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6.8E: Exercises for Section 6.8

https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.08%3A_Singular_Value_Decomposition/6.8E%3A_Exercises_for_Section_6.8

This page contains exercises on finding the Singular Value Decomposition (SVD) of various matrices, outlining the computation of matrices

$U$ ,

$\Sigma$ , and

$V$ . Two detailed examples are provid...This page contains exercises on finding the Singular Value Decomposition (SVD) of various matrices, outlining the computation of matrices

$U$ ,

$\Sigma$ , and

$V$ . Two detailed examples are provided, along with a fifth exercise concerning the determinant of an

$n \times n$ matrix and its singular values.

6.4E: Exercises for Section 6.4

https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/06%3A_Systems_of_ODEs/6.04%3A_Matrices_and_linear_systems/6.4E%3A_Exercises_for_Section_6.4

This page features an exercise set focused on matrix operations, including solving systems of equations with matrix inverses, computing determinants, and exploring matrix invertibility conditions. It ...This page features an exercise set focused on matrix operations, including solving systems of equations with matrix inverses, computing determinants, and exploring matrix invertibility conditions. It includes tasks like determining invertibility for matrices with variables, verifying matrix relationships, and provides solutions for all exercises. Key examples focus on determinant calculation and identifying nonzero matrices that meet specific multiplication criteria.

5.1E: Exercises for Section 5.1

https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/05%3A_The_Laplace_Transform/5.01%3A_The_Laplace_Transform/5.1E%3A_Exercises_for_Section_5.1

This page outlines exercises on finding Laplace transforms and their inverses for various functions, including polynomials, trigonometric, and piecewise functions. It provides examples and answers for...This page outlines exercises on finding Laplace transforms and their inverses for various functions, including polynomials, trigonometric, and piecewise functions. It provides examples and answers for certain problems, illustrating the application of Laplace transform rules. The exercises emphasize techniques such as integration by parts and the use of properties related to exponential and trigonometric functions within the context of Laplace transforms.

7.5: Fractions of One Percent

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/07%3A_Ratios_and_Rates/7.05%3A_Fractions_of_One_Percent

\(\begin{array} {l} {\dfrac{1}{2} \% = \dfrac{1}{2} \text{ of } 1\% = \dfrac{1}{2} \cdot \dfrac{1}{100} = \dfrac{1}{200}} \\ {\dfrac{3}{5} \% = \dfrac{3}{5} \text{ of } 1\% = \dfrac{3}{5} \cdot \dfrac...

$\begin{array} {l} {\dfrac{1}{2} \% = \dfrac{1}{2} \text{ of } 1\% = \dfrac{1}{2} \cdot \dfrac{1}{100} = \dfrac{1}{200}} \\ {\dfrac{3}{5} \% = \dfrac{3}{5} \text{ of } 1\% = \dfrac{3}{5} \cdot \dfrac{1}{100} = \dfrac{3}{500}} \\ {\dfrac{5}{8} \% = \dfrac{5}{8} \text{ of } 1\% = \dfrac{5}{8} \cdot \dfrac{1}{100} = \dfrac{5}{800}} \\ {\dfrac{7}{11} \% = \dfrac{7}{11} \text{ of } 1\% = \dfrac{7}{11} \cdot \dfrac{1}{100} = \dfrac{7}{1100}} \end{array}$

6.2: Converting a Decimal to a Fraction

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/06%3A_Decimals/6.02%3A_Converting_a_Decimal_to_a_Fraction

be able to convert an ordinary decimal and a complex decimal to a fraction \(\begin{array} {rcl} {4 + .006 \dfrac{1}{4}} & = & {4 + \dfrac{6 \dfrac{1}{4}}{1000}} \\ {} & = & {4 + \dfrac{\dfrac{25}{4}}...be able to convert an ordinary decimal and a complex decimal to a fraction

$\begin{array} {rcl} {4 + .006 \dfrac{1}{4}} & = & {4 + \dfrac{6 \dfrac{1}{4}}{1000}} \\ {} & = & {4 + \dfrac{\dfrac{25}{4}}{\dfrac{1000}{1}}} \\ {} & = & {4 + \dfrac{\begin{array} {c} {^1} \\ {\cancel{25}} \end{array}}{4} \cdot \dfrac{1}{\begin{array} {c} {\cancel{1000}} \\ {^{40}} \end{array}}} \\ {} & = & {4 + \dfrac{1 \cdot 1}{4 \cdot 40}} \\ {} & = & {4 + \dfrac{1}{160}} \\ {} & = & {4 \dfrac{1}{160}} \end{array}$

8.7: Proficiency Exam

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/08%3A_Techniques_of_Estimation/8.07%3A_Proficiency_Exam

Exercise

$\PageIndex{1}$ Exercise

$\PageIndex{2}$ Exercise

$\PageIndex{3}$ Exercise

$\PageIndex{4}$ Exercise

$\PageIndex{5}$ Exercise

$\PageIndex{6}$ After you have made an estimate, find ...Exercise

$\PageIndex{1}$ Exercise

$\PageIndex{2}$ Exercise

$\PageIndex{3}$ Exercise

$\PageIndex{4}$ Exercise

$\PageIndex{5}$ Exercise

$\PageIndex{6}$ After you have made an estimate, find the exact value.

$1 + \dfrac{1}{2} = 1 \dfrac{1}{2}$ (

$1 \dfrac{9}{16}$ )

$0 + \dfrac{1}{2} + \dfrac{1}{2} = 1$ (

$1 \dfrac{47}{300}$ )

$8 \dfrac{1}{2} + 14 = 22 \dfrac{1}{2}$ (

$22 \dfrac{31}{48}$ )

$5 \dfrac{1}{2} + 1 \dfrac{1}{2} + 6 \dfrac{1}{2} = 13 \dfrac{1}{2}$ (

$13 \dfrac{1}{3}$ )

4.6: Applications Involving Fractions

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/04%3A_Introduction_to_Fractions_and_Multiplication_and_Division_of_Fractions/4.06%3A_Applications_Involving_Fractions

\(\begin{array} {rcl} {M = \dfrac{9}{4} \div \dfrac{3}{8} = \dfrac{9}{4} \cdot \dfrac{8}{3}} & = & {\dfrac{

$\begin{array} {c} {^3} \\ {\cancel{9}} \end{array}$ }{\begin{array} {c} {\cancel{4}} \\ {^1} \e...

$\begin{array} {rcl} {M = \dfrac{9}{4} \div \dfrac{3}{8} = \dfrac{9}{4} \cdot \dfrac{8}{3}} & = & {\dfrac{\begin{array} {c} {^3} \\ {\cancel{9}} \end{array}}{\begin{array} {c} {\cancel{4}} \\ {^1} \end{array}} \cdot \dfrac{\begin{array} {c} {^2} \\ {\cancel{8}} \end{array}}{\begin{array} {c} {\cancel{3}} \\ {^1} \end{array}}} \\ {} & = & {\dfrac{3 \cdot 2}{1 \cdot 1}} \\ {} & = & {6} \end{array}$

3.3E: Exercises for Section 3.3

https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.03%3A_Trigonometric_Substitution/3.3E%3A_Exercises_for_Section_3.3

This page presents mathematical exercises focused on simplifying trigonometric and hyperbolic expressions, completing the square for trinomials, and performing integrals using trigonometric substituti...This page presents mathematical exercises focused on simplifying trigonometric and hyperbolic expressions, completing the square for trinomials, and performing integrals using trigonometric substitution. It includes notable results like simplifying

$9\sec^2θ−9$ to

$9\tan^2θ$ and evaluating various integrals.

3.4E: Exercises for Section 3.4

https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.04%3A_Constant_coefficient_second_order_linear_ODEs/3.4E%3A_Exercises_for_Section_3.4

This page provides a variety of exercises focused on solving second-order and one first-order differential equations. It includes challenges to find general or particular solutions, often with initial...This page provides a variety of exercises focused on solving second-order and one first-order differential equations. It includes challenges to find general or particular solutions, often with initial conditions, and requires different solving methods. Some tasks involve constructing equations from provided solutions, covering a range from basic to moderately complex scenarios.

1.6E: Exercises for the section 1.6

https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.06%3A_Linear_Equations_and_the_Integrating_Factor/1.6E%3A_Exercises_for_the_section_1.6

These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engin...These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.

1.4E: Exercises for Section 1.4

https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/01%3A_Systems_of_Equations/1.04%3A_Balancing_Chemical_Reactions/1.4E%3A_Exercises_for_Section_1.4

This page contains various exercises on balancing chemical reactions, featuring unbalanced equations with some providing answers. The goal is to equalize the number of atoms for each element on both s...This page contains various exercises on balancing chemical reactions, featuring unbalanced equations with some providing answers. The goal is to equalize the number of atoms for each element on both sides of the equation. Key examples include the balancing of propane with oxygen and phosphorus pentoxide with water. Some exercises are unsolved, indicating they require completion.

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