Question

1. Meteorologists can determine the duration of a storm by using the function defined by T(D)= 0.07D3/2, where D is the diameter of the storm in miles and T is the time in hours. Find the duration of a storm with a diameter of 16 mi. Round your answer to the nearest tenth of an hour.
2. The threshold weight T, in pounds, for a person is the weight above which the risk of death increases greatly. The threshold weight in pounds for men aged 40 – 49 is related to height h in inches by the function defined by h(T)=(1860.867T)1/3. What height corresponds to a threshold weight of 200 lb for a 46 yr – old man? Round your answer to the nearest inch and then to the nearest tenth of a foot.

Answer 1

Answer:

1. 4.48 hours

2. 72 inches and 6 feet.

Step-by-step explanation:

1. The function defined by$T(D) = 0.07D^{\frac{3}{2}}$ helps Meteorologists to determine the storm duration, where D is the diameter of the storm in miles and T is the time in hours.

So, the song duration in hours for a storm diameter of 16 miles will be

$T(16) = 0.07(16)^{\frac{3}{2}} = 4.48$ hours. (Answer)

2. The threshold weight (T), in pounds for men aged 40 – 49 is related to height h in inches by the function defined by $h(T) = (1860.867 T)^{\frac{1}{3} }$.

Therefore, the height in inches corresponding to a threshold weight of 200 lbs for a 46 yr-old man will be

$h(200) = (1860.867 \times 200)^{\frac{1}{3}} = 71.93$ inches ≈ 72 inches (to the nearest inches)

= 5.994 feet ≈ 6 feet ( to the nearest tenth of a foot) (Answer)