A cylindrical glass of water with diameter 3.5 in . sits on a horizontal counter top. a. Write an equation of the circular surface of the water. Assume that the origin is placed at the center of the circle. b. If the glass is tipped 30 ° , what shape will the surface of the water have? c. With the glass tipped 30 ° , the waterline makes a slope of 1 2 with the coordinate system shown. Determine the length of the major and minor axes. Round to 1 decimal place.
A cylindrical glass of water with diameter 3.5 in . sits on a horizontal counter top. a. Write an equation of the circular surface of the water. Assume that the origin is placed at the center of the circle. b. If the glass is tipped 30 ° , what shape will the surface of the water have? c. With the glass tipped 30 ° , the waterline makes a slope of 1 2 with the coordinate system shown. Determine the length of the major and minor axes. Round to 1 decimal place.
Solution Summary: The author explains the equation of the circular surface of water in a cylindrical glass of diameter 3.5in that sits on the horizontal counter top.
A cylindrical glass of water with diameter
3.5
in
.
sits on a horizontal counter top.
a. Write an equation of the circular surface of the water. Assume that the origin is placed at the center of the circle.
b. If the glass is tipped
30
°
,
what shape will the surface of the water have?
c. With the glass tipped
30
°
,
the waterline makes a slope of
1
2
with the coordinate system shown. Determine the length of the major and minor axes. Round to 1 decimal place.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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).
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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