Answer to Question #253495 in Differential Geometry | Topology for user1

Question

Porcelain bottles are used to hold the well-known Japanese drink, sake. The bottles are filled up to the narrow neck. A certain line of these bottles is designed as shown right, with the internal radii in cm shown at levels, which differ in height by 4 cm

1. The internal volume of the bottle is given by 𝑽 = ∫ A 𝒅s, where ds is the vertical distance up the bottle, and 𝑨 is the cross-sectional area. Estimate the internal volume correct to 3SF, using Simpson’s Rule.
2. Initial tests on a new type of electric car show that its maximum acceleration is given by the equation, 𝒂= 𝟑t, where 𝒂 is in 𝐦s^−𝟐 and 𝒕 are in seconds.

i. Determine the velocity after 4 s of travel from rest at maximum acceleration

ii. What maximum speed, in km/h, could the manufacturer claim that the vehicle can reach in 4 s?

iii. Find the distance travelled by the vehicle in this 4 s of travel time.

Answer 1

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