Learning. A college language class was chosen for a learning experiment. Using a list of 50 words, the experiment measured the rate of vocabulary memorization at different times during a continuous 5-hour study session. The average rate of learning for the entire class was inversely proportional to the time spent studying and was given approximately by V ′ ( t ) = 15 t 1 ≤ t ≤ 5 Find the area between the graph of V ′ and the t axis over the interval [2,4], and interpret the results.
Learning. A college language class was chosen for a learning experiment. Using a list of 50 words, the experiment measured the rate of vocabulary memorization at different times during a continuous 5-hour study session. The average rate of learning for the entire class was inversely proportional to the time spent studying and was given approximately by V ′ ( t ) = 15 t 1 ≤ t ≤ 5 Find the area between the graph of V ′ and the t axis over the interval [2,4], and interpret the results.
Solution Summary: The author calculates the area of the shaded region bounded by the graph of Vprime and the t axis over the interval.
Learning. A college language class was chosen for a learning experiment. Using a list of 50 words, the experiment measured the rate of vocabulary memorization at different times during a continuous 5-hour study session. The average rate of learning for the entire class was inversely proportional to the time spent studying and was given approximately by
V
′
(
t
)
=
15
t
1
≤
t
≤
5
Find the area between the graph of V′ and the t axis over the interval [2,4], and interpret the results.
One deck of cards is made of 4 suits (Spade, Diamond, Heart, Club) and 13 cards (A -> K), totaling 52 cards.
A flush is a combination of 5 cards with the same suit. e.g. 3d 5d 9d Jd Kd
A straight flush is a combination of 5 cards with the same suit, but also connected to each other. (e.g. highest straight flush is 10s Js Qs Ks As, the
lowest straight flush is Ah, 2h, 3h, 4h, 5h)
A straight flush is not considered a flush.
Question 2 of 4
Draw random 5 cards (in one action) from the 52 cards deck, and calculate the probability of a flush.
Provide the formula you used.
2. Consider the vector force: F(x, y, z) = 2xye²i + (x²e² + y)j + (x²ye² — z)k.
(A) [80%] Show that F satisfies the conditions for a conservative vector field, and find a potential
function (x, y, z) for F. Remark: To find o, you must use the method explained in the
lecture.
(B) [20%] Use the Fundamental Theorem for Line Integrals to compute the work done by F on
an object moves along any path from (0,1,2) to (2, 1, -8).
Game: dropping marbles from a 100-floor tower, given unlimited amount of identical marbles.
if marble breaks when dropped from level X -> it breaks from all levels higher than X
if marble doesn't break when dropped from level Y -> no marbles will break when dropped from level lower than Y
Goal of Game: Find the highest level, from which the marbles doesn't break.
Please design a testing plan to minimize the worst-case number-of-tests required to find the answer, with the constraint you
can only break max 2 marbles.
What is the minimum number of tests required? Explain your testing plan and how you arrived at this number.
Chapter 6 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)
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