 4
Alternatively,
New wind speed
= 2 ln 100(2h)
= 2 ln 100h(2)
= 2 ln 100h + 2 ln 2
= 2 ln 100h + ln 2²
= 2 ln 100h + ln 4
= Original wind speed + ln 4
Increase in wind speed = ln 4
Original wind speed = 2 ln 100h
New wind speed
= 2 ln 100(2h)
= 2 ln 200h
Increase in wind speed
= 2 ln 200h - 2 ln 100h
= 2 (ln 200h - ln 100h)
= 2 ln (200h/100h)
= 2 ln 2
= ln 2²
= ln 4
Alternatively,
New wind speed
= 2 ln 100(2h)
= 2 ln 100h(2)
= 2 ln 100h + 2 ln 2
= 2 ln 100h + ln 2²
= 2 ln 100h + ln 4
= Original wind speed + ln 4
Increase in wind speed = ln 4
Wind speed
= 2 ln 100h
= 2 logₑ100h
= 2 lg 100h / lg e
= 2/lg e (lg 100h)
= 2/lg e (lg 100 + lg h)
= 2/lg e (lg 10² + lg h)
= 2/lg e (2lg 10 + lg h)
= 2/lg e (2 + lg h)
Alternatively,
2 ln 100h
= 2 (ln 100 + ln h)
= 2 (logₑ100 + logₑ h)
= 2 (lg 100 / lg e + lg h / lg e)
= 2/lg e (lg 100 + lg h)
= 2/lg e (lg 10² + lg h)
= 2/lg e (2lg 10 + lg h)
= 2/lg e (2 + lg h)
= 2 ln 100h
= 2 logₑ100h
= 2 lg 100h / lg e
= 2/lg e (lg 100h)
= 2/lg e (lg 100 + lg h)
= 2/lg e (lg 10² + lg h)
= 2/lg e (2lg 10 + lg h)
= 2/lg e (2 + lg h)
Alternatively,
2 ln 100h
= 2 (ln 100 + ln h)
= 2 (logₑ100 + logₑ h)
= 2 (lg 100 / lg e + lg h / lg e)
= 2/lg e (lg 100 + lg h)
= 2/lg e (lg 10² + lg h)
= 2/lg e (2lg 10 + lg h)
= 2/lg e (2 + lg h)
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