Rita earns scores of 78, 82, 90, 80, and 75 on her five chapter tests for a certain class and a grade of 85 on the class project. The overall average for the course is computed as follows: the average of the five chapter tests makes up 60 % of the course grade; the project accounts for 10 % of the grade; and the final exam accounts for 30 % . What scores can Rita earn on the final exam to earn a “B� in the course if the cut-off for a “B� is an overall score greater then or equal to 80, but less than 90? Assume that 100 is the biggest score that can be earned on the final exam and that only whole- number scores are given.
Rita earns scores of 78, 82, 90, 80, and 75 on her five chapter tests for a certain class and a grade of 85 on the class project. The overall average for the course is computed as follows: the average of the five chapter tests makes up 60 % of the course grade; the project accounts for 10 % of the grade; and the final exam accounts for 30 % . What scores can Rita earn on the final exam to earn a “B� in the course if the cut-off for a “B� is an overall score greater then or equal to 80, but less than 90? Assume that 100 is the biggest score that can be earned on the final exam and that only whole- number scores are given.
Solution Summary: The author calculates the score Rita must score in the final exam to earn grade "B".
Rita earns scores of 78, 82, 90, 80, and 75 on her five chapter tests for a certain class and a grade of 85 on the class project. The overall average for the course is computed as follows: the average of the five chapter tests makes up
60
%
of the course grade; the project accounts for
10
%
of the grade; and the final exam accounts for
30
%
. What scores can Rita earn on the final exam to earn a “B� in the course if the cut-off for a “B� is an overall score greater then or equal to 80, but less than 90? Assume that 100 is the biggest score that can be earned on the final exam and that only whole- number scores are given.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.