4a. at what time range is the portion of the graph the steepest? explain what is happening during this time

4a. at what time range is the portion of the graph the steepest? explain what is happening during t

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patricialeon244

21.09.2020

Mathematics

465 mi/h

Step-by-step explanation:

$\frac{da}{dt}$ = Velocity of plane = 480 mi/h

a = Distance plane travels when it is 4 mi away from radar

$\frac{db}{dt}$ = Velocity of plane with respect to height = 0 mi/h (altitude is not changing)

b = Horizontal distance between plane and radar = 1 mi

c = Distance between plane and radar after some time = 4 mi

From Pythagoras theorem

a²+b² = c²

⇒a = √(c²-b²)

⇒a = √(4²-1²)

⇒a = √15 mi

a²+b² = c²

Now, differentiating with respect to time

$2a\frac{da}{dt}+2b\frac{db}{dt}=2c\frac{dc}{dt}\\\Rightarrow a\frac{da}{dt}+b\frac{db}{dt}=c\frac{dc}{dt}\\\Rightarrow \frac{dc}{dt}=\frac{a\frac{da}{dt}+b\frac{db}{dt}}{c}\\\Rightarrow \frac{dc}{dt}=\frac{\sqrt{15}\times 480+1\times 0}{4}\\\Rightarrow \frac{dc}{dt}=464.75=465\ mi/h$

∴ Rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station is 465 mi/h

Aplane flying horizontally at an altitude of 1 mi and a speed of 480 mi/h passes directly over a rad

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