Elementary Technical Mathematics
12th Edition
ISBN: 9781337630580
Author: Dale Ewen
Publisher: Cengage Learning
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Chapter 11.5, Problem 48E
Solve each
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By considering appropriate series expansions,
e². e²²/2. e²³/3.
....
=
= 1 + x + x² + ·
...
when |x| < 1.
By expanding each individual exponential term on the left-hand side
the coefficient of x- 19 has the form
and multiplying out,
1/19!1/19+r/s,
where 19 does not divide s. Deduce that
18! 1 (mod 19).
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.
Chapter 11 Solutions
Elementary Technical Mathematics
Ch. 11.1 - Solve each equation: x2+x=12Ch. 11.1 - Solve each equation: x23x+2=0Ch. 11.1 - Solve each equation: x2+x20=0Ch. 11.1 - Prob. 4ECh. 11.1 - Solve each equation: x22=xCh. 11.1 - Solve each equation: x215x=54Ch. 11.1 - Solve each equation: x21=0Ch. 11.1 - Solve each equation: 16n2=49Ch. 11.1 - Solve each equation: x249=0Ch. 11.1 - Prob. 10E
Ch. 11.1 - Solve each equation: w2+5w+6=0Ch. 11.1 - Solve each equation: x26x=0Ch. 11.1 - Prob. 13ECh. 11.1 - Solve each equation: c2+2=3cCh. 11.1 - Solve each equation: n26n60=0Ch. 11.1 - Solve each equation: x217x+16=0Ch. 11.1 - Solve each equation: 9m=m2Ch. 11.1 - Solve each equation: 6n215n=0Ch. 11.1 - Solve each equation: x2=108+3xCh. 11.1 - Solve each equation: x2x=42Ch. 11.1 - Solve each equation: c2+6c=16Ch. 11.1 - Solve each equation: 4x2+4x3=0Ch. 11.1 - Solve each equation: 10x2+29x+10=0Ch. 11.1 - Solve each equation: 2x2=17x8Ch. 11.1 - Solve each equation: 4x2=25Ch. 11.1 - Solve each equation: 25x=x2Ch. 11.1 - Solve each equation: 9x2+16=24xCh. 11.1 - Solve each equation: 24x2+10=31xCh. 11.1 - Solve each equation: 3x2+9x=0Ch. 11.1 - A rectangle is 5 ft longer than it is wide. (See...Ch. 11.1 - The area of a triangle is 66 m2, and its base is 1...Ch. 11.1 - A rectangle is 9 ft longer than it is wide, and...Ch. 11.1 - A heating duct has a rectangular cross section...Ch. 11.2 - Find the value of a, b, and c in each equation:...Ch. 11.2 - Find the value of a, b, and c in each equation:...Ch. 11.2 - Find the value of a, b, and c in each equation:...Ch. 11.2 - Prob. 4ECh. 11.2 - Find the value of a, b, and c in each equation:...Ch. 11.2 - Find the value of a, b, and c in each equation:...Ch. 11.2 - Find the value of a, b, and c in each equation:...Ch. 11.2 - Find the value of a, b, and c in each equation:...Ch. 11.2 - Solve each equation using the quadratic formula....Ch. 11.2 - Solve each equation using the quadratic formula....Ch. 11.2 - Solve each equation using the quadratic formula....Ch. 11.2 - Solve each equation using the quadratic formula....Ch. 11.2 - Solve each equation using the quadratic formula....Ch. 11.2 - Solve each equation using the quadratic formula....Ch. 11.2 - Solve each equation using the quadratic formula....Ch. 11.2 - Solve each equation using the quadratic formula....Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.2 - Solve each equation using the quadratic formula...Ch. 11.3 - A variable voltage in an electrical circuit is...Ch. 11.3 - A variable electric current is given by i=t27t+12,...Ch. 11.3 - A rectangular piece of sheet metal is 4 ft longer...Ch. 11.3 - A hole in the side of a large metal tank needs to...Ch. 11.3 - The area of the wings of a small Cessna is 175...Ch. 11.3 - The perimeter of a rectangle is 46 cm, and its...Ch. 11.3 - The perimeter of a rectangle is 160 m, and its...Ch. 11.3 - A rectangular field is fenced in by using a river...Ch. 11.3 - The dimensions of a doorway are 3 ft by 7 ft 6 in....Ch. 11.3 - A square, 4 in. on a side, is cut out of each...Ch. 11.3 - A square is cut out of each corner of a...Ch. 11.3 - The area of a rectangular lot 80 m by 100 m is to...Ch. 11.3 - Prob. 13ECh. 11.3 - A border of uniform width is printed on a page...Ch. 11.3 - A company needs to build a ware house with...Ch. 11.3 - A 2000-ft2 storage building 9 ft high is needed to...Ch. 11.3 - A landscaper is laying sod in a rectangular front...Ch. 11.3 - A rectangular forest plot contains 120 acres and...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.4 - Draw the graph of each equation and label each...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Express each number in terms of j (when necessary,...Ch. 11.5 - Simplify: j3Ch. 11.5 - Simplify: j6Ch. 11.5 - Simplify: j13Ch. 11.5 - Simplify: j16Ch. 11.5 - Simplify: j19Ch. 11.5 - Simplify: j31Ch. 11.5 - Simplify: j24Ch. 11.5 - Simplify: j26Ch. 11.5 - Simplify: j38Ch. 11.5 - Simplify: j81Ch. 11.5 - Simplify: 1jCh. 11.5 - Simplify: 1j6Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Determine the natural of the roots of each...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11.5 - Solve each quadratic equation using the quadratic...Ch. 11 - Prob. 1RCh. 11 - Solve for x:3x(x2)=0Ch. 11 - Solve each equation by factoring: x24=0Ch. 11 - Solve each equation by factoring: x2x=6Ch. 11 - Solve each equation by factoring: 5x26x=0Ch. 11 - Solve each equation by factoring: x23x28=0Ch. 11 - Solve each equation by factoring: x214x=45Ch. 11 - Solve each equation by factoring: x2183x=0Ch. 11 - Solve each equation by factoring: 3x2+20x+32=0Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - The area of a piece of plywood is 36 ft2. Its...Ch. 11 - A variable electric current is given by the...Ch. 11 - Draw the graph of each equation and label each...Ch. 11 - Draw the graph of each equation and label each...Ch. 11 - Express each number in terms of j: 36Ch. 11 - Express each number in terms of j: 73Ch. 11 - Simplify: j12Ch. 11 - Simplify: j27Ch. 11 - Determine the nature of the roots of each...Ch. 11 - Determine the nature of the roots of each...Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - A solar-heated house has a rectangular heat...Ch. 11 - A rectangular opening is 15 in. wide and 26 in....Ch. 11 - Solve each equation: x2=64Ch. 11 - Solve each equation: x28x=0Ch. 11 - Solve each equation: x2+9x36=0Ch. 11 - Solve each equation: 12x2+4x=1Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - Solve each equation using the quadratic formula...Ch. 11 - Prob. 7TCh. 11 - Prob. 8TCh. 11 - Prob. 9TCh. 11 - Prob. 10TCh. 11 - Draw the graph of y=x28x15 and label the vertex.Ch. 11 - Draw the graph of y=2x2+8x+11 and label the...Ch. 11 - Express each number in terms of j: 16Ch. 11 - Express each number in terms of j: 29Ch. 11 - Simplify: j9Ch. 11 - Simplify: j28Ch. 11 - Determine the nature of the roots of 3x2x+4=0...Ch. 11 - One side of a rectangle is 5 cm more that another....
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