Precalculus Ch 9, 10
10.1 question 8
A certain parabola has the equation Find the focus, directrix, and axis. What is the focus of the parabola?
10.1 question 11
A laboratory designed a radio telescope that had a diameter of 320320 ft and maximum depth of 4646 ft. decorative image (a) Write an equation of a parabola that models the cross section of the dish if the vertex is placed at the origin and the parabola opens up. (b) The receiver must be placed at the focus of the parabola. How far from the vertex should the receiver be located?
9.7 question 3
Add the following matrices. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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Change the exponential statement to an equivalent statement involving a logarithm. 25 equals 5 squared25=52 The equivalent logarithmic statement is
9.8 question 5
Decide whether or not the given matrices are inverses of each other. Are these two matrices inverses? Select the correct choice below and fill in the answer boxes to complete your choice.
10.2 question 2
Determine whether or not each equation is that of an ellipse. If it is not, state the kind of graph the equation has. Complete parts a through d below.
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Determine whether the equation defines y as a function of x. yequals=StartFraction 9 Over x minus 9 EndFraction9x−9 Does the equation define y as a function of x?
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Determine whether the equation defines y as a function of x. yequals=plus or minus StartRoot 10 minus x squared EndRoot±10−x2 Is the equation a function?
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Determine whether the equation defines y as a function of x. yequals=x squared minus 9 x minus 7x2−9x−7 Does the equation define y as a function of x?
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Evaluate the series.
9.5 question 1
Fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is The solution is
10.1 question 13/14/15
Find the equation of the parabola described below. Find the two points that define the latus rectum, and graph the equation. vertex at left parenthesis 6 comma negative 1 right parenthesis(6,−1), focus at left parenthesis 6 comma negative 3 right parenthesis(6,−3) Choose the correct answer below.
9.8 question 1
Find the following matrix product. Note that the product can be found mentally, without the use of a calculator or pencil-and-paper calculations.
10.2 question 3
Find the graph of the following ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and the foci.
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Find the graph of the following ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and the foci. Which graph is correct?
9.3 question 1/2/3/4
Find the value of the determinant. The determinant value is
9.7 question 16
Given A and B find the product BA if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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Given Aequals=Start 2 By 2 Table 1st Row 1st Column 2 2nd Column negative 3 2nd Row 1st Column 3 2nd Column 2 EndTable2−332 and Bequals=Start 3 By 2 Table 1st Row 1st Column 3 2nd Column 2 2nd Row 1st Column 0 2nd Column negative 3 3rd Row 1st Column 2 2nd Column 6 EndTable320−326, find the product BA if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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Given functions f and g, find (a) (fcircle◦g)(x) and its domain, and (b) (gcircle◦f)(x) and its domain.
10.1 question 5/6
Graph the following horizontal parabola, and give the domain and range.
9.5 question 2
How can we tell, before doing any work, that the below system cannot have more than two solutions? Choose the correct choice below.
9.7 question 4
Let A and B Find Bminus−A, if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
9.7 question 7
Let B Find B.
9.7 question 8
Let A and B Find −3A+3B.
9.7 question 6
Let A Find 5A.
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Solve The solution set is
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Solve the given logarithmic equation. log Subscript 1 divided by 3 Baseline left parenthesis x plus 3 right parenthesis equals negative 4log1/3(x+3)=−4 The solution set is
9.8 question 10
Solve the given system using the inverse of the coefficient matrix. What is the inverse of the coefficient matrix?
9.1 question 7
Solve the system. State whether it is inconsistent or has infinitely many solutions. If the system has infinitely many solutions, write the solution set with z arbitrary. Select the correct choice below and fill in any answer boxes within your choice.
9.1 question 1/4
Solve. The solution set is
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The marketing manager at a jeans company wishes to find a function that relates the demand D for men's jeans and p, the price of the jeans. The following data were obtained based on a price history of the jeans. Answer parts (a) through (g).
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Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.
9.7 question 17
Yummy Yogurt sells three types of yogurt: nonfat, regular, and super creamy, at three locations. Location I sells 4040 gal of nonfat, 8080 gal of regular, and 5050 gal of super creamy each day. Location II sells 1010 gal of nonfat, and Location III sells 2020 gal of nonfat each day. Daily sales of regular yogurt are 5050 gal at Location II and 100100 gal at Location III. At Location II, 3030 gal of super creamy are sold each day, and 3030 gal of super creamy are sold each day at Location III.
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Find: (a) f left parenthesis negative 3 right parenthesisf(−3) (b) nbsp f left parenthesis 0 right parenthesis f(0) (c) f left parenthesis 2 right parenthesisf(2)
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Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of the rational function. f(x)equals=StartFraction x squared minus 2 x minus 3 Over 2 x squared minus x minus 21 EndFractionx2−2x−32x2−x−21 Select the correct choice below and fill in any answer boxes within your choice.
10.2 question 4
Graph the following ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci.
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Graph the following horizontal parabola, and give the domain and range.
10.1 question 4
Graph the following horizontal parabola, and give the domain and range. Use the graphing tool to graph the parabola.
10.2 question 5
Graph the given ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and foci in the figure. Choose the correct graph below.
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High concentrations of carbon monoxide CO can cause coma and possible death. The time required for a person to reach a COHb level capable of causing a coma can be approximated by the quadratic model Tequals=.0002xsquared2minus−.316xplus+127.9, where T is the exposure time in hours necessary to reach this level and 500less than or equals≤xless than or equals≤800 is the amount of carbon monoxide present in the air in parts per million (ppm). a) What is the exposure time when xequals=650650? b) Estimate the concentration of CO necessary to produce a coma in 44 hr.
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How long does it take for an investment to double in value if it is invested at 2020% compounded monthly question mark monthly? Compounded continuously?
9.2 question 1
How many rows and how many columns does this matrix have? What is its dimension? The matrix has 2 2 row(s) and 4 4 column(s). The dimension of the matrix is 2 2 times ×4 4.
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Identify the graph with domain left parenthesis negative infinity comma negative 7 right parenthesis union left parenthesis negative 7 comma infinity right parenthesis(−∞,−7) ∪ (−7,∞). Choose the graph with the correct domain from the choices on the right.
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Identify the graph with rangeleft parenthesis negative infinity comma 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis(−∞,2) ∪ (2,∞). Choose the correct graph on the right.
9.2 question 15
If a building contractor hires 88 day laborers and 11 concrete finishernothing, his payroll for the day is $12721272. If he hires 1 day laborer and 55 concrete finishers, his daily cost is $939939. Find the daily wage for each type of worker. Solve the problem using matrices. The daily wage for the laborer is $139 139. The daily wage for the concrete finisher is $ nothing .$
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If a rock falls from a height of 2626 meters on Earth, the height H (in meters) after x seconds is approximately Upper H left parenthesis x right parenthesis equals 26 minus 4.9 x squared .H
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In 19951995, the sports league introduced a salary cap that limits the amount of money spent on players' salaries. The quadratic model y equals 0.2313 x squared plus 2.600 x plus 35.17y=0.2313x2+2.600x+35.17 approximates this cap in millions of dollars for the years 19951995-20062006, where xequals=0 represents 19951995, xequals=1 represents 19961996, and so on. Complete parts a and b. a. Approximate the sports league salary cap in 20042004.
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In a certain region, the average hourly wage in dollars from 1960 to 2010 can be modeled by the function f(x) below. Use f to estimate the average hourly wages in 1965, 1985, and 2005. Round to the nearest cent.
9.8 question 2
It can be shown that the following matrices are inverses. What is their product (in either order)?
10.1 question 1
Match each equation of a parabola in Column I with its description in Column II. Type the number of description, corresponding to each equation.
9.2 question 10
Use the Gauss-Jordan method to solve the system of equations. For infinitely many solutions, give the solution with y arbitrary. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
9.2 question 11/12/13
Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with z arbitrary. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
9.3 question 5/6/7/8/9/10
Use Cramer's rule to solve the system of equations. If Dequals=0, use another method to determine the solution set. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
9.8 question 3
What is the coefficient matrix of the following system? The coefficient matrix of the given system is
9.8 question 4
What is the matrix equation form of the following system? The matrix equation form of the given system is
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Determine whether the function is one-to-one. If so, (a) write an equation for the inverse function in the form yequals=f Superscript negative 1f−1(x), (b) graph f and f Superscript negative 1f−1 on the same axes, and (c) give the domain and range of f and f Superscript negative 1f−1. If the function is not one-to-one, say so.
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Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 1 plus one sixth plus StartFraction 1 Over 36 EndFraction plus times times times 1+16+136+••• Select the correct choice below and fill in any answer boxes within your choice.
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Find a88 and a Subscript nan for the arithmetic sequence.
10.2 question 7
Find the equation of an ellipse satisfying the given conditions. Foci: (minus−44, 0) and (44, 0); length of major axis: 14144 The equation of the ellipse is
10.1 question 12
Find the equation of the parabola described below. Find the two points that define the latus rectum, and graph the equation. focus at left parenthesis 6 comma 0 right parenthesis(6,0), directrix the line x equals negative 6x=−6 The equation of the parabola with focus left parenthesis 6 comma 0 right parenthesis(6,0) and directrix the
9.7 question 12/15
Find the matrix product if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
9.7 question 11/13/14
Find the product of the following matrices, if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
9.7 question 5
Find the difference, if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
10.1 question 7
Find the focus, directrix, and axis for the parabola.
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Find the half-life of a radioactive element, which decays according to the function A(t)equals=Upper A 0A0e Superscript negative 0.0138 te−0.0138t, where t is the time in years.
9.8 question 6/7
Find the inverse, if it exists, for the matrix. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
10.2 question 1
For an ellipse, the foci lie on a line called the __________ axis. For an ellipse, the foci lie on a line called the major axis.
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For the following function, one zero is given. Find all the others. f(x)equals=xcubed3minus−1111xsquared2plus+4040xminus−5050; 3 minus i3−i The zeros of f(x) are 3 minus i comma3−i, 3 plus i 3+i, and
10.1 question 2/3
For the parabola, give the vertex, focus, directrix, axis of symmetry, domain, and range.
9.5 question 3/4/5/6/7/8/9/10/11
Give all solutions of the nonlinear system of equations, including those with nonreal complex components. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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A sparkling-water distributor wants to make up 300300 gal of sparkling water to sell for $ 6.00$6.00 per gallon. She wishes to mix three grades of water selling for $99.00, $33.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as the $ 3.00 comma$3.00, water. How many gallons of each should she use? She should use 120 120 gal of $99.00, 60 60 gal $ 3.00 comma$3.00, and 120 120 gal of $4.50.
9.1 question 8
A sparkling-water distributor wants to make up 400400 gal of sparkling water to sell for $ 8.00$8.00 per gallon. She wishes to mix three grades of water selling for $1414.00, $33.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as the $ 3.00 comma$3.00, water. How many gallons of each should she use? She should use 160 160 gal of $1414.00, 80 80 gal $ 3.00 comma$3.00, and 160 160 gal of $4.50.
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Outpatient surgery as a percent of total surgery at hospitals has grown. The logarithmic function f left parenthesis x right parenthesis equals negative 1317 plus 303 ln xf(x)=−1317+303lnx, where x is the number of years since 1900, is the best-fitting logarithmic model. Use the function to estimate outpatient surgery as the percent of total surgeries in the year 19971997. What does this function estimate for the percent of outpatient surgeries in 19971997?
9.7 question 1
Perform the indicated operation if possible. Select the correct choice below and fill in any answer boxes present in your choice.
9.7 question 2
Perform the operation if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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Solve the quadratic inequality. Write the solution set in interval notation. x squared minus 4 x minus 32 greater than 0x2−4x−32>0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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Solve the system analytically. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
9.1 question 2/3
Solve the system analytically. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The solution set i
9.8 question 9
Solve the system by using the inverse of the coefficient matrix. The solution of the system is
9.8 question 11/12/13
Solve the system by using the inverse of the coefficient matrix. The solution set is
9.8 question 8
Solve the system by using the inverse of the coefficient matrix. What is the inverse of the coefficient matrix?
9.1 question 5/6
Solve the system. The solution set is
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State the open intervals over which the function is (a) increasing, (b) decreasing, and (c) constant.
9.7 question 10
Suppose that matrix A has dimension 11 times ×55 and that matrix B has dimension 55 times ×22. Decide whether the product BA can be calculated. If it can, determine its dimension. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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Suppose that matrix A has dimension 22 times ×22 and that matrix B has dimension 22 times ×55. Decide whether the product AB can be calculated. If it can, determine its dimension. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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Suppose that matrix A has dimension 33 times ×55 and that matrix B has dimension 55 times ×44. Decide whether the product BA can be calculated. If it can, determine its dimension. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
9.7 question 9
Suppose that matrix A has dimension 55 times ×22 and that matrix B has dimension 22 times ×44. Decide whether the product AB can be calculated. If it can, determine its dimension. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
10.1 question 16
The reflector of a searchlightsearchlight is in the shape of a paraboloid of revolution. Its diameter is 32 centimeters32 centimeters and its depth is 1616 centimeterscentimeters. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?
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Three varieties of coffee long dash— Coffee A, Coffee B, and Coffee C long dash— are combined and roasted, yielding a 5151-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for $12.7612.76 per lb, are needed as Coffee A, which sells for $15.9915.99 per lb. Coffee B retails for $12.4512.45 per lb. How many pounds of each coffee should be used in a blend that sells for $13.3413.34 per lb? Should be used 10.91 10.91 lb. of Coffee A, 18.27 18.27 lb. of Coffee B and 21.82 21.82 lb. of Coffee C. (Round to two decimal places as needed.)
9.2 question 17
Three varieties of coffee long dash— Coffee A, Coffee B, and Coffee C long dash— are combined and roasted, yielding a 5252-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for $9.959.95 per lb, are needed as Coffee A, which sells for $15.9915.99 per lb. Coffee B retails for $13.9913.99 per lb. How many pounds of each coffee should be used in a blend that sells for $12.8212.82 per lb? Should be used 10.01 10.01 lb. of Coffee A, 21.97 21.97 lb. of Coffee B and 20.02 20.02 lb. of Coffee C. (Round to two decimal places as needed.)
9.2 question 16
To manufacture an automobile requires painting, drying, and polishing. Epsilon Motor Company produces three types of cars, the Delta, the Beta, and the Sigma. Each Delta requires 99 hours for painting, 22 hours for drying, and 33 hours for polishing. A Beta requires 1717 hours for painting, 44 hours for drying, and 44 hours for polishing, and a Sigma requires 77 hours for painting, 33 hourshours for drying, and 55 hourshours for polishing. If the company has 270270 hours for painting, 7676 hours for drying, and 105105 hours for polishing per month, how many of each type of car are produced? Select the correct choice below and fill in any answer boxes within your choice.
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Use the properties of logarithms to rewrite the following expression as a single logarithm. Assume all variables represent positive real numbers.
9.2 question 7/8/9
Use the Gauss-Jordan method to solve the following system of equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
9.2 question 14
Use the Gauss-Jordan method to solve the system of equations. Select the correct choice below and fill in any answer boxes within your choice.
9.2 question 2/3
Write an augmented matrix for the following system of equations and give its size. What is the augmented matrix? What is the size of the matrix?
10.2 question 6
Write an equation for the ellipse with x-intercepts (plus or minus±66,0) and y-intercepts (0,plus or minus±44). An equation for the ellipse is
10.2 question 9/10
Write an equation for the ellipse. Type the left side of the equation in the box below.
10.2 question 8
Write an equation for the given ellipse that satisfies the following conditions. The equation for the given ellipse is
10.1 question 9
Write an equation for the parabola with a vertex at the origin and focus (99,0). What is the correct equation?
10.1 question 10
Write the equation for the parabola. An equation for this parabola is
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Write the first 4 terms of the sequence. a11equals=33, aSubscript nnequals=8 times 8•aSubscript n minus 1n−1plus+66, for n > 1 What is the first term?
9.2 question 5
Write the system of equations associated with the augmented matrix. Do not solve. Complete the system shown below. Use the letters x, y, and z to represent the terms from the first, second, and third columns of the matrix, respectively.
9.2 question 4
Write the system of equations associated with the given augmented matrix. Do not solve. Choose the correct answer below.
9.2 question 6
Write the system of equations associated with the given augmented matrix. Do not solve. Choose the correct answer below.