Use the given value of k to complete the table for the direct variation model $y = k x ^ { 2 }$ . Plot the points on a rectangular coordinate system. \[\begin{array}{l} \begin{array} { | l | l | l | l | l | l | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & & & & & \\ \hline \end{array}\\ k = 2 \end{array}\]

A) \[\begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 128 & 200 & 288 & 392 & 512 \\ \hline \end{array}\] B) \[\begin{array} { | c | r | r | r | r | r | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 8 & 10 & 12 & 14 & 16 \\ & & & & & \\ \hline \end{array}\] C) \[\begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 128 & 128 & 128 & 128 & 128 \\ \hline \end{array}\] D) \[\begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 512 & 392 & 288 & 200 & 128 \\ \hline \end{array}\] E) \[\begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 128 & 200 & 288 & 200 & 128 \\ \hline \end{array}\] A) \[\begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 128 & 200 & 288 & 392 & 512 \\ \hline \end{array}\] B) \[\begin{array} { | c | r | r | r | r | r | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 8 & 10 & 12 & 14 & 16 \\ & & & & & \\ \hline \end{array}\] C) \[\begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 128 & 128 & 128 & 128 & 128 \\ \hline \end{array}\] D) \[\begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 512 & 392 & 288 & 200 & 128 \\ \hline \end{array}\] E) \[\begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = k x ^ { 2 } & 128 & 200 & 288 & 200 & 128 \\ \hline \end{array}\]

Exam 10: Mathematical Modeling and Variation

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) P varies directly as x and inversely as the square of y.(P = $\frac { 3 } { 2 }$ when x = 25 and y = 10. )

(Multiple Choice)

4.8/5

(40)

Question 41

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) V varies jointly as p and q and inversely as the square of s.(ν = 1.4 when p = 4.4,q = 7.3 and s = 1.8. )

(Multiple Choice)

4.7/5

(35)

Question 42

Use the given value of k to complete the table for the inverse variation model $y = \frac { k } { x ^ { 2 } }$ . Plot the points on a rectangular coordinate system. x 8 10 12 14 16 y= $k = 20$

(Multiple Choice)

4.9/5

(43)

Question 43

Use the given value of k to complete the table for the direct variation model $y = k x ^ { 2 }$ . Plot the points on a rectangular coordinate system. x 8 10 12 14 16 y=k k=2

(Multiple Choice)

4.9/5

(47)

Question 44

The frequency of vibrations of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string.The middle A string has a frequency of 430 vibrations per second.Find the frequency of a string that has 1.25 times as much tension and is 1.4 times as long.

(Multiple Choice)

4.7/5

(39)

Question 45

An oceanographer took readings of the water temperatures C (in degrees Celsius)at several depths d (in meters).The data collected are shown in the table. Depth, d Temperature, C 1000 3. 2000 2. 3000 1. 4000 1. 5000 0. Sketch a scatter plot of the data.

(Multiple Choice)

4.9/5

(35)

Question 46

Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. If #28 copper wire (which has a diameter of 0.0126 inch)has a resistance of 68.17 ohms per thousand feet,what length of #28 copper wire will produce a resistance of 30.5 ohms?

(Multiple Choice)

4.8/5

(38)

Question 47

Assume that y is directly proportional to x.Use the given x-value and y-value to find a linear model that relates y and x. $x = 2 , y = 58$

(Multiple Choice)

4.9/5

(39)

Question 48

Hooke's law states that the magnitude of force,F,required to stretch a spring x units beyond its natural length is directly proportional to x.If a force of 3 pounds stretches a spring from its natural length of 10 inches to a length of 10.7 inches,what force will stretch the spring to a length of 11.5 inches? Round your answer to the nearest hundredth.

(Multiple Choice)

4.8/5

(37)

Question 49

Showing 41 - 49 of 49

Exam 10: Mathematical Modeling and Variation

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) ​ P varies directly as x and inversely as the square of y.(P = 32\frac { 3 } { 2 }23​ when x = 25 and y = 10. ) ​

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) ​ V varies jointly as p and q and inversely as the square of s.(ν = 1.4 when p = 4.4,q = 7.3 and s = 1.8. ) ​

Use the given value of k to complete the table for the inverse variation model​ y=kx2y = \frac { k } { x ^ { 2 } }y=x2k​ . Plot the points on a rectangular coordinate system. x 8 10 12 14 16 y= k=20k = 20k=20

Use the given value of k to complete the table for the direct variation model​ y=kx2y = k x ^ { 2 }y=kx2 . ​ Plot the points on a rectangular coordinate system. x 8 10 12 14 16 y=k k=2

An oceanographer took readings of the water temperatures C (in degrees Celsius)at several depths d (in meters).The data collected are shown in the table. Depth, d Temperature, C 1000 3. 2000 2. 3000 1. 4000 1. 5000 0. Sketch a scatter plot of the data.

Assume that y is directly proportional to x.Use the given x-value and y-value to find a linear model that relates y and x.​ x=2,y=58x = 2 , y = 58x=2,y=58 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Graphs of Polar Equations

Filters

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) P varies directly as x and inversely as the square of y.(P = $\frac { 3 } { 2 }$ when x = 25 and y = 10. )

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) V varies jointly as p and q and inversely as the square of s.(ν = 1.4 when p = 4.4,q = 7.3 and s = 1.8. )

Use the given value of k to complete the table for the inverse variation model $y = \frac { k } { x ^ { 2 } }$ . Plot the points on a rectangular coordinate system. x 8 10 12 14 16 y= $k = 20$

Use the given value of k to complete the table for the direct variation model $y = k x ^ { 2 }$ . Plot the points on a rectangular coordinate system. x 8 10 12 14 16 y=k k=2

Assume that y is directly proportional to x.Use the given x-value and y-value to find a linear model that relates y and x. $x = 2 , y = 58$