Pearson eText for Mathematics for Elementary Teachers with Activities -- Instant Access (Pearson+)
5th Edition
ISBN: 9780137442812
Author: Sybilla Beckmann
Publisher: PEARSON+
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Textbook Question
Chapter 12.2, Problem 2P
Flgure 12.14 shows the floor plan for a one-story house. Calculate the area of the floor of the house, explaining your reasoning.
Figure 12.14 Floor plan of a house.
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4.
The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x².
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MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
1
If ye y = sin x, find dy/dx and dy/dx²
at (0, 0).
Chapter 12 Solutions
Pearson eText for Mathematics for Elementary Teachers with Activities -- Instant Access (Pearson+)
Ch. 12.1 - You have a 5-foot-by-7-foot rectangular rug in...Ch. 12.1 - Draw a 3-cm-by-7-cm rectangle. Then discuss the...Ch. 12.1 - a. Explain how to decompose the large rectangle in...Ch. 12.1 - a. Explain how to decompose the large rectangle in...Ch. 12.1 - Draw a (fairly long) line segment and designate it...Ch. 12.2 - Make a shape that has area 25in2 but that has no...Ch. 12.2 - Flgure 12.14 shows the floor plan for a one-story...Ch. 12.2 - An area problem: The Johnsons are planning to...Ch. 12.2 - Figure 12.15 shows a design for an herb garden,...Ch. 12.2 - Figure 12.16 [g shows the floor plan for a modern,...
Ch. 12.2 - Use the moving and additivity principles to...Ch. 12.2 - Use the moving and additivity principles to...Ch. 12.3 - Use the moving and additivity principles to...Ch. 12.3 - For each triangle in Figure 12.31 , show the...Ch. 12.3 - Use a ruler and compass to draw three identical...Ch. 12.3 - Explain clearly in your own words why the...Ch. 12.3 - Explain clearly in your own words why the...Ch. 12.3 - Becky was asked to divide a rectangle into 4 equal...Ch. 12.3 - Explain how to use the additivity principle to...Ch. 12.3 - Determine the area of the shaded triangle that is...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Determine the area of the shaded triangle in...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Given that the rectangle ABCD in Figure 12.41 has...Ch. 12.4 - Josie has two wooden beams that are 15 feet long...Ch. 12.4 - Figure 12.47 shows a shaded parallelogram inside a...Ch. 12.4 - In the text, we saw a way to explain why the area...Ch. 12.4 - Figure 12.49 shows a trapezoid. This problem will...Ch. 12.4 - Use the moving and additivity principles to...Ch. 12.4 - Find a formula for the area of a rhombus (see...Ch. 12.4 - Determine the areas (in square units) of the 4...Ch. 12.4 - Determine the area (in square units) of the...Ch. 12.4 - Determine the area of the shaded shapes in Figure...Ch. 12.4 - A rug company weaves rugs that are made by...Ch. 12.4 - Determine the area of the shaded region in Figure...Ch. 12.4 - Given that the shaded shape in Figure 12.58 is a...Ch. 12.4 - Figure 12.59 shows a map of some land. Determine...Ch. 12.5 - Figure 12.68 shows a triangle on a pegboard....Ch. 12.5 - Make a drawing to show the result of shearing the...Ch. 12.5 - Prob. 3PCh. 12.5 - Make a drawing to show the result of shearing the...Ch. 12.5 - a. Make a drawing to show the result of shearing...Ch. 12.5 - The boundary between the Johnson and the Zhang...Ch. 12.5 - Suppose that in a trapezoid ABCD, as in Figure...Ch. 12.5 - Prob. 8PCh. 12.6 - In your own words. discuss how the diameter and...Ch. 12.6 - Tim works on the following exercise: For each...Ch. 12.6 - A large running track is constructed to have...Ch. 12.6 - Suppose you have a large spool used for winding...Ch. 12.6 - Suppose that when pizza dough is rolled out it...Ch. 12.6 - Lauriann and Kinsey are in charge of the annual...Ch. 12.6 - Penguins huddle together to stay warm in very cold...Ch. 12.6 - Jack has a truck that requires tires that are 26...Ch. 12.6 - Let r units denote the radius of each circle in...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.8 - Suppose that a student in your class wants to know...Ch. 12.8 - Sarah is confused about the difference between the...Ch. 12.8 - Describe a concrete way to demonstrate that many...Ch. 12.8 - Anya wants to draw many different rectangles that...Ch. 12.8 - On graph paper, draw 4 different rectangles that...Ch. 12.8 - Which of the lengths that follow could be the...Ch. 12.8 - a. Without using a calculator, fund the lengths...Ch. 12.8 - Draw 4 different rectangles, all of which have a...Ch. 12.8 - Draw 4 different rectangles, all of which have...Ch. 12.8 - A forest has a perimeter of 210 mi, but no...Ch. 12.8 - Bob wants to find the area of an irregular shape....Ch. 12.8 - Consider all rectangles whose area is 4 in2 ,...Ch. 12.9 - Jessica says she doesn‘t understand the...Ch. 12.9 - Town B is 380 km due south of town A. Town C is...Ch. 12.9 - What length ribbon will you need to stretch from...Ch. 12.9 - Rover the dog is on a 30-foot leash. One end of...Ch. 12.9 - Carmina and Antone measure that the distance...Ch. 12.9 - Use the Pythagorean theorem to help you determine...Ch. 12.9 - Assuming that the earth is a perfectly round,...
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