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PilotLPTM [1.2K]
2 years ago
15

17. A bottlenose dolphin jumps out of the water. The path the dolphin Travels can be

Mathematics
1 answer:
Anton [14]2 years ago
4 0

Answer:

a. 5 units

b. 5 units

Step-by-step explanation:

Given:

The path the dolphin Travels can be  modelled by h = -0.2d^2 + 2d where  h represents the height of the dolphin and d  represents horizontal distance.

To find: maximum height that the dolphin reaches and the distance covered by dolphin

Solution:

h = -0.2d^2 + 2d

Differentiate with respect to d

\frac{\mathrm{d} h}{\mathrm{d} d}=-0.4d+2

To find the critical point, put \frac{\mathrm{d} h}{\mathrm{d} d}=0

d=\frac{2}{0.4}\\=\frac{20}{4}\\=5 \,\,units

Differentiate \frac{\mathrm{d} h}{\mathrm{d} d} again with respect to d

\frac{\mathrm{d^2} h}{\mathrm{d} d^2}=-0.4

So, d=5 is a point of maxima

h(5) = -0.2(5)^2 + 2(5)\\=-0.2(25)+10\\=-5+10\\=5\,\,units

a. 5 units

b. 5 units

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