EBK A PROBLEM SOLVING APPROACH TO MATHE
13th Edition
ISBN: 9780135184103
Author: BOSCHMANS
Publisher: VST
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Chapter 8.3B, Problem 19A
To determine
a.
To find:
The value of
To determine
b.
To find:
For what value of
To determine
c.
To find:
What is domain of
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Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.
By considering appropriate series expansions,
ex · ex²/2 . ¸²³/³ . . ..
=
= 1 + x + x² +……
when |x| < 1.
By expanding each individual exponential term on the left-hand side
and multiplying out, show that the coefficient of x 19 has the form
1/19!+1/19+r/s,
where 19 does not divide s.
Let
1
1
r
1+
+ +
2 3
+
=
823
823s
Without calculating the left-hand side, prove that r = s (mod 823³).
Chapter 8 Solutions
EBK A PROBLEM SOLVING APPROACH TO MATHE
Ch. 8.1 - Student were asked to write an algebraic...Ch. 8.1 - a. Choose seven consecutive term in any arithmetic...Ch. 8.1 - A teacher instructed her class as follows: Take...Ch. 8.1 - A teacher instructed her class to take any number...Ch. 8.1 - Give an example of geometric sequence whose first...Ch. 8.1 - Joel says that there is no reason to have more...Ch. 8.1 - A student wonders if sets can ever be considered...Ch. 8.1 - A student wants to know how can she prove that a...Ch. 8.1 - Prob. 9MCCh. 8.1 - Prob. 11MC
Ch. 8.1 - Prob. 1NAEPCh. 8.1 - 2+n 5 3+n 6 4+n 7 5+n 8 What number does n...Ch. 8.1 - Prob. 3NAEPCh. 8.1 - Melissa saves money for six weeks to buy a...Ch. 8.1A - Translate the following phrases into algebraic...Ch. 8.1A - Prob. 2ACh. 8.1A - In the tile pattern for an arithmetic sequence of...Ch. 8.1A - Prob. 4ACh. 8.1A - In a college, there are P professors and S...Ch. 8.1A - Suppose a class has g girls and b boys, and there...Ch. 8.1A - Ryan is building matchstick sequences as shown....Ch. 8.1A - Prob. 8ACh. 8.1A - For a particular event, a student pays 5 per...Ch. 8.1A - Prob. 10ACh. 8.1A - Prob. 11ACh. 8.1A - Prob. 12ACh. 8.1A - Find the first term and the difference in an...Ch. 8.1A - Prob. 14ACh. 8.1A - A ball is dropped from a height of 10 ft and...Ch. 8.1A - Jake bought contact lenses and was told to wear...Ch. 8.1A - Construct a Fibonacci-like sequence that is also...Ch. 8.1A - Prob. 18ACh. 8.1B - Translate the following phrases into algebraic...Ch. 8.1B - Prob. 2ACh. 8.1B - Discover a possible tile pattern in the following...Ch. 8.1B - In the following descriptions, write an expression...Ch. 8.1B - Prob. 5ACh. 8.1B - Suppose there are c chairs and t tables in a...Ch. 8.1B - Prob. 7ACh. 8.1B - Prob. 8ACh. 8.1B - Prob. 9ACh. 8.1B - Matt has twice as many as stickers as David. If...Ch. 8.1B - Prob. 11ACh. 8.1B - Prob. 12ACh. 8.1B - Find the first term and the difference in an...Ch. 8.1B - Find the first term in a geometric sequence if the...Ch. 8.1B - A ball is dropped from a height of 20 meters and...Ch. 8.1B - Consider the following arithmetic sequences....Ch. 8.1B - Prob. 18ACh. 8.2 - Students were asked to find three consecutive...Ch. 8.2 - Prob. 2MCCh. 8.2 - Create an equation with x on both sides of the...Ch. 8.2 - Prob. 4MCCh. 8.2 - Prob. 5MCCh. 8.2 - Prob. 6MCCh. 8.2 - Prob. 7MCCh. 8.2 - Prob. 8MCCh. 8.2 - A student was told that in order to check a...Ch. 8.2 - Prob. 10MCCh. 8.2 - Olivier said that his teacher would not accept 5=x...Ch. 8.2 - A student claimed that the equation 2x=3y has...Ch. 8.2 - Prob. 13MCCh. 8.2 - Prob. 14MCCh. 8.2 - Prob. 15MCCh. 8.2 - Prob. 16MCCh. 8.2 - Prob. 17MCCh. 8.2 - Prob. 18MCCh. 8.2 - Write an algebraic equation relating the variables...Ch. 8.2 - a. Show that the sum of every three consecutive...Ch. 8.2 - Prob. 21MCCh. 8.2 - Prob. 22MCCh. 8.2 - Prob. 1NAEPCh. 8.2 - Prob. 2NAEPCh. 8.2 - Archaeologists measure the lengths of certain...Ch. 8.2 - Jessica makes clay bowls. The following equation...Ch. 8.2A - Consider the balances: What is the value of each...Ch. 8.2A - Prob. 2ACh. 8.2A - Solve each of the following if x is a real number....Ch. 8.2A - Ryan is building a matchstick sequence so that one...Ch. 8.2A - For a particular event, 812 tickets were sold for...Ch. 8.2A - An estate of 486,000 is left to three siblings....Ch. 8.2A - A 10-ft board is to be cut into three pieces: two...Ch. 8.2A - Prob. 8ACh. 8.2A - Miriam is 10 years older than Ricardo. Two years...Ch. 8.2A - In a college, 20 times as many undergraduate...Ch. 8.2A - A farmer has 1200 yd of fencing to enclose a...Ch. 8.2A - The sum of three consecutive terms in the...Ch. 8.2A - Carlos bought 430 feet of fencing. With this, he...Ch. 8.2A - The sum of four consecutive natural numbers is...Ch. 8.2B - Consider the following balances: a. Which shape...Ch. 8.2B - Prob. 2ACh. 8.2B - Prob. 3ACh. 8.2B - Prob. 4ACh. 8.2B - Prob. 5ACh. 8.2B - Prob. 6ACh. 8.2B - Prob. 7ACh. 8.2B - Matt has twice as many stickers as David. How many...Ch. 8.2B - Prob. 9ACh. 8.2B - Prob. 10ACh. 8.2B - Prob. 11ACh. 8.2B - Prob. 12ACh. 8.2B - Prob. 13ACh. 8.3 - Prob. 1MCCh. 8.3 - Prob. 2MCCh. 8.3 - Prob. 4MCCh. 8.3 - Prob. 7MCCh. 8.3 - Prob. 8MCCh. 8.3 - Prob. 9MCCh. 8.3 - Prob. 10MCCh. 8.3 - Prob. 11MCCh. 8.3 - Prob. 12MCCh. 8.3 - Prob. 13MCCh. 8.3 - Prob. 14MCCh. 8.3 - Prob. 15MCCh. 8.3 - Prob. 16MCCh. 8.3 - Prob. 17MCCh. 8.3 - Prob. 18MCCh. 8.3 - Refer to the School Book page on page 456 and...Ch. 8.3 - Prob. 20MCCh. 8.3 - Prob. 21MCCh. 8.3 - Prob. 22MCCh. 8.3 - Prob. 23MCCh. 8.3 - Prob. 24MCCh. 8.3 - Prob. 1NAEPCh. 8.3 - Prob. 2NAEPCh. 8.3 - Prob. 3NAEPCh. 8.3A - Prob. 1ACh. 8.3A - Which of the following are function from the set...Ch. 8.3A - a. Draw an arrow diagram of a function with domain...Ch. 8.3A - Suppose f(x)=2x+1 and the domain {0,1,2,3,4}....Ch. 8.3A - Prob. 5ACh. 8.3A - a. Make an arrow diagram for each of the...Ch. 8.3A - The dosage of a certain drug is related to the...Ch. 8.3A - For each of the following, guess what might be...Ch. 8.3A - Quick-Talk advertises monthly cellualr...Ch. 8.3A - For each of the following sequenceseither...Ch. 8.3A - Consider the following two function machines. Find...Ch. 8.3A - In problem 11, find the all inputs for which the...Ch. 8.3A - a. Repeat exercise 11 when the bottom machine...Ch. 8.3A - Consider the function f(x)=x+b, where b is a...Ch. 8.3A - Let t(n) be the function that assigns the nth term...Ch. 8.3A - a. If f(x)=x2 and the output is 2, find all...Ch. 8.3A - Consider a function machine that accepts inputs as...Ch. 8.3A - The following graph shows the relationship between...Ch. 8.3A - A ball is shot out of a cannon at ground level....Ch. 8.3A - Prob. 20ACh. 8.3A - Prob. 21ACh. 8.3A - Which of the following equations or inequalities...Ch. 8.3A - Which of the following are graphs of fucntions and...Ch. 8.3B - The following sets of ordered pairs are functions....Ch. 8.3B - Prob. 2ACh. 8.3B - Prob. 4ACh. 8.3B - Prob. 5ACh. 8.3B - Prob. 6ACh. 8.3B - Prob. 7ACh. 8.3B - Prob. 8ACh. 8.3B - Prob. 9ACh. 8.3B - Prob. 10ACh. 8.3B - Prob. 11ACh. 8.3B - In problem 11, find the all inputs for which the...Ch. 8.3B - Prob. 13ACh. 8.3B - Prob. 14ACh. 8.3B - Prob. 15ACh. 8.3B - Prob. 16ACh. 8.3B - Prob. 17ACh. 8.3B - Prob. 18ACh. 8.3B - Prob. 19ACh. 8.3B - Prob. 20ACh. 8.3B - Prob. 21ACh. 8.3B - Prob. 22ACh. 8.3B - Prob. 23ACh. 8.4 - In this chapter, an arithmetic sequence was...Ch. 8.4 - Prob. 2MCCh. 8.4 - Prob. 3MCCh. 8.4 - Prob. 4MCCh. 8.4 - Prob. 5MCCh. 8.4 - Prob. 6MCCh. 8.4 - Prob. 7MCCh. 8.4 - Prob. 8MCCh. 8.4 - Prob. 9MCCh. 8.4 - Prob. 10MCCh. 8.4 - Janis noticed that in the simultaneous equations...Ch. 8.4 - Prob. 12MCCh. 8.4 - Prob. 13MCCh. 8.4 - Prob. 14MCCh. 8.4 - Prob. 15MCCh. 8.4 - Prob. 16MCCh. 8.4 - Prob. 17MCCh. 8.4 - Prob. 18MCCh. 8.4 - Prob. 19MCCh. 8.4 - Prob. 20MCCh. 8.4 - Prob. 1NAEPCh. 8.4 - Prob. 2NAEPCh. 8.4 - Prob. 3NAEPCh. 8.4 - Prob. 4NAEPCh. 8.4A - The graph of y=mx is given in the following...Ch. 8.4A - Prob. 2ACh. 8.4A - Find the x-intercept and y-intercept for the...Ch. 8.4A - Prob. 4ACh. 8.4A - Write each of the following equations in...Ch. 8.4A - For each of the following, write the equation of...Ch. 8.4A - Find the coordinates of two other collinear points...Ch. 8.4A - Prob. 8ACh. 8.4A - Prob. 9ACh. 8.4A - Find the equation for each of the following lines....Ch. 8.4A - For each of the following, find the slope, if...Ch. 8.4A - Write the equation of each line in exercise 11....Ch. 8.4A - Wildlife experts found that the number of chirps C...Ch. 8.4A - The lines AB and BC shown in the figure are graph...Ch. 8.4A - What do the graphs of the following equations have...Ch. 8.4A - Suppose a car is travelling at constant speed of...Ch. 8.4A - Solve each of the following systems, if possible....Ch. 8.4A - The owner of a 5000-gal oil truck loads the truck...Ch. 8.4A - Josephines bank contains 27 coins. If all the...Ch. 8.4B - Prob. 2ACh. 8.4B - ASSESSMENT 8-4B Find the x-intercept and...Ch. 8.4B - Prob. 4ACh. 8.4B - Prob. 5ACh. 8.4B - Prob. 6ACh. 8.4B - ASSESSMENT 8-4B Find the coordinates of two other...Ch. 8.4B - Prob. 8ACh. 8.4B - Prob. 9ACh. 8.4B - ASSESSMENT 8-4B Find the equation for each of the...Ch. 8.4B - ASSESSMENT 8-4B For each of the following, find...Ch. 8.4B - ASSESSMENT 8-4B Write the equation of each line in...Ch. 8.4B - Prob. 13ACh. 8.4B - Prob. 14ACh. 8.4B - Prob. 15ACh. 8.4B - Prob. 16ACh. 8.4B - Solve each of the following systems, if possible....Ch. 8.CR - Each of the following is a geometric sequence....Ch. 8.CR - Prob. 2CRCh. 8.CR - a. If the first two terms of an arithmetic...Ch. 8.CR - There are 13 times as many students as professors...Ch. 8.CR - Write a sentence that gives the same information...Ch. 8.CR - Write an equation to find the number of feet given...Ch. 8.CR - The sum of n whole numbers is S. 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Use the slope formula to find the...
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