A Cylindrically-Shaped Mug with a 3cm Radius and a 10cm $\rho$

question 40

Multiple Choice

A cylindrically-shaped mug with a 3cm radius and a 10cm height is filled with tea.You have added some sugar to the tea, which tends to settle to the bottom of the mug.It turns out that the density $\rho$ of sugar (in gm/cm³) in the tea, as a function of the height, h, in cm, above the bottom of the mug, is given by the formula $\rho$ (h) = 0.025(10 - h) .Which of the following Riemann sums approximates the total mass of sugar (in grams) in the mug of tea?

• A) \(\sum_{\text {allslices }} 3 \pi(0.025)(10-h) \Delta h\)
• B) \(\sum_{\text {allslices }} 9 \pi(0.025)(10-h) \Delta h\)
• C) \(\sum_{\text {allslices }} 3 \pi(0.025)(10-h)^{2} \Delta h\)
• D) \(\sum_{\text {allslices }} 9 \pi(0.025)(10-h)^{2} \Delta h\)

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Definitions:

Social Connectedness

refers to the level at which individuals or groups interact with each other and form relationships, considered essential for psychological and physical well-being.

Secondary Reinforcer

A stimulus that gains reinforcement value through association with established reinforcers.

Money

A medium of exchange in the form of coins and banknotes; used as a way to value goods and services and facilitate trade.

Taste Aversions

The acquired aversion to specific food or beverage due to its connection with a distressing or sickening event.