Precalculus: A Unit Circle Approach (3rd Edition)
3rd Edition
ISBN: 9780134433042
Author: J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek
Publisher: PEARSON
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Textbook Question
Chapter 6.1, Problem 29E
In Exercises 27–32, find the trigonometric function values of each corresponding complementary angle.
Given that tan 27°~0.5095, find cot 63°.
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Students have asked these similar questions
A function is defined on the interval (-π/2,π/2) by this multipart rule:
if -π/2 < x < 0
f(x) =
a
if x=0
31-tan x
+31-cot x
if 0 < x < π/2
Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0.
a=
b= 3
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
1. Compute
Lo
F⚫dr, where
and C is defined by
F(x, y) = (x² + y)i + (y − x)j
r(t) = (12t)i + (1 − 4t + 4t²)j
from the point (1, 1) to the origin.
Chapter 6 Solutions
Precalculus: A Unit Circle Approach (3rd Edition)
Ch. 6.1 - If is an acute angle in a right triangle, then...Ch. 6.1 - The sum of the two acute angles in a right...Ch. 6.1 - If is an acute angle (measured in degrees) in a...Ch. 6.1 - When looking down, the acute angle between the...Ch. 6.1 - True or False. If 0 is an acute angle in a right...Ch. 6.1 - True or False. The leg adjacent to angle in a...Ch. 6.1 - True or False. The length of the hypotenuse of a...Ch. 6.1 - True or False. We can solve a right triangle if...Ch. 6.1 - In Exercises 9—14, find the exact values for the...Ch. 6.1 - In Exercises 9-14, find the exact values for the...
Ch. 6.1 - In Exercises 9—14, find the exact values for the...Ch. 6.1 - In Exercises 9—14, find the exact values for the...Ch. 6.1 - In Exercises 9—14, find the exact values for the...Ch. 6.1 - In Exercises 9—14, find the exact values for the...Ch. 6.1 - In Exercises 15–26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15–26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 15—26, use each given trigonometric...Ch. 6.1 - In Exercises 27–32, find the trigonometric...Ch. 6.1 - In Exercises 27–32, find the trigonometric...Ch. 6.1 - In Exercises 27–32, find the trigonometric...Ch. 6.1 - In Exercises 27–32, find the trigonometric...Ch. 6.1 - In Exercises 27–32, find the trigonometric...Ch. 6.1 - In Exercises 27–32, find the trigonometric...Ch. 6.1 - In Exercises 33—40, solve each right triangle;...Ch. 6.1 - In Exercises 33—40, solve each right triangle;...Ch. 6.1 - In Exercises 33—40, solve each right triangle;...Ch. 6.1 - In Exercises 33—40, solve each right triangle;...Ch. 6.1 - In Exercises 33—40, solve each right triangle;...Ch. 6.1 - In Exercises 33–40, solve each right triangle;...Ch. 6.1 - In Exercises 33—40, solve each right triangle;...Ch. 6.1 - In Exercises 33—40, solve each right triangle;...Ch. 6.1 - In Exercises 41—48, use the figure and the given...Ch. 6.1 - In Exercises 41—48, use the figure and the given...Ch. 6.1 - In Exercises 41—48, use the figure and the given...Ch. 6.1 - In Exercises 41—48, use the figure and the given...Ch. 6.1 - In Exercises 41—48, use the figure and the given...Ch. 6.1 - In Exercises 41—48, use the figure and the given...Ch. 6.1 - In Exercises 41—48, use the figure and the given...Ch. 6.1 - In Exercises 41—48, use the figure and the given...Ch. 6.1 - Positioning a ladder. An 18-foot ladder is resting...Ch. 6.1 - Positioning a ladder. The ladder from Exercise 49...Ch. 6.1 - In Exercises 51 and 52, use the following...Ch. 6.1 - In Exercises 51 and 52, use the following...Ch. 6.1 - Ski lift height. If a skier travels 5000 feet up a...Ch. 6.1 - Shadow length. At a time when the sun’s rays make...Ch. 6.1 - Height of a tree. The angle relative to the...Ch. 6.1 - Height of a cliff. The angle of elevation from a...Ch. 6.1 - Height of a flagpole. A flagpole is supported by a...Ch. 6.1 - Flying a kite. A girl 5 feet tail is flying a kite...Ch. 6.1 - Width of a river. Sal and his friend are on...Ch. 6.1 - Measuring the Empire State Building. From a...Ch. 6.1 - Sighting a mortar station. The angle of depression...Ch. 6.1 - Distance between Earth and the moon. If the radius...Ch. 6.1 - Sprinkler rotation. A sprinkler rotates back and...Ch. 6.1 - Irradiating flowers. A tray of flowers is being...Ch. 6.1 - In Exercises 65 and 66, use the figure to find the...Ch. 6.1 - In Exercises 65 and 66, use the figure to find the...Ch. 6.1 - Motorcycle racing. A video camera is set up 110...Ch. 6.1 - Viewing angle. The bottom of a 50-foot movie...Ch. 6.1 - Height of an airplane. From a tower 150 feet high...Ch. 6.1 - Camera angle. Raphael stands 12 feet from a large...Ch. 6.1 - Height of a building. The WCNC-TV Tower in Dallas....Ch. 6.1 - Height of a building. Suppose from the top of the...Ch. 6.1 - In the figure below, show that .
Ch. 6.1 - Height of a plane. A plane flies directly over two...Ch. 6.1 - Maturing the Statue Of Liberty. While sailing...Ch. 6.1 - Prob. 76ECh. 6.1 - Flagpole height. The angle of elevation of the top...Ch. 6.1 - Airplane height. A plane flying at a height of...Ch. 6.1 - In the figure below, show that .
Ch. 6.1 - Find the area of the triangle in the...Ch. 6.1 - Find the area of triangle ABC in the figure....Ch. 6.1 - Find the area of the segment (see the shaded...Ch. 6.1 - Draw a right triangle with acute angle . Then use...Ch. 6.1 - In a right triangle with acute angle , what value...Ch. 6.1 - Use the result of Exercise 84 to compare tan and...Ch. 6.1 - Let ABC be a triangle with right angle at C. The...Ch. 6.1 - In Exercises 87–90, let ABC be a triangle. Then...Ch. 6.1 - In Exercises 87–90, let ABC be a triangle. Then...Ch. 6.1 - In Exercises 87–90, let ABC be a triangle. Then...Ch. 6.1 - In Exercises 87–90, let ABC be a triangle. Then...Ch. 6.1 - In Exercises 91–96, solve each equation for x to...Ch. 6.1 - In Exercises 91–96, solve each equation for x to...Ch. 6.1 - In Exercises 91–96, solve each equation for x to...Ch. 6.1 - In Exercises 91–96, solve each equation for x to...Ch. 6.1 - In Exercises 91–96, solve each equation for x to...Ch. 6.1 - In Exercises 91–96, solve each equation for x to...Ch. 6.1 - In Exercises 97—100, find the height h to the...Ch. 6.1 - In Exercises 97—100, find the height h to the...Ch. 6.1 - In Exercises 97—100, find the height h to the...Ch. 6.1 - In Exercises 97—100, find the height h to the...Ch. 6.1 - In Exercises 101—1 04, find the area of each...Ch. 6.1 - In Exercises 101—1 04, find the area of each...Ch. 6.1 - In Exercises 101—1 04, find the area of each...Ch. 6.1 - In Exercises 101—1 04, find the area of each...Ch. 6.2 - If you know two angles of a triangle, then you can...Ch. 6.2 - Prob. 2ECh. 6.2 - You are given any two angles and one side, then...Ch. 6.2 - For given data a, A, and b, there can be no...Ch. 6.2 - True or False. The Law of Sines allows you to...Ch. 6.2 - True or False. A triangle is uniquely determined...Ch. 6.2 - True or False. In a triangle ABC, .
Ch. 6.2 - True or False. The Law of Sines cannot be used to...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 9—20, the data from a triangle ABC is...Ch. 6.2 - In Exercises 2 1—24, solve each triangle. Round...Ch. 6.2 - In Exercises 2 1—24, solve each triangle. Round...Ch. 6.2 - In Exercises 2 1—24, solve each triangle. Round...Ch. 6.2 - In Exercises 2 1—24, solve each triangle. Round...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 25—36, solve triangle ABC. Round each...Ch. 6.2 - In Exercises 37—40, solve each triangle. Round...Ch. 6.2 - In Exercises 37—40, solve each triangle. Round...Ch. 6.2 - In Exercises 37—40, solve each triangle. Round...Ch. 6.2 - In Exercises 37—40, solve each triangle. Round...Ch. 6.2 - In Exercises 41—46, determine the number of...Ch. 6.2 - In Exercises 41—46, determine the number of...Ch. 6.2 - In Exercises 41—46, determine the number of...Ch. 6.2 - In Exercises 41—46, determine the number of...Ch. 6.2 - In Exercises 41—46, determine the number of...Ch. 6.2 - In Exercises 41—46, determine the number of...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 47—66, solve each SSA mangle Indicate...Ch. 6.2 - In Exercises 67—72, find the exact value of the...Ch. 6.2 - In Exercises 67—72, find the exact value of the...Ch. 6.2 - In Exercises 67—72, find the exact value of the...Ch. 6.2 - In Exercises 67—72, find the exact value of the...Ch. 6.2 - In Exercises 67—72, find the exact value of the...Ch. 6.2 - In Exercises 67—72, find the exact value of the...Ch. 6.2 - In Exercises 73–80, find the area of each triangle...Ch. 6.2 - In Exercises 73–80, find the area of each triangle...Ch. 6.2 - In Exercises 73–80, find the area of each triangle...Ch. 6.2 - In Exercises 73–80, find the area of each triangle...Ch. 6.2 - In Exercises 73–80, find the area of each triangle...Ch. 6.2 - In Exercises 73–80, find the area of each triangle...Ch. 6.2 - In Exercises 73–80, find the area of each triangle...Ch. 6.2 - In Exercises 73–80, find the area of each triangle...Ch. 6.2 - In Exercises 81—84, find an angle between the...Ch. 6.2 - In Exercises 81—84, find an angle between the...Ch. 6.2 - In Exercises 81—84, find an angle between the...Ch. 6.2 - In Exercises 81—84, find an angle between the...Ch. 6.2 - Finding distance. Angela wants to find the...Ch. 6.2 - Finding distance. In Exercise 85, find the width...Ch. 6.2 - Target. A laser beam with an angle of elevation of...Ch. 6.2 - Height of a flagpole. Two surveyors stand 200 feet...Ch. 6.2 - Radio beacon. A ship sailing due east at the rate...Ch. 6.2 - Lighthouse. A boat sailing due north at the rate...Ch. 6.2 - Geostationary satellite. A camel rider was...Ch. 6.2 - Height of a tower. A flagpole 20 feet tall is...Ch. 6.2 - Prob. 93ECh. 6.2 - Distance between planets. The angle subtended at...Ch. 6.2 - Navigation. A point is located 30 miles southwest...Ch. 6.2 - Navigation. A lighthouse is 23 miles N 55º E of a...Ch. 6.2 - Geometry. The sides of a parallelogram are 15...Ch. 6.2 - Geometry. In the trapezoid shown, find the length...Ch. 6.2 - Area of the Bermuda Triangle. The angle formed by...Ch. 6.2 - Landscaping. A triangular region between the three...Ch. 6.2 - Suppose CD bisects angle C of triangle ABC. Show...Ch. 6.2 - Distance. A flagpole 15 feet high stands on a...Ch. 6.2 - Navigation. A point on an island is located 24...Ch. 6.2 - Geometry. A side or a parallelogram is 60 inches...Ch. 6.2 - Mollweide’s formula. In a triangle ABC, prove...Ch. 6.2 - Mollweide’s formula. In a triangle ABC, prove that...Ch. 6.2 - Law of Tangents. In a triangle ABC, prove that
Ch. 6.2 - Angle measure. Two sides of a mangle are feet and...Ch. 6.2 - In Exercises 109 and 110, give the most specific...Ch. 6.2 - Use the Law of Sines to show that any isosceles...Ch. 6.2 - Use the Law of Sines to show that any triangle...Ch. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - Prob. 120ECh. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - In Exercises 113—126, write the exact value of...Ch. 6.2 - Prob. 123ECh. 6.2 - Prob. 124ECh. 6.2 - Prob. 125ECh. 6.2 - Prob. 126ECh. 6.3 - One form of the Law of Cosines is cos...Ch. 6.3 - If we take the angle in the Law of Cosines to be...Ch. 6.3 - Triangles with SAS given are solved by the Law of...Ch. 6.3 - When one angle is found by the Law of Cosines,...Ch. 6.3 - True or False. The Law of Cosines is used to solve...Ch. 6.3 - True or False. For a triangle with SSS given, we...Ch. 6.3 - True or False. The Pythagorean Theorem is a...Ch. 6.3 - True or False. If , then no such triangle ABC...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 9—18, find the unknown part in...Ch. 6.3 - In Exercises 19—22, solve each triangle. Round...Ch. 6.3 - In Exercises 19—22, solve each triangle. Round...Ch. 6.3 - In Exercises 19—22, solve each triangle. Round...Ch. 6.3 - Prob. 22ECh. 6.3 - In Exercises 23—38, solve each mangle ABC. Round...Ch. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - In Exercises 23—38, solve each mangle ABC. Round...Ch. 6.3 - In Exercises 23—38, solve each mangle ABC. Round...Ch. 6.3 - In Exercises 23—38, solve each mangle ABC. Round...Ch. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - In Exercises 39—46, find the area of each triangle...Ch. 6.3 - Prob. 40ECh. 6.3 - In Exercises 39—46, find the area of each triangle...Ch. 6.3 - Prob. 42ECh. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - Prob. 45ECh. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.3 - In Exercises 47—60, round each answer to the...Ch. 6.3 - In Exercises 47—60, round each answer to the...Ch. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - Prob. 57ECh. 6.3 - Prob. 58ECh. 6.3 - Prob. 59ECh. 6.3 - Prob. 60ECh. 6.3 - In Exercises 61—64, round each answer to the...Ch. 6.3 - Prob. 62ECh. 6.3 - Prob. 63ECh. 6.3 - Prob. 64ECh. 6.3 - Prob. 65ECh. 6.3 - Prob. 66ECh. 6.3 - Prob. 67ECh. 6.3 - Prob. 68ECh. 6.3 - Prob. 69ECh. 6.3 - Prob. 70ECh. 6.3 - Prob. 71ECh. 6.3 - Prob. 72ECh. 6.3 - Prob. 73ECh. 6.3 - Prob. 74ECh. 6.3 - Prob. 75ECh. 6.3 - Prob. 76ECh. 6.3 - Prob. 77ECh. 6.3 - Prob. 78ECh. 6.3 - Prob. 79ECh. 6.3 - Prob. 80ECh. 6.3 - Prob. 81ECh. 6.3 - Prob. 82ECh. 6.3 - Prob. 83ECh. 6.3 - Prob. 84ECh. 6.3 - Prob. 85ECh. 6.3 - Prob. 86ECh. 6.3 - In Exercises 87—90, let l1 be the line passing...Ch. 6.3 - Prob. 88ECh. 6.3 - Prob. 89ECh. 6.3 - Prob. 90ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - In Exercises 37—46, find a unit vector u En the...Ch. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6.4 - Prob. 43ECh. 6.4 - Prob. 44ECh. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Prob. 49ECh. 6.4 - Prob. 50ECh. 6.4 - Prob. 51ECh. 6.4 - Prob. 52ECh. 6.4 - Prob. 53ECh. 6.4 - Prob. 54ECh. 6.4 - Prob. 55ECh. 6.4 - Prob. 56ECh. 6.4 - Prob. 57ECh. 6.4 - Prob. 58ECh. 6.4 - Prob. 59ECh. 6.4 - Prob. 60ECh. 6.4 - Prob. 61ECh. 6.4 - Prob. 62ECh. 6.4 - Prob. 63ECh. 6.4 - Prob. 64ECh. 6.4 - Prob. 65ECh. 6.4 - Prob. 66ECh. 6.4 - Prob. 67ECh. 6.4 - Prob. 68ECh. 6.4 - Prob. 69ECh. 6.4 - Prob. 70ECh. 6.4 - Prob. 71ECh. 6.4 - Prob. 72ECh. 6.4 - Prob. 73ECh. 6.4 - Prob. 74ECh. 6.4 - Prob. 75ECh. 6.4 - In Exercises 69—80, write each answer to the...Ch. 6.4 - Prob. 77ECh. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - Prob. 80ECh. 6.4 - In Exercises 81 and 82, find a single force that...Ch. 6.4 - Prob. 82ECh. 6.4 - Prob. 83ECh. 6.4 - Prob. 84ECh. 6.4 - Prob. 85ECh. 6.4 - Prob. 86ECh. 6.4 - Prob. 87ECh. 6.4 - Prob. 88ECh. 6.4 - Prob. 89ECh. 6.4 - Prob. 90ECh. 6.4 - Prob. 91ECh. 6.4 - Prob. 92ECh. 6.4 - Prob. 93ECh. 6.4 - Prob. 94ECh. 6.4 - Prob. 95ECh. 6.4 - Prob. 96ECh. 6.4 - Prob. 97ECh. 6.4 - Prob. 98ECh. 6.4 - Prob. 99ECh. 6.4 - Prob. 100ECh. 6.4 - Prob. 101ECh. 6.4 - Prob. 102ECh. 6.4 - Prob. 103ECh. 6.4 - Prob. 104ECh. 6.4 - Prob. 105ECh. 6.4 - Prob. 106ECh. 6.4 - Prob. 107ECh. 6.4 - Prob. 108ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Prob. 24ECh. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Prob. 27ECh. 6.5 - Prob. 28ECh. 6.5 - Prob. 29ECh. 6.5 - Prob. 30ECh. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - Prob. 35ECh. 6.5 - Prob. 36ECh. 6.5 - Prob. 37ECh. 6.5 - Prob. 38ECh. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Prob. 42ECh. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - Prob. 45ECh. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - Prob. 48ECh. 6.5 - Prob. 49ECh. 6.5 - Prob. 50ECh. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Prob. 53ECh. 6.5 - Prob. 54ECh. 6.5 - Prob. 55ECh. 6.5 - Prob. 56ECh. 6.5 - Prob. 57ECh. 6.5 - In Exercises 55—62, determine the scalar c so that...Ch. 6.5 - Prob. 59ECh. 6.5 - Prob. 60ECh. 6.5 - Prob. 61ECh. 6.5 - Prob. 62ECh. 6.5 - Prob. 63ECh. 6.5 - Prob. 64ECh. 6.5 - Prob. 65ECh. 6.5 - Prob. 66ECh. 6.5 - Prob. 67ECh. 6.5 - Prob. 68ECh. 6.5 - Prob. 69ECh. 6.5 - Prob. 70ECh. 6.5 - Prob. 71ECh. 6.5 - Prob. 72ECh. 6.5 - Prob. 73ECh. 6.5 - Prob. 74ECh. 6.5 - Prob. 75ECh. 6.5 - Prob. 76ECh. 6.5 - Prob. 77ECh. 6.5 - Prob. 78ECh. 6.5 - Prob. 79ECh. 6.5 - Prob. 80ECh. 6.5 - Prob. 81ECh. 6.5 - Prob. 82ECh. 6.5 - Prob. 83ECh. 6.5 - Prob. 84ECh. 6.5 - Prob. 85ECh. 6.5 - Prob. 86ECh. 6.5 - Prob. 87ECh. 6.5 - Prob. 88ECh. 6.5 - Prob. 89ECh. 6.5 - Prob. 90ECh. 6.5 - Prob. 91ECh. 6.5 - Prob. 92ECh. 6.5 - Prob. 93ECh. 6.5 - Prob. 94ECh. 6.5 - Prob. 95ECh. 6.5 - Prob. 96ECh. 6.5 - Prob. 97ECh. 6.5 - Prob. 98ECh. 6.5 - Prob. 99ECh. 6.5 - Prob. 100ECh. 6.5 - Prob. 101ECh. 6.5 - Prob. 102ECh. 6.5 - Prob. 103ECh. 6.5 - Prob. 104ECh. 6.5 - Prob. 105ECh. 6.5 - Prob. 106ECh. 6.5 - Prob. 107ECh. 6.5 - Prob. 108ECh. 6.5 - Prob. 109ECh. 6.5 - Prob. 110ECh. 6.5 - Prob. 111ECh. 6.5 - Prob. 112ECh. 6.5 - Prob. 113ECh. 6.5 - Prob. 114ECh. 6.5 - Prob. 115ECh. 6.5 - Prob. 116ECh. 6.6 - Prob. 1ECh. 6.6 - The positive value of r corresponds to a distance...Ch. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Prob. 5ECh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Prob. 8ECh. 6.6 - In Exercises 9—16, plot the point having the given...Ch. 6.6 - In Exercises 9—16, plot the point having the given...Ch. 6.6 - In Exercises 9—16, plot the point having the given...Ch. 6.6 - In Exercises 9—16, plot the point having the given...Ch. 6.6 - In Exercises 9—16, plot the point having the given...Ch. 6.6 - In Exercises 9—16, plot the point having the given...Ch. 6.6 - In Exercises 9—16, plot the point having the given...Ch. 6.6 - In Exercises 9—16, plot the point having the given...Ch. 6.6 - Prob. 17ECh. 6.6 - In Exercises 17—24, plot the point having the...Ch. 6.6 - Prob. 19ECh. 6.6 - In Exercises 17—24, plot the point having the...Ch. 6.6 - In Exercises 17—24, plot the point having the...Ch. 6.6 - In Exercises 17—24, plot the point having the...Ch. 6.6 - In Exercises 17—24, plot the point having the...Ch. 6.6 - In Exercises 17—24, plot the point having the...Ch. 6.6 - In Exercises 25–32, convert the given polar...Ch. 6.6 - In Exercises 25–32, convert the given polar...Ch. 6.6 - Prob. 27ECh. 6.6 - Prob. 28ECh. 6.6 - Prob. 29ECh. 6.6 - Prob. 30ECh. 6.6 - Prob. 31ECh. 6.6 - Prob. 32ECh. 6.6 - In Exercises 33–40, convert the rectangular...Ch. 6.6 - Prob. 34ECh. 6.6 - Prob. 35ECh. 6.6 - Prob. 36ECh. 6.6 - Prob. 37ECh. 6.6 - Prob. 38ECh. 6.6 - Prob. 39ECh. 6.6 - Prob. 40ECh. 6.6 - In Exercises 41—52, convert each rectangular...Ch. 6.6 - Prob. 42ECh. 6.6 - In Exercises 41—52, convert each rectangular...Ch. 6.6 - Prob. 44ECh. 6.6 - In Exercises 41—52, convert each rectangular...Ch. 6.6 - Prob. 46ECh. 6.6 - Prob. 47ECh. 6.6 - Prob. 48ECh. 6.6 - Prob. 49ECh. 6.6 - Prob. 50ECh. 6.6 - Prob. 51ECh. 6.6 - Prob. 52ECh. 6.6 - In Exercises 53–62, convert each polar equation to...Ch. 6.6 - In Exercises 53—62, convert each polar equation to...Ch. 6.6 - In Exercises 53—62, convert each polar equation to...Ch. 6.6 - Prob. 56ECh. 6.6 - Prob. 57ECh. 6.6 - Prob. 58ECh. 6.6 - Prob. 59ECh. 6.6 - Prob. 60ECh. 6.6 - Prob. 61ECh. 6.6 - Prob. 62ECh. 6.6 - Prob. 63ECh. 6.6 - Prob. 64ECh. 6.6 - Prob. 65ECh. 6.6 - Prob. 66ECh. 6.6 - Prob. 67ECh. 6.6 - Prob. 68ECh. 6.6 - Prob. 69ECh. 6.6 - Prob. 70ECh. 6.6 - Prob. 71ECh. 6.6 - Prob. 72ECh. 6.6 - Prob. 73ECh. 6.6 - Prob. 74ECh. 6.6 - Prob. 75ECh. 6.6 - Prob. 76ECh. 6.6 - Prob. 77ECh. 6.6 - Prob. 78ECh. 6.6 - Prob. 79ECh. 6.6 - Prob. 80ECh. 6.6 - Prob. 81ECh. 6.6 - Prob. 82ECh. 6.6 - Prob. 83ECh. 6.6 - Prob. 84ECh. 6.6 - Prob. 85ECh. 6.6 - Prob. 86ECh. 6.6 - In Exercises 87—90, determine the position of the...Ch. 6.6 - Prob. 88ECh. 6.6 - Prob. 89ECh. 6.6 - Prob. 90ECh. 6.6 - Prob. 91ECh. 6.6 - Prob. 92ECh. 6.6 - Prob. 93ECh. 6.6 - Prob. 94ECh. 6.6 - Prob. 95ECh. 6.6 - Prob. 96ECh. 6.6 - Prob. 97ECh. 6.6 - Prob. 98ECh. 6.6 - Prob. 99ECh. 6.6 - Prob. 100ECh. 6.6 - Prob. 101ECh. 6.6 - Prob. 102ECh. 6.6 - Prob. 103ECh. 6.6 - Prob. 104ECh. 6.6 - Prob. 105ECh. 6.6 - Prob. 106ECh. 6.6 - Prob. 107ECh. 6.6 - Prob. 108ECh. 6.6 - Prob. 109ECh. 6.6 - Prob. 110ECh. 6.6 - Prob. 111ECh. 6.6 - Prob. 112ECh. 6.6 - Prob. 113ECh. 6.6 - Prob. 114ECh. 6.6 - Prob. 115ECh. 6.6 - Prob. 116ECh. 6.6 - Prob. 117ECh. 6.6 - Prob. 118ECh. 6.6 - Prob. 119ECh. 6.6 - Prob. 120ECh. 6.6 - Prob. 121ECh. 6.6 - Prob. 122ECh. 6.6 - Prob. 123ECh. 6.6 - Prob. 124ECh. 6.6 - Prob. 125ECh. 6.6 - Prob. 126ECh. 6.6 - Prob. 127ECh. 6.6 - Prob. 128ECh. 6.6 - Prob. 129ECh. 6.6 - Prob. 130ECh. 6.6 - Prob. 131ECh. 6.6 - Prob. 132ECh. 6.6 - Prob. 133ECh. 6.6 - Prob. 134ECh. 6.6 - Prob. 135ECh. 6.6 - Prob. 136ECh. 6.6 - Prob. 137ECh. 6.6 - Prob. 138ECh. 6.6 - Prob. 139ECh. 6.6 - Prob. 140ECh. 6.6 - Prob. 141ECh. 6.6 - Prob. 142ECh. 6.7 - Prob. 1ECh. 6.7 - Prob. 2ECh. 6.7 - Prob. 3ECh. 6.7 - Prob. 4ECh. 6.7 - Prob. 5ECh. 6.7 - Prob. 6ECh. 6.7 - Prob. 7ECh. 6.7 - Prob. 8ECh. 6.7 - Prob. 9ECh. 6.7 - Prob. 10ECh. 6.7 - Prob. 11ECh. 6.7 - Prob. 12ECh. 6.7 - Prob. 13ECh. 6.7 - Prob. 14ECh. 6.7 - Prob. 15ECh. 6.7 - Prob. 16ECh. 6.7 - Prob. 17ECh. 6.7 - Prob. 18ECh. 6.7 - Prob. 19ECh. 6.7 - Prob. 20ECh. 6.7 - Prob. 21ECh. 6.7 - Prob. 22ECh. 6.7 - Prob. 23ECh. 6.7 - Prob. 24ECh. 6.7 - Prob. 25ECh. 6.7 - Prob. 26ECh. 6.7 - In Exercises 17—28, write each complex number in...Ch. 6.7 - Prob. 28ECh. 6.7 - Prob. 29ECh. 6.7 - Prob. 30ECh. 6.7 - Prob. 31ECh. 6.7 - Prob. 32ECh. 6.7 - Prob. 33ECh. 6.7 - Prob. 34ECh. 6.7 - Prob. 35ECh. 6.7 - Prob. 36ECh. 6.7 - Prob. 37ECh. 6.7 - Prob. 38ECh. 6.7 - Prob. 39ECh. 6.7 - Prob. 40ECh. 6.7 - Prob. 41ECh. 6.7 - Prob. 42ECh. 6.7 - Prob. 43ECh. 6.7 - Prob. 44ECh. 6.7 - Prob. 45ECh. 6.7 - Prob. 46ECh. 6.7 - Prob. 47ECh. 6.7 - Prob. 48ECh. 6.7 - Prob. 49ECh. 6.7 - Prob. 50ECh. 6.7 - Prob. 51ECh. 6.7 - Prob. 52ECh. 6.7 - Prob. 53ECh. 6.7 - Prob. 54ECh. 6.7 - Prob. 55ECh. 6.7 - Prob. 56ECh. 6.7 - Prob. 57ECh. 6.7 - Prob. 58ECh. 6.7 - Prob. 59ECh. 6.7 - Prob. 60ECh. 6.7 - Prob. 61ECh. 6.7 - Prob. 62ECh. 6.7 - Prob. 63ECh. 6.7 - Prob. 64ECh. 6.7 - Prob. 65ECh. 6.7 - Prob. 66ECh. 6.7 - Prob. 67ECh. 6.7 - Prob. 68ECh. 6.7 - Prob. 69ECh. 6.7 - Prob. 70ECh. 6.7 - Prob. 71ECh. 6.7 - Prob. 72ECh. 6.7 - In Exercises 71—78, find all complex roots. Write...Ch. 6.7 - Prob. 74ECh. 6.7 - Prob. 75ECh. 6.7 - Prob. 76ECh. 6.7 - Prob. 77ECh. 6.7 - Prob. 78ECh. 6.7 - Prob. 79ECh. 6.7 - Prob. 80ECh. 6.7 - Prob. 81ECh. 6.7 - Prob. 82ECh. 6.7 - Prob. 83ECh. 6.7 - Prob. 84ECh. 6.7 - Prob. 85ECh. 6.7 - Prob. 86ECh. 6.7 - Prob. 87ECh. 6.7 - Prob. 88ECh. 6.7 - Prob. 89ECh. 6.7 - Prob. 90ECh. 6.7 - Prob. 91ECh. 6.7 - Prob. 92ECh. 6.7 - In Exercises 91—96, find all complex solutions or...Ch. 6.7 - Prob. 94ECh. 6.7 - Prob. 95ECh. 6.7 - Prob. 96ECh. 6.7 - Prob. 97ECh. 6.7 - Prob. 98ECh. 6.7 - Prob. 99ECh. 6.7 - Prob. 100ECh. 6.7 - Prob. 101ECh. 6.7 - Prob. 102ECh. 6.7 - Prob. 103ECh. 6.7 - Prob. 104ECh. 6.7 - Prob. 105ECh. 6.7 - Prob. 106ECh. 6.7 - Prob. 107ECh. 6.7 - Prob. 108ECh. 6.7 - Prob. 109ECh. 6.7 - Prob. 110ECh. 6.7 - Prob. 111ECh. 6.7 - Prob. 112ECh. 6.7 - Prob. 113ECh. 6.7 - Prob. 114ECh. 6.7 - Prob. 115ECh. 6.7 - Prob. 116ECh. 6.7 - Prob. 117ECh. 6.7 - Prob. 118ECh. 6.7 - Prob. 119ECh. 6.7 - Prob. 120ECh. 6 - In Exercises 1—10, solve right triangle ABC with...Ch. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - In Exercises 55—58, plot each point in polar...Ch. 6 - In Exercises 59–62, convert the rectangular...Ch. 6 - In Exercises 59–62, convert the rectangular...Ch. 6 - In Exercises 59–62, convert the rectangular...Ch. 6 - In Exercises 59–62, convert the rectangular...Ch. 6 - In Exercises 63–66, convert each rectangular...Ch. 6 - Prob. 64RECh. 6 - In Exercises 63–66, convert each rectangular...Ch. 6 - Prob. 66RECh. 6 - Prob. 67RECh. 6 - Prob. 68RECh. 6 - Prob. 69RECh. 6 - Prob. 70RECh. 6 - Prob. 71RECh. 6 - Prob. 72RECh. 6 - Prob. 73RECh. 6 - Prob. 74RECh. 6 - Prob. 75RECh. 6 - Prob. 76RECh. 6 - Prob. 77RECh. 6 - Prob. 78RECh. 6 - Prob. 79RECh. 6 - Prob. 80RECh. 6 - Prob. 81RECh. 6 - Prob. 82RECh. 6 - Prob. 83RECh. 6 - Prob. 84RECh. 6 - Prob. 85RECh. 6 - Prob. 86RECh. 6 - Prob. 87RECh. 6 - Prob. 88RECh. 6 - Prob. 89RECh. 6 - Prob. 90RECh. 6 - In Exercises 89—92, find all complex roots. Write...Ch. 6 - Prob. 92RECh. 6 - Prob. 93RECh. 6 - Angle of elevation of a hill. A tower 120 feet...Ch. 6 - Prob. 95RECh. 6 - Prob. 96RECh. 6 - Prob. 97RECh. 6 - Resultant force. Two forces of magnitudes 16 and...Ch. 6 - Prob. 99RECh. 6 - AC current. The total impedance in an AC circuit...Ch. 6 - Prob. 1PTACh. 6 - Prob. 2PTACh. 6 - Prob. 3PTACh. 6 - Prob. 4PTACh. 6 - Prob. 5PTACh. 6 - Prob. 6PTACh. 6 - A surveyor, starting from point A, walks 580 feet...Ch. 6 - Prob. 8PTACh. 6 - Prob. 9PTACh. 6 - Prob. 10PTACh. 6 - Prob. 11PTACh. 6 - Prob. 12PTACh. 6 - Prob. 13PTACh. 6 - Prob. 14PTACh. 6 - Prob. 15PTACh. 6 - Prob. 16PTACh. 6 - Prob. 17PTACh. 6 - Prob. 18PTACh. 6 - Prob. 19PTACh. 6 - Prob. 20PTACh. 6 - Prob. 1PTBCh. 6 - Prob. 2PTBCh. 6 - Prob. 3PTBCh. 6 - Prob. 4PTBCh. 6 - Prob. 5PTBCh. 6 - Prob. 6PTBCh. 6 - Prob. 7PTBCh. 6 - Prob. 8PTBCh. 6 - Prob. 9PTBCh. 6 - Prob. 10PTBCh. 6 - Prob. 11PTBCh. 6 - Prob. 12PTBCh. 6 - Prob. 13PTBCh. 6 - Prob. 14PTBCh. 6 - Prob. 15PTBCh. 6 - Prob. 16PTBCh. 6 - Prob. 17PTBCh. 6 - Prob. 18PTBCh. 6 - Prob. 19PTBCh. 6 - Prob. 20PTBCh. 6 - Prob. 1CRECh. 6 - Prob. 2CRECh. 6 - Prob. 3CRECh. 6 - Prob. 4CRECh. 6 - Prob. 5CRECh. 6 - Prob. 6CRECh. 6 - Prob. 7CRECh. 6 - In Exercises 7 and 8, find all complex roots....Ch. 6 - Prob. 9CRECh. 6 - Prob. 10CRECh. 6 - Prob. 11CRECh. 6 - Prob. 12CRECh. 6 - Prob. 13CRECh. 6 - Prob. 14CRECh. 6 - Prob. 15CRECh. 6 - Prob. 16CRECh. 6 - Prob. 17CRECh. 6 - Prob. 18CRECh. 6 - Prob. 19CRECh. 6 - Prob. 20CRE
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- 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).arrow_forwardhelp pleasearrow_forwardIn each of Problems 1 through 4, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of y at t = 0, describe the dependency.1. y′ = 3 − 2yarrow_forward
- B 2- The figure gives four points and some corresponding rays in the xy-plane. Which of the following is true? A B Angle COB is in standard position with initial ray OB and terminal ray OC. Angle COB is in standard position with initial ray OC and terminal ray OB. C Angle DOB is in standard position with initial ray OB and terminal ray OD. D Angle DOB is in standard position with initial ray OD and terminal ray OB.arrow_forwardtemperature in degrees Fahrenheit, n hours since midnight. 5. The temperature was recorded at several times during the day. Function T gives the Here is a graph for this function. To 29uis a. Describe the overall trend of temperature throughout the day. temperature (Fahrenheit) 40 50 50 60 60 70 5 10 15 20 25 time of day b. Based on the graph, did the temperature change more quickly between 10:00 a.m. and noon, or between 8:00 p.m. and 10:00 p.m.? Explain how you know. (From Unit 4, Lesson 7.) 6. Explain why this graph does not represent a function. (From Unit 4, Lesson 8.)arrow_forwardFind the area of the shaded region. (a) 5- y 3 2- (1,4) (5,0) 1 3 4 5 6 (b) 3 y 2 Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. STEP 1: Consider the figure in part (a). Since this region is simply a triangle, you may use precalculus methods to solve this part of the problem. First determine the height of the triangle and the length of the triangle's base. height 4 units units base 5 STEP 2: Compute the area of the triangle by employing a formula from precalculus, thus finding the area of the shaded region in part (a). 10 square units STEP 3: Consider the figure in part (b). Since this region is defined by a complicated curve, the problem seems to require calculus. Find an approximation of the shaded region by using a graphical approach. (Hint: Treat the shaded regi as…arrow_forward
- Solve this differential equation: dy 0.05y(900 - y) dt y(0) = 2 y(t) =arrow_forwardSuppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The graph models the depth of the submarine as a function of time. What is the domain and range of the function in the graph? 1- t (time) 1 2 4/5 6 7 8 -2 -3 456700 -4 -5 -6 -7 d (depth) -8 D: 00 t≤ R:arrow_forward0 5 -1 2 1 N = 1 to x = 3 Based on the graph above, estimate to one decimal place the average rate of change from x =arrow_forwardComplete the description of the piecewise function graphed below. Use interval notation to indicate the intervals. -7 -6 -5 -4 30 6 5 4 3 0 2 1 -1 5 6 + -2 -3 -5 456 -6 - { 1 if x Є f(x) = { 1 if x Є { 3 if x Єarrow_forwardComplete the description of the piecewise function graphed below. 6 5 -7-6-5-4-3-2-1 2 3 5 6 -1 -2 -3 -4 -5 { f(x) = { { -6 if -6x-2 if -2< x <1 if 1 < x <6arrow_forwardLet F = V where (x, y, z) x2 1 + sin² 2 +z2 and let A be the line integral of F along the curve x = tcost, y = t sint, z=t, starting on the plane z = 6.14 and ending on the plane z = 4.30. Then sin(3A) is -0.598 -0.649 0.767 0.278 0.502 0.010 -0.548 0.960arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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