Precalculus
17th Edition
ISBN: 9780078035609
Author: Miller, Julie, Gerken, Donna.
Publisher: Mcgraw-hill Education,
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Textbook Question
Chapter 6.3, Problem 25PE
Two planes leave the same airport. The first plane leaves at
a. How far apart are the planes at
b. What is the bearing from the first plane to the second plane at that time? Round to the nearest degree.
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Students have asked these similar questions
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
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Chapter 6 Solutions
Precalculus
Ch. 6.1 - Solve the right triangle. Round the lengths of the...Ch. 6.1 - A 40-ft ladder on a fire truck leans against a...Ch. 6.1 - From an eye level of 6ft , an observer standing...Ch. 6.1 - A straight hiking trail is 2500ft long with a gain...Ch. 6.1 - Prob. 5SPCh. 6.1 - Prob. 6SPCh. 6.1 - A plane leaves an airport heading S50E at 450mph ....Ch. 6.1 - For Exercise 1-2, refer triangle to ABC . If the...Ch. 6.1 - For Exercise 1-2 refer triangle to ABC . The...Ch. 6.1 - Prob. 3PE
Ch. 6.1 - The acute angle used to express the bearing...Ch. 6.1 - For exercise 5-12 given right triangle ABC ,...Ch. 6.1 - For exercise 5-12 given right triangle ABC ,...Ch. 6.1 - For exercise 5-12 given right triangle ABC ,...Ch. 6.1 - For exercise 5-12 given right triangle ABC ,...Ch. 6.1 - For exercise 5-12 given right triangle ABC ,...Ch. 6.1 - For exercise 5-12 given right triangle ABC ,...Ch. 6.1 - Prob. 11PECh. 6.1 - Prob. 12PECh. 6.1 - For Exercises 13-18, solve the right triangle for...Ch. 6.1 - For Exercises 13-18, solve the right triangle for...Ch. 6.1 - For Exercises 13-18, solve the right triangle for...Ch. 6.1 - For Exercises 13-18, solve the right triangle for...Ch. 6.1 - For Exercises 13-18, solve the right triangle for...Ch. 6.1 - For Exercises 13-18, solve the right triangle for...Ch. 6.1 - A boat is anchored off Elliot Key, Florida. From...Ch. 6.1 - A swimming pool has a depth of 4ft at the shallow...Ch. 6.1 - An airplane climbs at an angle of 11 at an average...Ch. 6.1 - An airplane begins its descent with an average...Ch. 6.1 - A railroad bridge over New Scotland Road in...Ch. 6.1 - At 11:30AM. the angle of elevation of the sun for...Ch. 6.1 - Prob. 25PECh. 6.1 - Roberto has plans to build a tree house in a large...Ch. 6.1 - A police officer hiding between two bushes 50 ft...Ch. 6.1 - A large weather balloon is tethered by two ropes....Ch. 6.1 - The Duquesne Incline is a century-old railroad...Ch. 6.1 - The Jackson Hole Aerial Tram takes passengers from...Ch. 6.1 - To approximate the distance from the Earth to...Ch. 6.1 - To approximate the distance from the Earth to...Ch. 6.1 - A sewer line must have a minimum slope of 0.25in....Ch. 6.1 - In order for gravel roads to have proper drainage,...Ch. 6.1 - The weather satellite NOAA-15 orbits the Earth...Ch. 6.1 - A communications satellite is in geosynchronous...Ch. 6.1 - Prob. 37PECh. 6.1 - Prob. 38PECh. 6.1 - Prob. 39PECh. 6.1 - For Exercises 39-42, make a sketch to illustrate...Ch. 6.1 - For Exercises 39-42,, make a sketch to illustrate...Ch. 6.1 - For Exercises 39-42,, make a sketch to illustrate...Ch. 6.1 - For Exercises 43-46, find the bearing of the ship....Ch. 6.1 - For Exercises 43-46, find the bearing of the ship....Ch. 6.1 - For Exercises 43-46, find the bearing of the ship....Ch. 6.1 - For Exercises 43-46, find the bearing of the ship....Ch. 6.1 - For Exercises 47-50, find the bearing to the...Ch. 6.1 - For Exercises 47-50, find the bearing to the...Ch. 6.1 - For Exercises 47-50, find the bearing to the...Ch. 6.1 - For Exercises 47-50, find the bearing to the...Ch. 6.1 - For Exercises 51-54, round answers to the nearest...Ch. 6.1 - Prob. 52PECh. 6.1 - For Exercises 51-54, round answers to the nearest...Ch. 6.1 - For Exercises 51-54, round answers to the nearest...Ch. 6.1 - A ship leaves port at 8 knots heading N27W . After...Ch. 6.1 - Prob. 56PECh. 6.1 - A boat leaves a dock at a bearing of N42W and...Ch. 6.1 - Prob. 58PECh. 6.1 - For Exercises 59-60, find the lengths of the sides...Ch. 6.1 - For Exercises 59-60, find the lengths of the sides...Ch. 6.1 - Find the measures of the sides and angles. Round...Ch. 6.1 - A rectangular prism measures 6in. by 4in. by 3in ....Ch. 6.1 - Two children sit on either end of an 18-ft teeter...Ch. 6.1 - A light fixture mounted 24ft above the ground...Ch. 6.1 - For Exercises 65-66, refer to the table giving the...Ch. 6.1 - For Exercises 65-66, refer to the table giving the...Ch. 6.1 - OSHA safety regulations require that the base of a...Ch. 6.1 - An A-frame storage shed is constructed such that...Ch. 6.1 - An airplane needs to fly to an airfield located...Ch. 6.1 - Software used to program video games often uses an...Ch. 6.1 - Two ships leave port at the same time. One travels...Ch. 6.1 - Prob. 72PECh. 6.1 - Explain how to represent the bearing from point P...Ch. 6.1 - What is meant by solving a triangle?Ch. 6.1 - A contractor building eight ocean-front...Ch. 6.1 - A circle is inscribed within an isosceles triangle...Ch. 6.1 - A tool requires a V-shaped block to hold two...Ch. 6.1 - Pipe for a water line must be installed from a...Ch. 6.1 - A woman participating in a triathlon can run...Ch. 6.2 - Solve ABC with B=70 , C=48, and b=15cm . Round the...Ch. 6.2 - Solve ABC with A=33 , B=112 , and c=16 . Round the...Ch. 6.2 - Solve ABC with A=49 , a=32 , and b=28 . Round the...Ch. 6.2 - Solve ABC with B=31 , b=3 , a=6.2 . Round the...Ch. 6.2 - Solve ABC with A=40 , a=22 , and b=25 . 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The first plane...Ch. 6.3 - Two boats leave a marina at the same time. The...Ch. 6.3 - A 40-ft boom on a crane is attached to the crane...Ch. 6.3 - Prob. 28PECh. 6.3 - A regulation fast-pitch softball diamond for high...Ch. 6.3 - The Flatiron Building in New York City is said to...Ch. 6.3 - The distance between Dallas, Texas, and Atlanta,...Ch. 6.3 - A bicyclist is at point A on a paved road and must...Ch. 6.3 - A 150-ft tower is anchored on a hill by two guy...Ch. 6.3 - A 75-ft tower is located on the side of a hill...Ch. 6.3 - In Exercises 35-38, use Heron's formula to find...Ch. 6.3 - In Exercises 35-38, use Heron's formula to find...Ch. 6.3 - In Exercises 35-38, use Heron's formula to find...Ch. 6.3 - In Exercises 35-38, use Heron's formula to find...Ch. 6.3 - A triangular sail for a Bolger Tortise sailboat...Ch. 6.3 - Find the area of the grassy region from Exercise...Ch. 6.3 - A farmer wants to fertilize a triangular field...Ch. 6.3 - An artist lays down a white triangular background...Ch. 6.3 - For Exercises 43-46, the vertices of a triangle...Ch. 6.3 - For Exercises 43-46, the vertices of a triangle...Ch. 6.3 - For Exercises 43-46, the vertices of a triangle...Ch. 6.3 - For Exercises 43-46, the vertices of a triangle...Ch. 6.3 - Three mutually tangential circles with radii...Ch. 6.3 - Prob. 48PECh. 6.3 - A parallelogram has adjacent sides of 12.2cm and...Ch. 6.3 - A regular octagon (8- sided figure with sides of...Ch. 6.3 - Why is the law of sines not an option to solve a...Ch. 6.3 - To solve a triangle given SAS , the law of cosines...Ch. 6.3 - Given the lengths of the three sides of a triangle...Ch. 6.3 - When applying the law of cosines (or law of sines)...Ch. 6.3 - Suppose that ABC is a right triangle with right...Ch. 6.3 - If the measures of the three angles in a triangle...Ch. 6.3 - A piston in an engine is attached to a connector...Ch. 6.3 - Use the law of cosines to show that...Ch. 6.3 - Use the law of cosines to show that a=bcosC+ccosBCh. 6.3 - Prob. 60PECh. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - For Exercises 1-12, solve ABC subject to the given...Ch. 6.3 - Refer to the figure. 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If...Ch. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - A plane flies due west for 2hr then due south for...Ch. 6 - A boat travels 3mi east then 7mi south. To the...Ch. 6 - A ship leaves a dock on a bearing of S48.2W ....Ch. 6 - A plane flying 275mph on a bearing of N73.5W...Ch. 6 - For Exercises 15-20, solve ABC subject to the...Ch. 6 - Prob. 16RECh. 6 - For Exercises 15-20, solve ABC subject to the...Ch. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - For Exercises 21-22, find the area of a triangle...Ch. 6 - Prob. 22RECh. 6 - Points on a straight shoreline, A and B , are...Ch. 6 - Two landing points, A and B , lie on the straight...Ch. 6 - A ranger station at a point R in a wilderness area...Ch. 6 - Standing on top of a 30-ft lifeguard tower, an...Ch. 6 - PointsA,B, and P are collinear points along a...Ch. 6 - A surveyor fixes a baseline of 64 ft between two...Ch. 6 - For Exercises 29-32, solve ABC subject to the...Ch. 6 - Prob. 30RECh. 6 - For Exercises 29-32, solve ABC subject to the...Ch. 6 - Prob. 32RECh. 6 - For Exercises 33-34, find the measures of the...Ch. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - In Exercises 35-36, find the area of the triangle...Ch. 6 - Two straight jogging paths begin at a kiosk in a...Ch. 6 - Given points A6,2 and B1,4 on the coordinate...Ch. 6 - Prob. 39RECh. 6 - Two planes take off from an airport at the same...Ch. 6 - Two sides of a triangular plot of land measure...Ch. 6 - Prob. 42RECh. 6 - For Exercises 43-46, suppose that an object moves...Ch. 6 - Prob. 44RECh. 6 - For Exercises 43-46, suppose that an object moves...Ch. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - For Exercises 47-48, a block is attached to a...Ch. 6 - The angular displacement (in radians) for a...Ch. 6 - A Ferris wheel is 200ft in diameter with its...Ch. 6 - For Exercises 51-52, use a graphing utility to...Ch. 6 - For Exercises 51-52, use a graphing utility to...Ch. 6 - For Exercises 1-8, solve ABC subject to the given...Ch. 6 - For Exercises 1-8, solve ABC subject to the given...Ch. 6 - For Exercises 1-8, solve ABC subject to the given...Ch. 6 - For Exercises 1-8, solve ABC subject to the given...Ch. 6 - Prob. 5TCh. 6 - Prob. 6TCh. 6 - For Exercises 1-8, solve ABC subject to the given...Ch. 6 - Prob. 8TCh. 6 - Prob. 9TCh. 6 - Prob. 10TCh. 6 - For Exercises 9-12, find the area of ABC with the...Ch. 6 - Prob. 12TCh. 6 - A ship travels west at 25 knots. 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- Find the slope of the tangent line to the graph of the function at the given point. f(x) = -4x + 5 at (-1, 9) m Determine an equation of the tangent line. y = Need Help? Read It Watch It SUBMIT ANSWERarrow_forwardFind the slope of the tangent line to the graph of the function at the given point. f(x) = 5x-4x² at (-1, -9) m Determine an equation of the tangent line. y = Need Help? Read It Master It SUBMIT ANSWERarrow_forwardFor what value of A and B the function f(x) will be continuous everywhere for the given definition?..arrow_forward
- 2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.006.MI. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 7y2 y² 11 dy Need Help? Read It Master It SUBMIT ANSWER 3. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.009. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) tan³(12/z) dz Need Help? Read It Watch It SUBMIT ANSWER 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.014. Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 5 sinб12x dx Need Help? Read Itarrow_forwardPlease refer belowarrow_forwardy"-9y+20y= 80t-156 y(0) = −6, y'(0) = 5 y(t) =arrow_forward
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