On an interstate highway under dry conditions, the maximum safe speed in miles per hour around a curve with radius of curvature r in feet is approximated by the equation f(r)=square root of (1.6r).
The corresponding function g(r) for the maximum safe speed under wet conditions is compressed vertically by a factor of about (5/8). Write the corresponding function g(r) for the maximum safe speed on a rainy day, and use it to estimate the maximum safe speed around a curve with a radius of curvature of 1000 feet.
The corresponding function g(r) for the maximum safe speed under wet conditions is compressed vertically by a factor of about (5/8). Write the corresponding function g(r) for the maximum safe speed on a rainy day, and use it to estimate the maximum safe speed around a curve with a radius of curvature of 1000 feet.
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Given that:
f(r) = (1.6r)^0.5
then:
g(r) = 5/8 x f(r)
then:
g(r) = 5/8 x (1.6r)^0.5
substituting "r" with 1000 (feet) in g(r) to get the safe speed on a rainy day.
g(1000) = 5/8 x (1.6 x 1000)^0.5
then:
g(1000) = 5/8 x (1600)^0.5
So:
g(1000) = 5/8 x 40 = 25 mph (mile per hour)
Final answer: 25 mph is the maximum safe speed around a curve of 1000 feet in wet conditions.
Note: the notation (^.5) used above is equivalent to "square root".
f(r) = (1.6r)^0.5
then:
g(r) = 5/8 x f(r)
then:
g(r) = 5/8 x (1.6r)^0.5
substituting "r" with 1000 (feet) in g(r) to get the safe speed on a rainy day.
g(1000) = 5/8 x (1.6 x 1000)^0.5
then:
g(1000) = 5/8 x (1600)^0.5
So:
g(1000) = 5/8 x 40 = 25 mph (mile per hour)
Final answer: 25 mph is the maximum safe speed around a curve of 1000 feet in wet conditions.
Note: the notation (^.5) used above is equivalent to "square root".
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