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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 logarithm/73581: Carbon 14 dating assumes that the carbon dioxide on Earth today has the same radioactive content as it did centuries ago. If this is true, the amount of Carbon 14 absorbed by a tree that grew several centuries ago should be the same as the amount of Carbon 14 absorbed by a tree growing today. A piece of ancient charcoal contains only 15% as much radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal if the half-life of Carbon 14 is 5715 years?1 solutions Answer 52632 by stanbon(57302)   on 2007-03-06 20:54:02 (Show Source): You can put this solution on YOUR website!A piece of ancient charcoal contains only 15% as much radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal if the half-life of Carbon 14 is 5715 years? ======== A(t) = Ao(1/2)^(t/5715) (0.15)Ao = Ao(1/2)^(t/5715) 0.15 = (1/2)^t/5715 Take the log of both sides to get: log0.15 = (t/5715)log0.5 t/5715 = log0.15/log0.5 t = 5715(2.736965594... t = 15641.76 years =========== Cheers, Stan H.
 Polynomials-and-rational-expressions/73582: I need help in solving equations by factoring: 2t^2+7t=4. THANK YOU1 solutions Answer 52628 by stanbon(57302)   on 2007-03-06 20:46:35 (Show Source): You can put this solution on YOUR website!I need help in solving equations by factoring: 2t^2+7t=4. 2t^2+7t-4=0 (t+4)(2t-1)=0 t=-4 or t=1/2 ========= Cheers, Stan H.
 Graphs/73562: I think I may have submitted this one before but I am really having trouble with it still. Business and finance. The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). (a) If the fixed cost is \$40 and the variable cost is \$10, write the cost equation. This is what I came up for this part. C = 10x + 40 b) Graph the cost equation. (c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation. (d) How many items must be produced for the revenue to equal the cost (the break-even point)? 1 solutions Answer 52627 by stanbon(57302)   on 2007-03-06 20:43:37 (Show Source): You can put this solution on YOUR website!Business and finance. The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). (a) If the fixed cost is \$40 and the variable cost is \$10, write the cost equation. This is what I came up for this part. C = 10x + 40 b) Graph the cost equation. (c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation. Done (d) How many items must be produced for the revenue to equal the cost (the break-even point)? R=C 50x = 10x+40 40x=40 x= 1 (number of items that must be produced to break even) ============= Cheers, Stan H.
 Graphs/73570: I have no clue what this is asking of me. Please help? Rewrite into Standard Form Write the equation of the line passing through each of the given points with the indicated slope. Give your results in slope-intercept form, where possible. (0,5), m=-3/51 solutions Answer 52624 by stanbon(57302)   on 2007-03-06 20:36:17 (Show Source): You can put this solution on YOUR website!You are told the slope and you are told the intercept. So, y=(-3/5)x+5 ======== Cheers, Stan H.
 Money_Word_Problems/73573: Business and finance. If the inventor in exercise 53 charges \$4 per unit, then her profit for producing and selling x units is given by the function P(x)= 2.25x - 7000 (a) What is her profit if she sells 2000 units? (b) What is her profit if she sells 5000 units? (c) What is the break-even point for sales?1 solutions Answer 52623 by stanbon(57302)   on 2007-03-06 20:34:02 (Show Source): You can put this solution on YOUR website!finance. If the inventor in exercise 53 charges \$4 per unit, then her profit for producing and selling x units is given by the function P(x)= 2.25x - 7000 (a) What is her profit if she sells 2000 units? (b) What is her profit if she sells 5000 units? (c) What is the break-even point for sales? ----------------- a) P(2000) = 2.25*2000-7000 =4500-7000 =-\$2500 She loses \$2500 ================ P(5000) = 2.25*5000-7000 =11250-7000 =\$4125 =========== If 2.25x-7000=0 Then 2.25x = 7000 x=3112 units ========= Cheers, Stan H.
 Graphs/73572: I just do not know how to do these. Please help? Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form, where possible. (-1, 3) and (4, -2) 1 solutions Answer 52622 by stanbon(57302)   on 2007-03-06 20:24:03 (Show Source): You can put this solution on YOUR website!Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form, where possible. ---------------- (-1, 3) and (4, -2) slope = (-2-3)/(4--1) = -5/5= -1 The equation you want has form y=mx+b You are told y=3 when x=-1 and you just determined m=-1 Use those facts to solve for b, as follows: 3=-1(-1)+b b=2 ------EQUATION: y=-x+2 ========= Cheers, Stan H.
 Numbers_Word_Problems/73578: This question is from textbook The numerator of a fraction exceeds 8 times the denominator by 2. The value of the fraction is (17/2). Find the fraction. 1 solutions Answer 52620 by stanbon(57302)   on 2007-03-06 20:17:39 (Show Source): You can put this solution on YOUR website!The numerator of a fraction exceeds 8 times the denominator by 2. The value of the fraction is (17/2). Find the fraction. --------- Let the denominator be "x" Then the numerator is 8x+2. Then (8x+2)/x = 17/2 Cross multiply to get: 16x+4 =17x x=4 The fraction is (8*4+2)/4 = 17/2 Cheers, Stan H.
 Money_Word_Problems/73569: A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continuous compounding, what is the answer? Round to the hundredth's place. PLEASE HELP!!! I Would Appreciate it!1 solutions Answer 52619 by stanbon(57302)   on 2007-03-06 20:06:40 (Show Source): You can put this solution on YOUR website!A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continuous compounding, what is the answer? Round to the hundredth's place. ---------------- Continuous compounding gives A = Pe^rt P is the initial investment; if you double it you get 2P 2P = Pe^rt Divide both sides by P to get: 2 = e^rt Take the natural log of boh sides to get: ln2 = rt t= (1/r)ln2 If r=10% you get: t = (1/0.1)(0.69314...) t= 6.9314 years to double your money at 10% annual interest. This is usually called "the rule of 7". ========= Cheers, Stan H.
 Polynomials-and-rational-expressions/73574: I need help in solving equations by factoring: 2t^2+7t=4. THANK YOU1 solutions Answer 52618 by stanbon(57302)   on 2007-03-06 19:57:58 (Show Source): You can put this solution on YOUR website!I need help in solving equations by factoring: 2t^2+7t=4. 2t^2+7t-4 Use the quadratic formula to get: t=[-7+-sqrt(49-4*2*-4)]/4 t=[-7+-sqrt(81)]/4 t=[-7+-9]/4 t=(-7+9)/4 = 1/2 or t=(-7-9)/4 = -4 The factors are: (t+4)(2t-1) ============ Cheers, Stan H. ============
 Numbers_Word_Problems/73559: This question is from textbook what number must be added to both the numerator and denominator of the fraction (5/23) to give a fraction equal to (1/3).1 solutions Answer 52615 by stanbon(57302)   on 2007-03-06 19:39:26 (Show Source): You can put this solution on YOUR website!what number must be added to both the numerator and denominator of the fraction (5/23) to give a fraction equal to (1/3). ------- Let the number be "x". Then: (5+x)/(23+x) = 1/3 Cross multiply to get: 3(5+x) = 1(23+x) 15+3x = 23+x 2x=8 x=4 That is the number you want. ============= Cheers, Stan H.
 Points-lines-and-rays/73465: Find the equation of the line satisfying the given conditions : parallel to the x-axis and passes through the point (-5,-3).1 solutions Answer 52586 by stanbon(57302)   on 2007-03-06 09:24:01 (Show Source): You can put this solution on YOUR website!The equation of the x-axis is y=0 because the x-axis contains all the points where y=0. You want the line where all the points have y=-3. That is the equation of the line you want. Cheers, Stan H.
 Geometry_proofs/73426: This question is from textbook Geometry Please help i dont understand proofs: Given: MI=LD Prove:ML=ID for reasons name the propety that makes the statement is true Statements Reasons MI=LD Given IL=IL Reflexive MI+IL=LD+IL I think addition MI+IL=ML;LD+IL=ID I have no clue ML=ID I think substitution1 solutions Answer 52579 by stanbon(57302)   on 2007-03-06 07:38:39 (Show Source): You can put this solution on YOUR website!Given: MI=LD Prove:ML=ID for reasons name the propety that makes the statement is true Statements Reasons MI=LD Given IL=IL Reflexive MI+IL=LD+IL I think addition MI+IL=ML I is the point connecting two line segments, MI and LI. LD+IL=ID You are substituting LD for MI because MI=LD and L is the point connecting DL and IL ML=ID I think substitution; that is correct. ============== Cheers, Stan H.
 Equations/73440: please factor by grouping x-y-x^2+2xy-y21 solutions Answer 52578 by stanbon(57302)   on 2007-03-06 07:29:09 (Show Source): You can put this solution on YOUR website!please factor by grouping x-y-x^2+2xy-y2 =(x-y)-(x^2-2xy+y^2 =(x-y)-(x-y)^2 =(x-y)[1-(x-y)] =(x-y)(1-x+y) Cheers, Stan H.
 Probability-and-statistics/73213: you are eating dinner at a restaurant. the restaurant offers 6 appetizers, 12 main dishes, 6 side orders and 8 desserts. if you can order one of each of these, how many different dinners can you order?1 solutions Answer 52576 by stanbon(57302)   on 2007-03-06 07:24:46 (Show Source): You can put this solution on YOUR website!you are eating dinner at a restaurant. the restaurant offers 6 appetizers, 12 main dishes, 6 side orders and 8 desserts. if you can order one of each of these, how many different dinners can you order? ---------- 6*12*6*8=3456 different dinners ======= Cheers, Stan H.
 Probability-and-statistics/73336: This question is from textbook basic statistics A school organization is holding a raffle. The prizes are a ski trip worth \$200 and 5 secind prizes of \$20 gift certificates to Ski's R Us. The club is selling 500 tickets. a.what is the expected value of exactly one ticket? b.If the tickets cost\$1 each, what is the expected winnings someone who purchased 5 tickets?1 solutions Answer 52547 by stanbon(57302)   on 2007-03-05 22:19:48 (Show Source): You can put this solution on YOUR website!A school organization is holding a raffle. The prizes are a ski trip worth \$200 and 5 secind prizes of \$20 gift certificates to Ski's R Us. The club is selling 500 tickets. a.what is the expected value of exactly one ticket? Values associated with one ticket are X=200,or 20,or 20 or 20, or 20, or 20, or zero. Therefore E(x)=(1/500)200+5(1/500)20+(499/500)*0 = (2/5)+1/5=\$(3/5) or 60 cents ---------------- b.If the tickets cost\$1 each, what is the expected winnings someone who purchased 5 tickets? E(X)=(5/500)(200+5*20)+(499/500)(-5) =3-4.99 = - \$1.99 ============== Cheers, Stan H.
 test/73422: identify three methods you can use to solve a system of equations and explain when to use each method. write example systems that illustrate when to use each method 1 solutions Answer 52541 by stanbon(57302)   on 2007-03-05 21:34:28 (Show Source):
 test/73419: Can someone help me figure out this graph. Thank you. Graph:f(x)=-3x^2-31 solutions Answer 52539 by stanbon(57302)   on 2007-03-05 21:27:59 (Show Source): You can put this solution on YOUR website!Graph:f(x)=-3x^2-3 Plot some points: If x=0,y=-3 That is the vertex If x=1,y=-6 If x=-1, y=-6 Connect the points and finish the downward opening parabola. --------- Cheers, Stan H.
 test/73421: Graph: g ( x ) = - 3/4 x^2 + 2 Thank you!!!!!1 solutions Answer 52537 by stanbon(57302)   on 2007-03-05 21:24:10 (Show Source): You can put this solution on YOUR website!Graph: g ( x ) =(-3/4)x^2 + 2 Plot a few points: If x=0, y=2 giving you point (0,2) If x=2, y=-1 giving you point (2,-1) If x=-2, y=-1 giving you point (-2,-1) The point (0,2) is the vertex and the parabola opens downward. ---------------- Cheers, Stan H.
 Rate-of-work-word-problems/73418: This question is from textbook Leo fnished 2/3 of a job in 12 hours. When he was joined by Ed, they completed the job in 2 hours. How many hours would it take Ed to do the job alone.1 solutions Answer 52536 by stanbon(57302)   on 2007-03-05 21:18:04 (Show Source): You can put this solution on YOUR website!Leo fnished 2/3 of a job in 12 hours. When he was joined by Ed, they completed the job in 2 hours. How many hours would it take Ed to do the job alone. --------------- Leo DATA: Time = (2/3) job/12 hr = 3/2[(2/3)job/12 hr](2/3)= 2job/36hr=1job/18hr Rate = (1/18)job/hr. ---------- Together DATA: Time = 12 hrs/job ; Rate = (1/12)job/hr -------------- Ed Data: Time = x hrs/job ; Rate = (1/x) job/hr ============== EQUATION: rate + rate = rate together 1/18 +1/x = 1/12 Multiply thru by 36x to get: 2x + 36 = 3x x=36 hrs (Time for Ed to do the job alone.) ------- Cheers, Stan H.
 Exponents/73224: THE DEGREE THREE POLYNOMIAL f(x) WITH REAL COEFFICIENTS AND LEADING COEFFICIENT 1, HAS -3 AND + 4i AMONG ITS ROOTS. EXPRESS f(x) AS A PRODUCT OF LINEAR AND QUADRATIC POLYNOMIALS WITH REAL COEFFICIENTS. 1 solutions Answer 52446 by stanbon(57302)   on 2007-03-04 20:38:50 (Show Source): You can put this solution on YOUR website!THE DEGREE THREE POLYNOMIAL f(x) WITH REAL COEFFICIENTS AND LEADING COEFFICIENT 1, HAS -3 AND + 4i AMONG ITS ROOTS. EXPRESS f(x) AS A PRODUCT OF LINEAR AND QUADRATIC POLYNOMIALS WITH REAL COEFFICIENTS. --------- If 4i is a root and the polynomial has real coefficients then -4i is also a root. The polynomial is: f(x)=(x+3)(x+4i)(x-4i) f(x)=(x+3)(x^2+16) Cheers, Stan H.
 Exponents/73225: A BACTERIA CULTURE STARTED WITH A COUNT OF 720 AT 8:00 A.M., AND AFTER t HOURS IS EXPECTED TO GROW TO f(t)= 720(3/2)^t. ESTIMATE THE NUMBER OF BACTERIA IN THE CULTURE AT 11:00 A.M. THE SAME DAY. 1 solutions Answer 52445 by stanbon(57302)   on 2007-03-04 20:35:52 (Show Source): You can put this solution on YOUR website!A BACTERIA CULTURE STARTED WITH A COUNT OF 720 AT 8:00 A.M., AND AFTER t HOURS IS EXPECTED TO GROW TO f(t)= 720(3/2)^t. ESTIMATE THE NUMBER OF BACTERIA IN THE CULTURE AT 11:00 A.M. THE SAME DAY. f(t)=720(3/2)^t 8:00AM to 11:00AM is 3 hrs. f(3)=720(3/2)^3 f(3)=720(27/8) f(3)=2430 bacteria by 11:00AM -------- Cheers, Stan H.
 Probability-and-statistics/73212: if you randomly select 2 cards from a standard 52-card deck. find the probability that the first card and the second card is red if a: you replace the first card before selecting the second b: you do not replace the first card1 solutions Answer 52443 by stanbon(57302)   on 2007-03-04 19:56:46 (Show Source): You can put this solution on YOUR website!if you randomly select 2 cards from a standard 52-card deck. find the probability that the first card and the second card is red if a: you replace the first card before selecting the second Ans: If you replace the card the events are independent; that means what happened on the 1st draw has no effect on what happens on the 2nd draw. In that case P(red and red)= p(red)*P(red) = 1/2*1/2 = 1/4=0.25 ----------------- b: you do not replace the first card Now the events are dependent because you are drawing the 2nd card from a "different" deck; the deck is not missing one red card. P(red and red) = p(red)*P(red|red) = (26/52) * (25/51) = (1/2)(25/51) =25/102=0.245098... ---------- Cheers, Stan H.
 logarithm/73211: Solve for x: log (2 lower)(x+2) + log (2lower)x=3 log (2 lower)[x(x+2)] = 3 2^3=x(x+2) 8=x^2 + 2x x^2 + 2x-8=0 (x+4)(x-2)=0 x=-4, x=2 log(2 lower)(-4 + 2) + log (2 lower) (-4)=3 this is where i get stuck and need some help. Thanks!1 solutions Answer 52442 by stanbon(57302)   on 2007-03-04 19:30:35 (Show Source): You can put this solution on YOUR website!log (2 lower)[x(x+2)] = 3 2^3=x(x+2) 8=x^2 + 2x x^2 + 2x-8=0 (x+4)(x-2)=0 x=-4, x=2 log(2 lower)(-4 + 2) + log (2 lower) (-4)=3 this is where i get stuck and need some help. ------------ You found that x=-4 or x=2 You began to check the x=-4 answer and got stuck. Right. x=-4 cannot be an answer of the original problem because log(-4) has no meaning. -------- So check x=2 to see if it is a good answer. log(2+2) + log2 = 3 Using base 2 you get: 2+1=3 Which is true. So x=2 is a good answer and is the only answer. ---------- Cheers, Stan H.
 logarithm/73210: Use the properties of logarithms to expand. log(4 lower)xy^3/z Any and all help would be appreciated1 solutions Answer 52441 by stanbon(57302)   on 2007-03-04 19:24:48 (Show Source): You can put this solution on YOUR website!Remember: log(ab)=loga + logb log(a/b)=loga - logb loga^b = bloga -------------- Just keep in mind this is all base 4: log(4 lower)xy^3/z =log(x)+log(y^3)-logz =log(x) +3log(y) -log(z) ----------- Cheers, Stan H.
 Matrices-and-determiminant/73203: What is the product of this matrix equation using inverse matrices? [3 -4 x [a = [6 2 1] x b] = 7] (That is supposed to be a 2x2, a 1x1, and another 1x1. I put the equal and multiplication signs on both top and bottom to make the matrices look a little more aligned.) Thank you! 1 solutions Answer 52440 by stanbon(57302)   on 2007-03-04 19:19:51 (Show Source): You can put this solution on YOUR website!What is the product of this matrix equation using inverse matrices? [3 -4] x [a] = [6] [2 1] x [b] = [7] ---------------- The inverse of the 2x2 is [3 -4] [2 1] ------------------ Multiply that 2x2 times [6] [7] to get a=-10; b=19 -------- Cheers, Stan H>
 Matrices-and-determiminant/73188: Help! I don't know if I'm doing this right. Use the matrix method. x+y-z = -9 2x-y-2z=-3 x+2y+3z=14 I'm confused I seen one way adding R1+R3 to start and another saying interchange row 1 and 3????? This is what I have done: R1 1 1 -1 | -9 R2 2 -1 -2 | -3 R3 1 2 3 | 14 R1 1 2 3 | 14 R2 2 -1 -2 | -3 R3 1 1 -1 | -9 R1 1 2 3 | 14 R2 0 -5 -8 |-31 R3 1 1 -1 | -9 R1 1 2 3 | 14 R2 0 -5 -8 |-31 R3 0 -1 -4 |-23 R1 1 2 3 | 14 R2 0 1 8/5 | 31/5 R3 0 -1 -4 |-23 ?????????????????????????????????? 1 solutions Answer 52436 by stanbon(57302)   on 2007-03-04 18:37:38 (Show Source): You can put this solution on YOUR website!Use the matrix method. x+y-z = -9 2x-y-2z=-3 x+2y+3z=14 I'm confused I seen one way adding R1+R3 to start and another saying interchange row 1 and 3????? This is what I have done: R1 1 1 -1 | -9 R2 2 -1 -2 | -3 R3 1 2 3 | 14 OK ------------------------- R1 1 2 3 | 14 R2 2 -1 -2 | -3 R3 1 1 -1 | -9 ok --------------------- R1 1 2 3 | 14 R2 0 -5 -8 |-31 R3 1 1 -1 | -9 OK ------------------ R1 1 2 3 | 14 R2 0 -5 -8 |-31 R3 0 -1 -4 |-23 OK ------------------- Multiply thru R3 by -1 and interchange R2 and R3 R1 1 2 3 | 14 R2 0 1 4 | 23 R3 0 -5 -8 |-31 -------------------- Multiply R2 by 5 and add it to R3 to get R1 1 2 3 | 14 R2 0 1 4 | 23 R3 0 0 12 | 84 OK ----------------------- Divide R3 by 12 to solve for "z" z=7 -------- Substitute z=7 into R2 to solve for "y" y +4*7 =23 y=-5 ------- Substitute y=-5 and z=7 into R1 to solve for "x" x + 2*-5 +3*7 = 14 x -10+21 = 14 x = 3 --------- Solution: x=3 ; y=-5 ; z = 7 ============== Cheers, Stan H. -------- ??????????????????????????????????
 expressions/73186: Could I please get some help with problem solving an inequality expressing. Question: A electronic store wants to order at least 3 times as many DVD players as VHS players. Write an inequality expressing this relationship. x+ 3x is this correct?1 solutions Answer 52432 by stanbon(57302)   on 2007-03-04 17:14:25 (Show Source): You can put this solution on YOUR website!Question: A electronic store wants to order at least 3 times as many DVD players as VHS players. Write an inequality expressing this relationship. Let the number of VHS players be "x". Let the number of DVD players be "y". INEQUALITY: y >= 3x ------- Cheers, Stan H.
 Matrices-and-determiminant/73181: Solve by either elimination, substitution or Crammer's Rule. I am not sure how to do this problem since there is more than one # on the right side of the =. Please help. y=10-2z-x 4x-y=2 -5+5z=4x+3y1 solutions Answer 52430 by stanbon(57302)   on 2007-03-04 17:02:39 (Show Source): You can put this solution on YOUR website!Rearrange the equations in the form ax+by+cz = d y=10-2z-x 4x-y=2 -5+5z=4x+3y ------------- x+y+2z = 10 4x-y+0z = 2 4x+3y-5z=-5 ---------------- The "coefficient" matrix has determinant (5+24+0)-(-8+0-20)=57 The "x" matrix determinant is 62 The "y" matrix determinant is 134 The "z" matrix determinant is 187 --------- x=62/57 y=134/57 z=187/57 ----------- Using matrix multiplication (A^-1B) I get the same answer. Cheer, Stan H.
 Rectangles/73176: A rectangle is placed under the parabolic arch by f(x)=27-3x^2 by using a point (x,y) on the parabola,as shown on the figure.Write a formula for the function A(x) that gives the area of the rectangle as a function of the x-coordinate of the point chosen. answers are: a.f(x)=6(27-3x^2) b.f(x)=27x-3x^3 c.f(x)=54x-6x^3 d.f(x)=162x-6x^31 solutions Answer 52429 by stanbon(57302)   on 2007-03-04 16:45:30 (Show Source): You can put this solution on YOUR website!A rectangle is placed under the parabolic arch by f(x)=27-3x^2 by using a point (x,y) on the parabola,as shown on the figure.Write a formula for the function A(x) that gives the area of the rectangle as a function of the x-coordinate of the point chosen. answers are: a.f(x)=6(27-3x^2) b.f(x)=27x-3x^3 c.f(x)=54x-6x^3 d.f(x)=162x-6x^3 ----------------- I don't have the figure but you do. The base of the rectangle is 2x because it goes x to the right of the y axis and x to the left of the y axis. The height of the rectangle is y which equals 27-3x^2 -------- The Area is base*height A(x) = (2x)(27-3x^2) A(x) = 54x -6x^3 which is answer "c". cheers, Stan H.