Semester Grades A professor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. Students may choose one of three schemes summarized in the accompanying matrix for weighting the points from the four items. Use matrix multiplication to determine the most advantageous weighting scheme for a student who earned 97 points on homework, 72 points on the quizzes, 83 points on the midterm exam, and 75 points on the final exam. Items HW Qu ME FE Scheme I Scheme II Scheme III [ .10 .10 .30 .50 .10 .20 .30 .40 .15 .15 .35 .35 ]
Semester Grades A professor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. Students may choose one of three schemes summarized in the accompanying matrix for weighting the points from the four items. Use matrix multiplication to determine the most advantageous weighting scheme for a student who earned 97 points on homework, 72 points on the quizzes, 83 points on the midterm exam, and 75 points on the final exam. Items HW Qu ME FE Scheme I Scheme II Scheme III [ .10 .10 .30 .50 .10 .20 .30 .40 .15 .15 .35 .35 ]
Solution Summary: The author explains that the most advantageous weighting scheme is calculated by multiplying the scheme with points a student got.
Semester Grades A professor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. Students may choose one of three schemes summarized in the accompanying matrix for weighting the points from the four items. Use matrix multiplication to determine the most advantageous weighting scheme for a student who earned 97 points on homework, 72 points on the quizzes, 83 points on the midterm exam, and 75 points on the final exam.
Items
HW
Qu
ME
FE
Scheme
I
Scheme
II
Scheme
III
[
.10
.10
.30
.50
.10
.20
.30
.40
.15
.15
.35
.35
]
Determine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.
Velocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of
the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a.
A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t².
(a) What is the average velocity of the ball over the following time intervals?
[3,4]
[3, 3.5]
[3, 3.1]
ft/sec
ft/sec
ft/sec
(b) What is the instantaneous velocity at time t = 3?
ft/sec
(c) What is the instantaneous velocity at time t = 7?
ft/sec
Is the ball rising or falling at this time?
O rising
falling
(d) When will the ball hit the ground?
t =
sec
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Chapter 2 Solutions
Finite Mathematics & Its Applications (12th Edition)
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