An Object Is in the Shape Drawn Below; Its Boundary $y=2 x^{2}$

question 39

Essay

An object is in the shape drawn below; its boundary is obtained by rotating the parabola $y=2 x^{2}$ (for 0 $\le$ x $\le$ 1)around the y axis.(Units are in centimeters.)Suppose that the density of this object varies with height according to the rule $\rho$ (y)= 8 (2 - y)grams/cm³.Compute the mass in grams of this object.Give an exact answer and then round it to 2 decimal places.

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Definitions:

Common Biases

Prejudices or tendencies that influence judgment and decision-making in a non-objective way.

Impressions

The initial thoughts, feelings, or perceptions one forms about another person or entity based on limited information.

Attributing

The process of explaining the cause of behaviors or events, often associating them with particular factors or motives.

Halo Effect

The rating of an individual on one trait or characteristic tends to colour ratings on other traits or characteristics.