what a function tells us in mathematics.

Question

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Answer 1

Question

Chapter 9.A, Problem 1QQ

To determine

what a function tells us in mathematics.

Expert Solution & Answer

Answer to Problem 1QQ

Solution: In mathematics, a function tells us a) how one variable depends on another.

Explanation of Solution

Given: In mathematics, a function tells us

a) how one variable depends on another.

b) how an operation, such as multiplication or division, works.

c) how inputs and outputs are affected by machines.

A function:

A function describes how a dependent variable changes with respect to one or more independent variables. When there are two variables, we may denote their relationship as an ordered pair with the independent variable first: (independent variable, dependent variable)

If x is the independent variable and y is the dependent variable, we write the function as $y = f (x)$ .

Thereby in mathematics, a function tells us a) how one variable depends on another.

Conclusion:

In mathematics, a function tells us a) how one variable depends on another.

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Students have asked these similar questions

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.

Answer 2

Question

Chapter 9.A, Problem 1QQ

To determine

what a function tells us in mathematics.

Expert Solution & Answer

Answer to Problem 1QQ

Solution: In mathematics, a function tells us a) how one variable depends on another.

Explanation of Solution

Given: In mathematics, a function tells us

a) how one variable depends on another.

b) how an operation, such as multiplication or division, works.

c) how inputs and outputs are affected by machines.

A function:

A function describes how a dependent variable changes with respect to one or more independent variables. When there are two variables, we may denote their relationship as an ordered pair with the independent variable first: (independent variable, dependent variable)

If x is the independent variable and y is the dependent variable, we write the function as $y = f (x)$ .

Thereby in mathematics, a function tells us a) how one variable depends on another.

Conclusion:

In mathematics, a function tells us a) how one variable depends on another.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 9.A, Problem 1QQ

To determine

what a function tells us in mathematics.

Expert Solution & Answer

Answer to Problem 1QQ

Solution: In mathematics, a function tells us a) how one variable depends on another.

Explanation of Solution

Given: In mathematics, a function tells us

a) how one variable depends on another.

b) how an operation, such as multiplication or division, works.

c) how inputs and outputs are affected by machines.

A function:

A function describes how a dependent variable changes with respect to one or more independent variables. When there are two variables, we may denote their relationship as an ordered pair with the independent variable first: (independent variable, dependent variable)

If x is the independent variable and y is the dependent variable, we write the function as $y = f (x)$ .

Thereby in mathematics, a function tells us a) how one variable depends on another.

Conclusion:

In mathematics, a function tells us a) how one variable depends on another.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 9.A, Problem 1QQ

To determine

what a function tells us in mathematics.

Expert Solution & Answer

Answer to Problem 1QQ

Solution: In mathematics, a function tells us a) how one variable depends on another.

Explanation of Solution

Given: In mathematics, a function tells us

a) how one variable depends on another.

b) how an operation, such as multiplication or division, works.

c) how inputs and outputs are affected by machines.

A function:

A function describes how a dependent variable changes with respect to one or more independent variables. When there are two variables, we may denote their relationship as an ordered pair with the independent variable first: (independent variable, dependent variable)

If x is the independent variable and y is the dependent variable, we write the function as $y = f (x)$ .

Thereby in mathematics, a function tells us a) how one variable depends on another.

Conclusion:

In mathematics, a function tells us a) how one variable depends on another.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 9.A, Problem 1QQ

To determine

what a function tells us in mathematics.

Expert Solution & Answer

Answer to Problem 1QQ

Solution: In mathematics, a function tells us a) how one variable depends on another.

Explanation of Solution

Given: In mathematics, a function tells us

a) how one variable depends on another.

b) how an operation, such as multiplication or division, works.

c) how inputs and outputs are affected by machines.

A function:

A function describes how a dependent variable changes with respect to one or more independent variables. When there are two variables, we may denote their relationship as an ordered pair with the independent variable first: (independent variable, dependent variable)

If x is the independent variable and y is the dependent variable, we write the function as $y = f (x)$ .

Thereby in mathematics, a function tells us a) how one variable depends on another.

Conclusion:

In mathematics, a function tells us a) how one variable depends on another.

Answer 6

Chapter 9.A, Problem 1QQ

To determine

what a function tells us in mathematics.

Expert Solution & Answer

Answer to Problem 1QQ

Solution: In mathematics, a function tells us a) how one variable depends on another.

Explanation of Solution

Given: In mathematics, a function tells us

a) how one variable depends on another.

b) how an operation, such as multiplication or division, works.

c) how inputs and outputs are affected by machines.

A function:

A function describes how a dependent variable changes with respect to one or more independent variables. When there are two variables, we may denote their relationship as an ordered pair with the independent variable first: (independent variable, dependent variable)

If x is the independent variable and y is the dependent variable, we write the function as $y = f (x)$ .

Thereby in mathematics, a function tells us a) how one variable depends on another.

Conclusion:

In mathematics, a function tells us a) how one variable depends on another.

Answer 7

Chapter 9.A, Problem 1QQ

To determine

what a function tells us in mathematics.

Answer 8

Expert Solution & Answer

Answer to Problem 1QQ

Solution: In mathematics, a function tells us a) how one variable depends on another.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given: In mathematics, a function tells us

a) how one variable depends on another.

b) how an operation, such as multiplication or division, works.

c) how inputs and outputs are affected by machines.

A function:

A function describes how a dependent variable changes with respect to one or more independent variables. When there are two variables, we may denote their relationship as an ordered pair with the independent variable first: (independent variable, dependent variable)

If x is the independent variable and y is the dependent variable, we write the function as $y = f (x)$ .

Thereby in mathematics, a function tells us a) how one variable depends on another.

Conclusion:

In mathematics, a function tells us a) how one variable depends on another.