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 Quadratic_Equations/149715: When a rock is dropped from a cliff into an ocean, it travels approximately 16t squared feet in t seconds. If the splash is heard 4 seconds later and the speed of sound is 1100 ft/sec, approximate the height of the cliff.1 solutions Answer 109854 by ankor@dixie-net.com(15746)   on 2008-07-25 14:52:00 (Show Source): You can put this solution on YOUR website!When a rock is dropped from a cliff into an ocean, it travels approximately 16t squared feet in t seconds. If the splash is heard 4 seconds later and the speed of sound is 1100 ft/sec, approximate the height of the cliff. : Let t = time it takes for the rock to hit the water then (4-t) = time of the sound from the splash to the thrower : Write a distance equation; Dist = speed * time ; Dist falling = distance sound traveled 16t^2 = 1100(4-t) : 16t^2 = 4400 - 1100t : A quadratic equation: 16t^2 + 1100t - 4400 = 0 : Simplify, divide by 4 4t^2 + 275t - 1100 = 0 : Solve this using the quadratic formula: a=4; b=275; c=-1100 : I got a positive solution of about 3.791 sec : Find the dist falling (16t^2) 16(3.791^2) = 229.9 ft : Confirm the dist with the sound: 4 - 3.791 = .209 sec for the sound .209 * 1100 = 229.9 ft is the cliff height
 Exponents-negative-and-fractional/149735: What is the GCF? 16a^4b^2 + 20a^2b^2 - 4ab^21 solutions Answer 109840 by ankor@dixie-net.com(15746)   on 2008-07-25 11:55:37 (Show Source): You can put this solution on YOUR website!16a^4b^2 + 20a^2b^2 - 4ab^2 : 4ab^2 is the GCF : 4ab^2(4a^3 + 5a - 1)
 Miscellaneous_Word_Problems/149618: A field has 11 fence posts along one side. Each post is 1 foot wide, and each post is spaced 10 feet from the next post.How wide is this side of the field?1 solutions Answer 109807 by ankor@dixie-net.com(15746)   on 2008-07-24 21:11:23 (Show Source): You can put this solution on YOUR website!A field has 11 fence posts along one side. Each post is 1 foot wide, and each post is spaced 10 feet from the next post.How wide is this side of the field? : Wouldn't be (10 * 10) + 11 = 111
 Surface-area/149568: The length of a rectangular garden is twice its breadth. A square playground measuring 600 m2 occupies one-third of the total area of the garden. The length of the garden in metres is 1 solutions Answer 109806 by ankor@dixie-net.com(15746)   on 2008-07-24 20:59:58 (Show Source): You can put this solution on YOUR website!The length of a rectangular garden is twice its breadth. A square playground measuring 600 m2 occupies one-third of the total area of the garden. The length of the garden in metres is: : If = 600, the total will be 3*600 ft : Let x = garden width then 2x = garden length : The simple equation: 2x * x = 3(600) ; 2x^2 = 1800 : x^2 = ; x^2 = 900 x = x = 30 m is the width then 60 m = the length
 Travel_Word_Problems/149591: Car A and car B are traveling in the same direction. Car A is traveling at a constant velocity of 60 mph and car B is traveling at a constant velocity of 75mph. If car A reaches mile marker M 20 minutes before car B, how much time will elapse between the time that car B reaches mile marker M and the time that car B reaces car A?1 solutions Answer 109801 by ankor@dixie-net.com(15746)   on 2008-07-24 19:52:17 (Show Source): You can put this solution on YOUR website!Car A and car B are traveling in the same direction. Car A is traveling at a constant velocity of 60 mph and car B is traveling at a constant velocity of 75mph. If car A reaches mile marker M 20 minutes before car B, how much time will elapse between the time that car B reaches mile marker M and the time that car B reaches car A? : During the 20 min that elapses for car B to get to the marker, car A will have traveled: * 60 = 20 miles (from the marker) : Let t = time for the car B to catch car A : Write a distance equation Distance = speed * time : Car B distance = Car A distance + 20 miles 75t = 60t + 20 75t - 60t = 20 15t = 20 t = t = = 1 hrs : Another easy way: Using relative speed. 75 - 60 = 15 mph Assume that Car A is stationary and car B is traveling at 15 mph : How long will it take Car B to travel 20 mi at 15 mph? time = = 1 hrs
 Mixture_Word_Problems/149606: a contractor has a 24-pound mixture that is no-fourth cement, and three-fourths sand. How much of a mixture that is half cement and half sand needs to be added to produce a mixture that is one-third cement?1 solutions Answer 109783 by ankor@dixie-net.com(15746)   on 2008-07-24 16:40:25 (Show Source): You can put this solution on YOUR website!a contractor has a 24-pound mixture that is no-fourth cement, and three-fourths sand. How much of a mixture that is half cement and half sand needs to be added to produce a mixture that is one-third cement? : We can write an equation based on the amt of cement ; Let x = amt of half cement mixture required : (24) + x = (x+24) Multiply equation by 12 to get rid of the denominators : 3(24) + 6x = 4(x+24) : 72 + 6x = 4x + 96 : 6x - 4x = 96 - 72 : 2x = 24 x = x = 12 lb of the half cement mixture ; : we can check solution base on the amt of sand: (24) + (12) = (12+24) 18 + 6 = *36
 test/149581: Write a variable expression for "7 divided by the sum of x and 5"1 solutions Answer 109770 by ankor@dixie-net.com(15746)   on 2008-07-24 15:55:05 (Show Source): You can put this solution on YOUR website!Write a variable expression for "7 divided by the sum of x and 5" ; Wouldn't it just be: ?
 Linear_Equations_And_Systems_Word_Problems/149574: A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. How long would it take each working alone to do the job?1 solutions Answer 109769 by ankor@dixie-net.com(15746)   on 2008-07-24 15:52:11 (Show Source): You can put this solution on YOUR website!A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. How long would it take each working alone to do the job? ; Let a = time required when A works alone Let b = time required when B works alone : Let the completed job = 1 : write an equation for each scenario : "A and B working together can do a job in 24 hours." + = 1 Multiply equation by ab to get rid of the denominators, results 24b + 24a = ab 24a = ab - 24b 24a = b(a-24) = b : "After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. That means a worked 27 hrs + = 1 Multiply equation by ab to get rid of the denominators, results 27b + 20a = ab 20a = ab - 27b 20a = b(a-27) = b : Therefore: = Cross multiply: 24a(a-27) = 20a(a-24) : 24a^2 - 648a = 20a^2 - 480a : 24a^2 - 20a^2 -648a + 480a = 0 : 4a^2 - 168a = 0 : 4a(a - 42) = 0 : a = +42 A's hrs alone ; Use + = 1 to find b, substitute 42 for a + = 1 Multiply equation by 42b 24b + 42(24) = 42b : 1008 = 42b - 24b : 1008 = 18b b = b = 56 hrs is B's time alone ; : You can check solution using a calc on both equations, a=42, b=56
 Age_Word_Problems/149563: the four oldest people in Golden City have lived 384 years. the difference in ages for the youngest and the next oldest is 14. the next youngest is 3 years older than the youngest. the oldest is 20 years older than the average of the next oldest and youngest. How old is each?1 solutions Answer 109748 by ankor@dixie-net.com(15746)   on 2008-07-24 13:44:30 (Show Source): You can put this solution on YOUR website!the four oldest people in Golden City have lived 384 years. the difference in ages for the youngest and the next oldest is 14. the next youngest is 3 years older than the youngest. the oldest is 20 years older than the average of the next oldest and youngest. How old is each? : Let the 4 people be w,x,y,& z (youngest to oldest) : Write an equation for each statement : "the four oldest people in Golden City have lived 384 years." w + x + y + z = 384 : "the difference in ages for the youngest and the next oldest is 14." y - w = 14 y = w + 14 : "the next youngest is 3 years older than the youngest. x = w + 3 : the oldest is 20 years older than the average of the next oldest and youngest. z = + 20 multiply equation by 2 to get rid of the denominator 2z = w + y + 2(20) 2z = w + y + 40 Replace y with (w+14) 2z = w + (w+14) + 40 2z = 2w + 54 Divide equation by 2: z = w + 27 : How old is each? : Replace x, y, and z in the total equation with the above equations: w + (w+3) + (w+14) + (w+27) = 384 : 4w + 44 = 384 : 4w = 384 - 44 : 4w = 340 w = w = 85 yrs is the youngest oldie then x = 85 +3 x = 88 yrs is the next oldie and y = 85 + 14 y = 99 yrs and z = 85 + 27 z = 112 yrs is real old guy ; : Check solution by finding the total 85 + 88 + 99 + 112 = 84
 Quadratic_Equations/149541: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? 1 solutions Answer 109723 by ankor@dixie-net.com(15746)   on 2008-07-24 10:15:58 (Show Source): You can put this solution on YOUR website!A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? : Draw a rectangle representing the 18 by 13 ft garden, then draw a larger rectangle around that one, enclosing the path around the garden. : Label the width of the path as x It will be apparent that the overall dimensions will be (18+2x) by (13+2x) FOIL this to get the overall area: (18+2x)*(13+2x) = 234 + 36x + 26x + 4x^2 = 234 + 62x + 4x^2 : Garden area; 18 * 13 = 234 : The equation: Overall area - garden area = path area (given as 516 sq/ft) (4x^2 + 62x + 234) - 234 = 516 : 4x^2 + 62x - 516 = 0; our old friend, the quadratic equation Simply divide equation by 2: 2x^2 + 31x - 258 = 0 Factor this to: (2x + 43)(x - 6) = 0 Positive solution x = +6 ft is the width of the path : : We can check this: overall dimensions will be (18+12) by (13+12) (30*25) - 234 = 750 - 234 = 516, confirms our solution : : Did this make sense? Any questions?
 Finance/149383: PLEASE HELP: I have to find the total amount due for each simple interest loan for \$6100 at 5.7% interest for 4 years 9 months.1 solutions Answer 109659 by ankor@dixie-net.com(15746)   on 2008-07-23 19:18:21 (Show Source): You can put this solution on YOUR website!find the total amount due for each simple interest loan for \$6100 at 5.7% interest for 4 years 9 months. : Find the interest due for 4.75 yrs : i = p*r*t p = 6100 r = .057 t = 4.75 : i = 6100 * .057 * 4.75 i = 1651.58 add to the principal 1651.58 + 6100 = \$7,751.58
 Travel_Word_Problems/149434: A man in a canoe is paddling upstream. He passes a floating log (going downstream) at the Elk's Lodge. He continues to paddle for 90 more minutes, before turning around to go downstream. The canoer reaches the log again at the sewer plant which is exactly 1 mile from the Elk's lodge. At what rate is the river flowing?1 solutions Answer 109657 by ankor@dixie-net.com(15746)   on 2008-07-23 18:56:24 (Show Source): You can put this solution on YOUR website!A man in a canoe is paddling upstream. He passes a floating log (going downstream) at the Elk's Lodge. He continues to paddle for 90 more minutes, before turning around to go downstream. The canoer reaches the log again at the sewer plant which is exactly 1 mile from the Elk's lodge. At what rate is the river flowing? : Here's what I think: : The trip away from log will take the same time as the trip back to the log The speed is the same both ways in relation to the water. : 2 * 90 min = 3 hr During this time the log travels 1 mi in relation to the land. Current = mph
 Age_Word_Problems/149431: In three years, Alex will be 3 times as old as Precy. A year ago, Alex was 7 times as old as Precy. How old are they now?1 solutions Answer 109634 by ankor@dixie-net.com(15746)   on 2008-07-23 16:41:41 (Show Source): You can put this solution on YOUR website!In three years, Alex will be 3 times as old as Precy. A year ago, Alex was 7 times as old as Precy. How old are they now? : Let A and P = their present ages : Write an equation for each statement, simplify: : "In three years, Alex will be 3 times as old as Precy." A+3 = 3(P+3) A + 3 = 3P + 9 A = 3P + 9 - 3 A = 3P + 6 : "A year ago, Alex was 7 times as old as Precy." A-1 = 7(P-1) A - 1 = 7P - 7 A = 7P - 7 + 1 A = 7p - 6 : How old are they now? : Substitute (3P+6) for A in the above equation 3P + 6 = 7p - 6 6 + 6 = 7P - 3P 12 = 4P P = P = 3 yrs old Precy's present age and A = 3(3)+ 6 A = 15 yrs old is Alex's present age ; : Check the solution in the statement: "A year ago, Alex was 7 times as old as Precy." 15 - 1 = 7(3-1)
 Quadratic_Equations/149411: Create a real-life situation that fits into the equation (x+4)(x-7) = 0 and express the situation as the same equation.1 solutions Answer 109627 by ankor@dixie-net.com(15746)   on 2008-07-23 16:23:52 (Show Source): You can put this solution on YOUR website!Create a real-life situation that fits into the equation (x+4)(x-7) = 0 and express the situation as the same equation. : A simple problems would be. You want a rectangular area of 28 sq/ft You want the length to be 3 ft longer than the width, Find the dimensions: ; Let x = length then (x-3) = width and Area = x(x-3) = x^2 - 3x : Area equation: x^2 - 3x = 28 : A quadratic equation x^2 -3x - 28 = 0 : factor this to: (x-7)(x+4) = 0 : Positive solution: x = +7 is the length
 Quadratic_Equations/149412: How many solutions exist for a quadratic equation? How do we determine whether the solutions are real or complex?1 solutions Answer 109626 by ankor@dixie-net.com(15746)   on 2008-07-23 15:55:27 (Show Source): You can put this solution on YOUR website!We use the discriminant: with the equation in the form ax^2 + bx + c; Use the values for a, b, c in: b^2 - 4*a*c = The rules for the discriminant are are: b^2 - 4*a*c = 0; one real number solution, a double root b^2 - 4*a*c > 0; two real number solutions, that are not equal b^2 - 4*a*c < 0; two complex number solutions
 Linear_Equations_And_Systems_Word_Problems/149344: The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4 feet wide. If the area of the walk is 748 feet^2, determine the dimensions of the pool.1 solutions Answer 109625 by ankor@dixie-net.com(15746)   on 2008-07-23 15:30:37 (Show Source): You can put this solution on YOUR website!the length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4 feet wide. If the area of the walk is 748 ft^2, determine the dimensions of the pool. : Let x = the width of the pool then 2x = the length and 2x^2 = area of the pool : Overall area including the walk = (x+8)*(2x+8) = 2x^2 + 24x + 64 : The equation: Overall area - pool area = 748 sq/ft (walkway area) (2x^2 + 24x + 64) - 2x^2 = 748 : 24x = 748 - 64 : 24x = 684 x = x = 28.5 ft width of the pool and 2(28.5) = 57 ft, length of the pool : : Check solution: Overall area = 65 * 36.5 = 2372.5 ---Pool area = 57 * 28.5 = 1624.5 ---------------------------------- leaving the walkway area = 748
 Travel_Word_Problems/149371: This question is from textbook Intermediate Algebra with Applications A cyclist rode 40 mi. before having a flat tire and then walking 5 mi to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was 5 h. Find the rate at which the cyclist was riding.1 solutions Answer 109597 by ankor@dixie-net.com(15746)   on 2008-07-23 13:36:41 (Show Source): You can put this solution on YOUR website!A cyclist rode 40 mi. before having a flat tire and then walking 5 mi to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was 5 h. Find the rate at which the cyclist was riding. : Let x = the walking rate then 4x = the riding rate : Write a time equation: Time = : Riding time + walking time = 5 hrs + = 5 Reduce the fraction: + = 5 = 5 Multiply both sides by x 5x = 15 x = x = 3 mph is the walking rate then 4(3) = 12 mph is the riding rate ; : Check solution + = 3 + 1 = 5 hrs
 Travel_Word_Problems/149374: A plane which can fly 100 miles an hour in still air can fly 500 miles with a wind which is blowing at a certain rate in 5/8 of the time it would require to fly 500 miles against a wind blowing at the same rate. What was the rate of the wind?1 solutions Answer 109594 by ankor@dixie-net.com(15746)   on 2008-07-23 13:05:19 (Show Source): You can put this solution on YOUR website!A plane which can fly 100 miles an hour in still air can fly 500 miles with a wind which is blowing at a certain rate in 5/8 of the time it would require to fly 500 miles against a wind blowing at the same rate. What was the rate of the wind? : Let x = the rate of the wind then (100-x) = speed against the wind and (100+x) = speed with the wind : Write a time equation: Time = : With the wind time = Against time * = * = = Cross multiply: 2500(100+x) = 500(800-8x) : 250000 + 2500x = 400000 - 4000x ; 2500x + 4000x = 400000 - 250000 : 6500x = 150000 x = x = 23.1 mph, the rate of the wind : : Check solution, find the time for each trip = 4.06 hrs * = 4.06 hr
 Distributive-associative-commutative-properties/149362: Can You Help Me??? Please Simplify: 3x^2-22x+71 solutions Answer 109582 by ankor@dixie-net.com(15746)   on 2008-07-23 10:55:39 (Show Source): You can put this solution on YOUR website!Please Simplify: 3x^2-22x+7 : You can factor this to: (3x - 1)(x - 7)
 Volume/149349: I'm trying to calculate the volume of a house attic with triangular roof. The dimensions are: 6.5 meters wide, 7 meters long and 2.8 meters high at the top of the triangular roof.1 solutions Answer 109575 by ankor@dixie-net.com(15746)   on 2008-07-23 10:15:43 (Show Source): You can put this solution on YOUR website!Treat it like a triangular prism, the formula for that is: V = * L * W * H : Your attic: V = * 7 * 6.5 * 2.8 : V = 63.7 cu meters
 Quadratic_Equations/149314: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.1 solutions Answer 109540 by ankor@dixie-net.com(15746)   on 2008-07-22 21:56:39 (Show Source): You can put this solution on YOUR website!Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. : Let s = his speed : Write a time equation: Time = : = + 1 Multiply equation by s(s+10), results: : 200(s+10) = 200s + s(s+10) : 200s + 2000 = 200s + s^2 + 10s : Subtract 200s from both sides. Arrange as a quadratic equation: s^2 + 10s - 2000 = 0 Factor: (s+50)(s-40) = 0 The positive solution s = 40 mph : : Check solution 200/40 = 200/50 + 1
 Travel_Word_Problems/149269: Car A and car B are traveling in the same direction. Car A is traveling at a constant velocity of 60 mph. and car B is traveling at a constant velocity of 75mph. If car A reaches mile marker M 4 minutes after car B, how much time will elapse between the time that car A reaches mile marker M, and the time that the cars are 20 miles apart? 1 solutions Answer 109537 by ankor@dixie-net.com(15746)   on 2008-07-22 21:45:18 (Show Source): You can put this solution on YOUR website!Car A and car B are traveling in the same direction. Car A is traveling at a constant velocity of 60 mph. and car B is traveling at a constant velocity of 75mph. : If car A reaches mile marker M 4 minutes after car B, how much time will elapse between the time that car A reaches mile marker M, and the time that the cars are 20 miles apart? : When car A reaches the M marker, car B will have traveled * 75 = 5 miles The relative speed between the two cars: 75 - 60 = 15 mph : Think of car A being stationary, car B is 5 mi away traveling at 15 mph : How long would it take Car B to travel another 15 mi at 15 mph? : They will be 20 mi apart in 1 hr from the time Car A is at the marker :
 Rectangles/149281: The length of a rectangle must be 4 feet more than the width, and the perimeter must be at least 32 feet. What is the range of values for the width?1 solutions Answer 109527 by ankor@dixie-net.com(15746)   on 2008-07-22 19:30:08 (Show Source): You can put this solution on YOUR website!The length of a rectangle must be 4 feet more than the width, and the perimeter must be at least 32 feet. What is the range of values for the width? : Let x = width then (x+4) = length : Perimeter 2(x+4) + 2x => 32 ; 2x + 8 + 2x => 32 : 4x => 32 - 8 : x => x => 6 ft width
 Circles/149254: Find the total grazing area of a goat G, The animal is tied to a corner of a 40'x40' barn, by an 80' rope. One of the sides of the barn is extended by a fence. assume that the area is grass everywhere except inside of the barn. 1 solutions Answer 109522 by ankor@dixie-net.com(15746)   on 2008-07-22 18:56:09 (Show Source): You can put this solution on YOUR website!Find the total grazing area of a goat G, The animal is tied to a corner of a 40'x40' barn, by an 80' rope. One of the sides of the barn is extended by a fence. assume that the area is grass everywhere except inside of the barn. ; The side that is extended by the fence will make a difference : If the fence is opposite the corner, where the rope is tied, then is will not effect it. : The larger area is of circle with 80' radius A = A = 15079.6 sq/ft and 2 each circles with a radius of 40' A = A = 2513.3 sq/ft : Total: 15079.6 + 2513.3 = 17,593 sq/ft
 Polynomials-and-rational-expressions/149248: (x-8/x+5)/(x-9/x+4) why cant -5, 9, and -4 not allowable replacements for the variable x. 1 solutions Answer 109502 by ankor@dixie-net.com(15746)   on 2008-07-22 16:26:34 (Show Source): You can put this solution on YOUR website!All these values would put 0 as the denominator, a big no-no in algebra
 Miscellaneous_Word_Problems/149245: Problem A sheet metal worker is planning to make an open top box by cutting equal squares(x-in by x-in) from the corners of a 10in by 14 in piece of copper. A second box is to be made in the same manner from an 8 in by 10 in piece of aluminum, but its height is to be one half that of the first box. 1.Find the polynomial function for the volume of each box 2.find the values of x for which the copper box is 72 cubic inch larger than the aluminum box 3.write the difference between the two volumes (d) as a function of x 4.find d for x=1.5 5.for what value of x is the difference between the two volumes the largest 6. explain the steps to solve this problem1 solutions Answer 109498 by ankor@dixie-net.com(15746)   on 2008-07-22 16:13:50 (Show Source): You can put this solution on YOUR website!i) Problem: A sheet metal worker is planning to make an open-top box by cutting equal squares (x-in. by x-in.) from the corners of a 10-in. by 14-in. piece of copper. A second box is to be made in the same manner from an 8-in. by 10-in. piece of aluminum, but its height is to be one-half that of the first box. : (1)Find a polynomial function for the volume of each box. : 1st box dimensions: (10-2x) by (14-2x) by x Vol = x*(10-2x)*(14-2x) FOIL f(x) = x(140 - 48x + 4x^2) f(x) = 4x^3 - 48x^2 + 140x : 2nd box cut out will be .5x in. by .5x in.,(height 1/2 the 1st box), therefore: the dimensions will be: (10-x) by (8-x) by .5x Vol = .5x*(10-x)*(8-x) FOIL f(x) = .5x(80 - 18x + x^2) f(x) = .5x^3 - 9x^2 + 40x : : (2)Find the values of x for which the copper box is 72 cubic in. larger than the aluminum box. : Big box vol - small box vol = 72 cu in (4x^3 - 48x^2 + 140x) - (.5x^3 - 9x^2 + 40x) = 72 Remove brackets 4x^3 - 48x^2 + 140x - .5x^3 + 9x^2 - 40x = 72 Group like terms 4x^3 - .5x^3 - 48x^2 + 9x^2 + 140x - 40x - 72 = 0 : 3.5x^3 - 39x^2 + 100x - 72 = 0 : Solve this by graphing y = 3.5x^3 - 39x^2 + 100x - 72 : The integer solution x = 2; & x ~ 1.3; the third solution x ~ 7.8 isn't reasonable : (3)Write the difference between the two volumes (d) as a function of x. d(x) = (4x^3 - 48x^2 + 140x) - (.5x^3 - 9x^2 + 40x) which is d(x) = 3.5x^3 - 39x^2 + 100x : (4)Find d for x=1.5 d(x) = 3.5(1.5^3) - 39(1.5^2) + 100(1.5) d(x) = 3.5(3.375) - 39(2.25) + 150 d(x) = 11.8125 - 87.75 + 150 d(x) = 74.0625 : (5)For what value of x is the difference between the two volumes the largest? Graph d(x) = 3.5x^3 - 39x^2 + 100x: : Greatest difference appears to be at x = 1.7 which is a difference of about 74.5
 Numbers_Word_Problems/149189: Hello, can you please help me solve this problems: 1.) One number is 3 more than the other. Their sum is 7. Find the numbers. 2.) The denominator of a fraction is twice the numerator. If the sum of the terms is 3, what is the fraction? 3.) The sum of two numbers is 165 and their difference is 29. Find the numbers. 4.) If the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. If the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. Find the original fraction.1 solutions Answer 109495 by ankor@dixie-net.com(15746)   on 2008-07-22 15:38:40 (Show Source): You can put this solution on YOUR website!1.) One number is 3 more than the other. Their sum is 7. Find the numbers. Let x = "one number then (x-3) = "other number : "Their sum is 7" x + (x-3) = 7 2x = 7 + 3 x = x = 5 : Check: 5 - 3 = 2: 5 + 2 = 7 : : 2.) The denominator of a fraction is twice the numerator. If the sum of the terms is 3, what is the fraction? Let x = the numerator then 2x = denominator Obviously, if x + 2x = 3, then x = 1 and the fraction is : : 3.) The sum of two numbers is 165 and their difference is 29. Find the numbers. x + y = 165 x - y = 29 ------------adding eliminates y: 2x + 0 = 194 x = x = 97 I'll let you find y : : 4.) If the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. = : If the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. - 1 = = + 1 = + = Find the original fraction. : ; Check solution in the 1st statement: = = = ; confirms our solutions :
 Money_Word_Problems/149172: Walt made an extra 9000 last year from a part time job. He invested part of the money at 9% and the rest at 8%. He made a total of \$770.00 in interest. How much was invested at 8%?1 solutions Answer 109478 by ankor@dixie-net.com(15746)   on 2008-07-22 13:02:37 (Show Source): You can put this solution on YOUR website!Walt made an extra 9000 last year from a part time job. He invested part of the money at 9% and the rest at 8%. He made a total of \$770.00 in interest. How much was invested at 8%? : Let x = amt invested at 8% The total was given as \$9000, therefore: (9000-x) = amt invested at 9% : Write an interest equation: : interest at 8% + interest at 9% = \$770 .08x + .09(9000-x) = 770 Multiply what's inside the brackets .08x + 810 - .09x = 770 : .08x - .09x = 770 - 810 : -.01x = -40 x = x = \$4000 invested at 8% : : Check solution (\$5000 invested at 9%) .08(4000) + .09(5000) = 320 + 450 = 770; confirms our solution
 Polynomials-and-rational-expressions/149210: I need the answers and steps for these five. Even though this is my first question of the day I know it counts as 5 so I will only ask one other today Thanks 1.(2a5)3 2.(-3xy3)4 3. (5a3b4)2 4.(-mn8)3 5. (-2x2y)3 * (5xy3)2 1 solutions Answer 109475 by ankor@dixie-net.com(15746)   on 2008-07-22 12:50:11 (Show Source): You can put this solution on YOUR website!1. Cube each term :You multiply when you raise one power to another power : 2. ; a negative raised to an even power will be positive : 3. : 4. : 5. ; a negative raised to an odd power will be negative : add exponents of like terms when you multiply : This is the method, check each step to ensure I did not make a dumb math mistake here