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const2013 [10]
3 years ago
6

A small aircraft starts its descent from an altitude of h = 1.4 miles, 4 miles west of the runway

Mathematics
1 answer:
notsponge [240]3 years ago
8 0

Answer:

Step-by-step explanation:

From the question we are told that

Altitude of Height 1.4miles

4miles west

a) From the question

f(x)=ax3+bx2+cx+d on interval (-4,0)

The descent can be expressed in \triangle _x =-4,0

therefore  initial points is (-4 , 1.4).

final co-ordinate is given by (0,0) as its landing

Mathematically solving in above  cubic equation

 0 = 0 + 0 + 0 + d \\

d = 0

1.4 = -64a + 16b -4c + d

1 = -45.7a + 11.4b-2.9c+d

Generally in this case Slope of tangent at point of descent is zero.assuming flight was initially straight before descent

     f'(x) = 3ax^2 + 2bx+c

    f'(-4) = 48a -8b + c = 0

    f'(0) = c = 0

Mathematically solving above equations we have

a = \frac{1}{40} \ and \ b = \frac{3}{20}

Therefore having found a and b the Cubic equation is given as

f(x) = \frac{1}{40}x^3 + \frac{3}{20}x^2

b)descent at its greatest rate

f(x)=\frac{1.4}{40} x^3 + \frac{129}{20} x^2

f(x)=\frac{1.4}{40} x^3 + \frac{129}{20} x^2

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