Determine whether the variation model is of the form $y = k x$ or $y = \frac { k } { x }$ and find k.Then write a model that relates y and x. \[\begin{array} { | c | c | c | c | c | c | } \hline x & 5 & 10 & 15 & 20 & 25 \\ \hline y & - 1.5 & - 3 & - 4.5 & - 6 & - 7.5 \\ \hline \end{array}\]

A) $y = - \frac { 3 } { 10 x }$ B) $y = \frac { 10 } { 3 } x$ C) $y = - \frac { 3 } { 10 } x$ D) $y = \frac { 3 } { 10 } x$ E) $y = - \frac { 10 } { 3 } x$ A) $y = - \frac { 3 } { 10 x }$ B) $y = \frac { 10 } { 3 } x$ C) $y = - \frac { 3 } { 10 } x$ D) $y = \frac { 3 } { 10 } x$ E) $y = - \frac { 10 } { 3 } x$

Exam 10: Mathematical Modeling and Variation

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State sales tax is based on retail price.An item that sells for $180.99 has a sales tax of $17.4.Find a mathematical model that gives the amount of sales tax y in terms of the retail price x.Use the model to find the sales tax on a $589.99 purchase.(Round your answer to four decimal places. )

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Question 1

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An overhead garage door has two springs,one on each side of the door (see figure).A force of $20$ pounds is required to stretch each spring 1 foot.Because of a pulley system,the springs stretch only one-half the distance the door travels.The door moves a total of $x = 18$ feet,and the springs are at their natural length when the door is open.Find the combined lifting force applied to the door by the springs when the door is closed.

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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=

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Question 3

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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=5

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Question 4

On a yardstick with scales in inches and centimeters,you notice that 11 inches is approximately the same length as 33 centimeters.Use this information to find a mathematical model that relates centimeters y to inches x.Then use the model to find the numbers of centimeters in 60 inches and 70 inches.(Round your answer to one decimal place. )

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Question 5

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. $x = 38 , y = 2400$

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Question 6

Determine whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ . x 12 24 36 48 60 Y $\frac { 1 } { 18 }$ $\frac { 1 } { 36 }$ $\frac { 1 } { 54 }$ $\frac { 1 } { 72 }$ $\frac { 1 } { 90 }$

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Question 7

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) F is jointly proportional to r and the third power of s. $( F = 24750 \text { when } r = 18 \text { and } s = 5 . )$

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Question 8

Determine whether the variation model is of the form $y = k x$ or $y = \frac { k } { x }$ and find k.Then write a model that relates y and x. x 5 10 15 20 25 y -1.5 -3 -4.5 -6 -7.5

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Question 9

Determine whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ . x 13 26 39 52 65 Y 3 6 9 12 15

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Question 10

Find a mathematical model for the verbal statement: "m varies directly as the square of w and inversely as s."

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Question 11

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) Y varies inversely as x. $( y = 9 \text { when } x = 45 . )$

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Question 12

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. $x = 5 , y = 380$

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Question 13

The coiled spring of a toy supports the weight of a child.The spring is compressed a distance of 1.6 inches by the weight of a 35-pound child.The toy will not work properly if its spring is compressed more than 6 inches.What is the weight of the heaviest child who should be allowed to use the toy? (Round your answer to two decimal places. )

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Question 14

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= $k = 10$ $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. \begin{array} { | c | c | c | c | c | c | } \hline x & 8 & 10 & 12 & 14 & 16 \\ \hline y = \frac { k } { x ^ { 2 } } & & & & & \\ \hline \end{array} k = 10 $

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Question 15

When buying gasoline,you notice that 16 gallons of gasoline is approximately the same amount of gasoline as 51 liters.Use this information to find a linear model that relates liters y to gallons x.Then use the model to find the numbers of liters in 25 gallons and 45 gallons. (Round your answer to one decimal place. )

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Question 16

The sales tax on an item with a retail price of $972 is $68.04.Create a variational model that gives the retail price,y,in terms of the sales tax,x,and use it to determine the retail price of an item that has a sales tax of $82.62.

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Question 17

Use the fact that the diameter of the largest particle that can be moved by a stream varies approximately directly as the square of the velocity of the stream. A stream with a velocity of $\frac { 1 } { 5 }$ mile per hour can move coarse sand particles about 0.07 inch in diameter.Approximate the velocity required to carry particles 0.2 inch in diameter.(Round your answer to two decimal places. )

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Question 18

Find a mathematical model for the verbal statement: "Q is jointly proportional to the cube of h and the square root of m."

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Question 19

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=

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Question 20

Showing 1 - 20 of 49

Exam 10: Mathematical Modeling and Variation

State sales tax is based on retail price.An item that sells for $180.99 has a sales tax of $17.4.Find a mathematical model that gives the amount of sales tax y in terms of the retail price x.Use the model to find the sales tax on a $589.99 purchase.(Round your answer to four decimal places. ) ​

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=

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=5

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=38,y=2400x = 38 , y = 2400x=38,y=2400 ​ ​

Determine whether the variation model below is of the form y=kxy = k xy=kx or y=kxy = \frac { k } { x }y=xk​ . x 12 24 36 48 60 Y 118\frac { 1 } { 18 }181​ ​ 136\frac { 1 } { 36 }361​ ​ 154\frac { 1 } { 54 }541​ ​ 172\frac { 1 } { 72 }721​ ​ 190\frac { 1 } { 90 }901​

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) ​ F is jointly proportional to r and the third power of s. (F=24750 when r=18 and s=5.)( F = 24750 \text { when } r = 18 \text { and } s = 5 . )(F=24750 when r=18 and s=5.) ​

Determine whether the variation model is of the form y=kxy = k xy=kx or y=kxy = \frac { k } { x }y=xk​ and find k.Then write a model that relates y and x. x 5 10 15 20 25 y -1.5 -3 -4.5 -6 -7.5

Determine whether the variation model below is of the form y=kxy = k xy=kx or y=kxy = \frac { k } { x }y=xk​ . x 13 26 39 52 65 Y 3 6 9 12 15

Find a mathematical model for the verbal statement: "m varies directly as the square of w and inversely as s."

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) ​ Y varies inversely as x. (y=9 when x=45.)( y = 9 \text { when } x = 45 . )(y=9 when x=45.) ​

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=5,y=380x = 5 , y = 380x=5,y=380 ​

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=10k = 10k=10 ​

The sales tax on an item with a retail price of $972 is $68.04.Create a variational model that gives the retail price,y,in terms of the sales tax,x,and use it to determine the retail price of an item that has a sales tax of $82.62.

Find a mathematical model for the verbal statement: ​ "Q is jointly proportional to the cube of h and the square root of m." ​

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=

Rectangular Coordinates

Graphs of Equations

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Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

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Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

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Nonlinear Inequalities

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Properties of Logarithms

Exponential and Logarithmic Equations

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Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

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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

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Linear Programming

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The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

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Mathematical Induction

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State sales tax is based on retail price.An item that sells for $180.99 has a sales tax of $17.4.Find a mathematical model that gives the amount of sales tax y in terms of the retail price x.Use the model to find the sales tax on a $589.99 purchase.(Round your answer to four decimal places. )

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=

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=5

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. $x = 38 , y = 2400$

Determine whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ . x 12 24 36 48 60 Y $\frac { 1 } { 18 }$ $\frac { 1 } { 36 }$ $\frac { 1 } { 54 }$ $\frac { 1 } { 72 }$ $\frac { 1 } { 90 }$

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) F is jointly proportional to r and the third power of s. $( F = 24750 \text { when } r = 18 \text { and } s = 5 . )$

Determine whether the variation model is of the form $y = k x$ or $y = \frac { k } { x }$ and find k.Then write a model that relates y and x. x 5 10 15 20 25 y -1.5 -3 -4.5 -6 -7.5

Determine whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ . x 13 26 39 52 65 Y 3 6 9 12 15

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) Y varies inversely as x. $( y = 9 \text { when } x = 45 . )$

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. $x = 5 , y = 380$

Find a mathematical model for the verbal statement: "Q is jointly proportional to the cube of h and the square root of m."

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=