Differential Geometry | Topology Answers

Find Torison r=(a (3u, u³), 3au², 3a (3u+u³)

Prove that

gamma=(a(3u,u^ 8 ), 3a * u ^ 2, 3a * (3u + u ^ 3)

tau = 1/(k ^ 2) * (r*gamma)

Find curvature r(t) = ( ½ Cost, 1-sint, -3/2 cost)

iii) find curvature r(t) = ( ½ Cost, 1-sint, -3/2 cost)

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.

Find the level curve each of function at indicated point? (a) 𝒇(𝒙, 𝒚) = 𝒙 𝟐 − 𝒚 𝟐 , 𝒂𝒕 𝒄 = 𝟏. (b) 𝒈(𝒙, 𝒚) = 𝒆 𝒙𝒚 , 𝒂𝒕 𝒄 = 𝟎. 𝟓, 𝟑. (c) 𝒉(𝒙, 𝒚) = 𝒍𝒏 (𝒙 𝟐 + 𝒚 𝟐 ) 𝒂𝒕 𝒄 = −𝟏, 𝟎, 𝟏. 

if x={1,2,3,4} suppose that Σ={{1},{1,2},{2,3,4},{1,2,3}}, what is T(Σ)?