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# Recent problems solved by 'mananth'

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 Rational-functions/331660: Hello,Can someoe help me solve by multiplying and simplify by factoring assuming that all expressions under radicals represent non-negetive numbers ∛y^4∛81y^5 Thank you 1 solutions Answer 237803 by mananth(12270)   on 2010-08-14 07:06:53 (Show Source): You can put this solution on YOUR website!cuberoot(y^3*y)*cuberoot ((3^3)*3*(y^3)*y^2) y * cuberoot(y)*3y(cuberoot(3y^2) 3y^2*cuberoot(3y^3) 3y^3cuberoot(3)
 Linear_Equations_And_Systems_Word_Problems/331742: Two brothers took turns washing the family car on weekends. John could usually wash the car in 45 min, whereas Jim took 30 min for the job. One weekend they were in a hurry to go to a football game; so they worked together. How long did it take them?1 solutions Answer 237802 by mananth(12270)   on 2010-08-14 06:57:53 (Show Source): You can put this solution on YOUR website! 1/45 + 1/30 of the job they can do in 1 minute LCD = 1350 75/1350 job they do in 1 minute they will take 1350 / 75 = 18 minutes to do the job.
 Linear_Equations_And_Systems_Word_Problems/331741: Jo Beth left her college town on a bus that traveled 60 mi/h. three hours later, her father left home driving at a speed of 50mi/h to meet the bus. If the college was 345 mi from Jo Beth’s home and the father met the bus as it was arrived at the station, how long did the father drive to meet the bus?1 solutions Answer 237801 by mananth(12270)   on 2010-08-14 06:51:16 (Show Source): You can put this solution on YOUR website!.. let bus station be x miles from home. .. jo beth traveled 3 hours at 60 mph before father left home she traveled 180 miles. .. so she traveled 345-180 = 165 miles from the time her dad started. time taken by her to travel 165-x miles = 165-x /60 hours time taken by Dad to reach bus station = x/50 .. times are equal. x/50 = 165-x / 60 60x=50(165-x) 60x=8250-50x 110x = 8250 x= 8250/110 x= 75 miles distance from home to bus station.
 Linear_Equations_And_Systems_Word_Problems/331743: Lyman can mow the family yard in 75 mins, while Jean can mow it in 60 mins. If they worked together, how long will be needed for the job?1 solutions Answer 237800 by mananth(12270)   on 2010-08-14 06:33:08 (Show Source): You can put this solution on YOUR website!Lyman can mow the family yard in 75 mins, Jean can mow it in 60 mins. .. lyman can do 1/75 of job in 1 minute jean can do 1/60 of job in 1 minute .. together 1/75+1/60 = 4+5 /300 9/300 of the job in 1 minute. so together they will do in 300/9 minutes .. 33.33 minutes ..
 Linear_Equations_And_Systems_Word_Problems/331744: Mrs Windell spent 1 h addressing one-third of the family christmas cards, and Mr. Windell spent 1 ¼ h addressing another third. Continuing the addressing together, how long did they take to finish the rest of the cards? 1 solutions Answer 237799 by mananth(12270)   on 2010-08-14 06:28:54 (Show Source): You can put this solution on YOUR website!Mrs Windell spent 1 h addressing one-third of the family christmas cards, Mr. Windell spent 1 ¼ h addressing another third. .. Mr. Windell took 5/4 hours for 1/3 job so she will do in 1 hour (1/3 )/(5/4) =1/3*4/5 = 4/15 of the job in 1 hour. .. together they can do 1/3 + 4/15 of the job in 1 hour =5+4 / 15 =9/15 =3/5 of the job in 1 hour.together .. They have already completed 1/3 +1/3 = 2/3 of the job. so balance job is 1-2/3 =1/3 job .. 3/5 of job they take 1 hour 1/3 of job they take (1/3) / (3/5) 1/3*5/3= 5/9 hours
 Linear_Equations_And_Systems_Word_Problems/331745: Three people using word processor worked together preparing a group of form letters . Koonce could have done them alone in 2 h, Schaeffer in 3 h and Yeldell in 2h. how long did they need to do the letters working together?1 solutions Answer 237798 by mananth(12270)   on 2010-08-14 06:18:31 (Show Source): You can put this solution on YOUR website!Koonce 2 hours 1/2 job in 1 hour Schaeffer - 3 hours 1/3 job in 1 hour Yeldell - 2hours 1/2 job in 1 hour .. together they will take 1/2 + 1/3 +1/2 job in 1 hour 4/3 hours so they will together do the job in 3/4 hours ..
 Linear_Equations_And_Systems_Word_Problems/331746: A chemical mixing tank can be filled by two hoses. One requires 42 min to fill the tank , and the other 30 min . If both hoses are used, how much time is needed to fill the tank?1 solutions Answer 237797 by mananth(12270)   on 2010-08-14 06:13:25 (Show Source): You can put this solution on YOUR website!one hose takes 42 minutes so it does 1/42 of the job in 1 minute. .. the other fills in 30 minutes so it does 1/30 of the job in 1 minute . together they can do 1/30+1/42 of the job in 1 minute .. 30+42/ 32*40 of the job in 1 minute 72/1280 So they will together fill the tank in 1280/72= 17.7 minutes
 Linear_Equations_And_Systems_Word_Problems/331707: Two students are 350 m apart and begin walking toward one another at constant rates. One travels at 1.6 m/s and other at 1.9 m/s. how long will they walk until they meet? how far has each of them gone?1 solutions Answer 237796 by mananth(12270)   on 2010-08-14 05:24:28 (Show Source): You can put this solution on YOUR website!let one travel x meters before they meet. the other will walk 350-x meters speed of one is 1.6 m / s other is 1.9 m/s .. the time they walk before they meet is the same. x/1.6 = 350-x/1.9 1.9x=1.6(350-x) 1.9x=560-1.6x 2.5x=560 x=560/2.5 x= 224 m the other travels 350-244=106 m .. the time they meet will be 224/1.6 =140 seconds after they start
 Angles/331713: the base of a triangle is 8cm greater than the height. the area is 42 cm spuared. find the height and length of the base. 1 solutions Answer 237795 by mananth(12270)   on 2010-08-14 05:06:22 (Show Source): You can put this solution on YOUR website!let height = h base = h+8 .. Area of traingle = 1/2 * base * height 42= 1/2 * h * (h+8) 42=1/2*(h^2+8h) 84= h^2+8h h^2+8h-84=0 h^2+14h-6h-84=0 h(h+14)-6(h+14)=0 (h+14)(h-6)=0 h= 6 Or -14 ignore negative value h=6 cm base = h+8=14 cm
 test/331720: Solve for the variable 2y=2y(y-1)1 solutions Answer 237794 by mananth(12270)   on 2010-08-14 04:59:27 (Show Source): You can put this solution on YOUR website!2y=2y(y-1) 2y=2y^2-2y 2y^2-4y=0 2y(y-2)=0 y= 0 OR y=2
 Angles/331712: factor completely. 27w^4-8w1 solutions Answer 237793 by mananth(12270)   on 2010-08-14 04:55:45 (Show Source): You can put this solution on YOUR website!27w^4-8w w(27w^3-8) w((3w)^3-(2)^3) w(3w-2)(9w^2+6w+4)
 test/331728: Solve the system: y^2=1-x^2 y^2=x^2-3x+21 solutions Answer 237791 by mananth(12270)   on 2010-08-14 04:35:19 (Show Source): You can put this solution on YOUR website!y^2=1-x^2 y^2=x^2-3x+2 .. x^2-3x+2=1-x^2 2x^2-3x+1=0 2x^2-2x-x+1=0 2x(x-1)-1(x-1)=0 (x-1)(2x-1)=0 x=1 OR 1/2 plug the value of x to get value of y y=0 OR sqrt 3/4
 Travel_Word_Problems/331734: One person walks 1 mph faster than another. If the faster person can walk 12 miles in the same time as the other can walk 9 miles. How fast is each walking? Solve and show the equation.1 solutions Answer 237790 by mananth(12270)   on 2010-08-14 04:31:35 (Show Source): You can put this solution on YOUR website!let one of them walk at x mph he walks 9 miles the other walks at x+1 mph. he walks 12 mile they take same time .. time = distance / speeed 9/x = 12/x+1 9(x+1)=12x 9x+9=12x 12x-9x=9 3x=9 x=3 mph the other 4 mph
 Rational-functions/331729: Hello , How do you solve this expression simplify by taking roots of the numerator and denominator. √144/y^2 Thank you1 solutions Answer 237787 by mananth(12270)   on 2010-08-14 03:25:26 (Show Source): You can put this solution on YOUR website!sqrt(144) /sqrt(y^2) 12/y
 Rational-functions/331730: Hello, Please solve divide simplify by taking roots if necessary. ∛24/∛3 Thank you 1 solutions Answer 237785 by mananth(12270)   on 2010-08-14 02:37:00 (Show Source): You can put this solution on YOUR website!cuberoot 24/cuberoot3 cuberoot 2^3*3 / cuberoot 3 2cuberoot3/cuberoot3 =2
 Rational-functions/331731: Hello , can some one solve please. Multiply (4√3-12√2)(5√3+15√2) Thank you 1 solutions Answer 237784 by mananth(12270)   on 2010-08-14 02:31:13 (Show Source): You can put this solution on YOUR website! .. .. .. 20*-15 =-300
 Age_Word_Problems/331693: Dear Sir/Madam; Pls. kindly see the problem below: Question: In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter's age squared. How old is Janice? I wrote out an Algebraic expression for this problem as follows: denoting the daughter's age by x to be able to solve for her daughter's age first, so Janice's age in three years would be: 3x+3, and her age six years ago would have been x2-6; x2-6+3x+3=0, which when simplified will look like this; x2+3x-3=0. But I do not think I am right. Could you please help. Thank you.1 solutions Answer 237783 by mananth(12270)   on 2010-08-14 02:20:00 (Show Source): You can put this solution on YOUR website!let daughter's age be x now. after 3 years daughter will be x+3 .. after 3 years Janice will be 3*(x+3) years .. 6 years ago daughter's age = x-6. janice ' age was (x-6)^2 .. 3x+9-9 =3x 3x= (x-6)^2 3x=x^2-12x+36 x^2-15x+36=0 x^2-12x-3x+36=0 x(x-12)-3(x-12)=0 (x-12)(x-3)=0 x=12 OR 3 After 3 years Janice will be x(x+3) plug value of x 3(12+3)=45 So now Janice will be 45-3 = 42 years ( this makes sense) .. For value x=3 3(x+3) plug value of 3 3(3+3)= 18 This was 3 years later now she will be 15
 Travel_Word_Problems/331676: While on a treadmill, Marlena walked 2 miles an hour for one-third of the time and 4 miles an hour for two-thirds of the time. She walked a total of 2.5 miles. What amount of time, in hours, did Marlena walk on the treadmill?1 solutions Answer 237768 by mananth(12270)   on 2010-08-13 21:04:15 (Show Source): You can put this solution on YOUR website!let her walk for x hours on the tread mill x/3 hours at 2mph .. 2x/3 hours at 4 mph Distance = speed * time .. 2x/3 + 8x/3= 5/2 2x/3 +2x=5/2 10x / 3= 5/2 20x = 15 x=15/20 x=3/4 hour
 Quadratic_Equations/331681: f(x) = x2 – 4 apply the quadratic formula to find the roots of the given function, and then graph the function. 1 solutions Answer 237765 by mananth(12270)   on 2010-08-13 20:43:49 (Show Source): You can put this solution on YOUR website!f(x)=x^2-4 a=1,b=0,c=-4 .. x1= (0+sqrt(0+16))/2 x1=2 x2= (0-sqrt(0+16))/2 x2= -2 ..
 Numbers_Word_Problems/331687: 5 times a number increased by 8 is 32.Find the number1 solutions Answer 237763 by mananth(12270)   on 2010-08-13 20:21:55 (Show Source): You can put this solution on YOUR website!number be x 5 times number= 5x add 8, 5x+8 5x+8=32 add -8 5x+8-8=32-8 5x=24 x=24/5
 Quadratic_Equations/331570: 3x^8-15x^7+24x^6: Please factor this. 1 solutions Answer 237659 by mananth(12270)   on 2010-08-13 10:50:17 (Show Source): You can put this solution on YOUR website!3x^8-15x^7+24x^6 .. 3x^6(x^2-5x+8)
 Quadratic_Equations/331571: 4r^2+4r divided by 36r^2+16r I have been asked to simplify by removing the 1 factor. I can't remember how to do this.Please help. 1 solutions Answer 237657 by mananth(12270)   on 2010-08-13 10:47:54 (Show Source): You can put this solution on YOUR website! .. ..
 test/331572: 8f3-271 solutions Answer 237654 by mananth(12270)   on 2010-08-13 10:41:22 (Show Source): You can put this solution on YOUR website!8f3-27 .. ..
 Expressions-with-variables/331565: simplify y^2-x^-2/y-x^-11 solutions Answer 237650 by mananth(12270)   on 2010-08-13 10:20:15 (Show Source): You can put this solution on YOUR website! .. ..
 Expressions-with-variables/331537: If a boat travels 30 miles upstream in 4 hours and the trip downstream takes 2.5 hours, what is the rate of the boat in still water? Need help.1 solutions Answer 237639 by mananth(12270)   on 2010-08-13 09:45:24 (Show Source): You can put this solution on YOUR website! let speed of boat in still water be xmph speed of current be y mph 30/(x-y)=4 30=4x-4y.............1 .. 30/(x+y)=5/2 60=5x+5y divide by 5 12=x+y................2 .. multiply equation 2 by 4 and it to equation 1 48+30=4x+4y+4x-4y 78=8x 9.75=x speed of boat in still water = 9.75 mph
 Polynomials-and-rational-expressions/331550: simplify by removing factors of 1. 3m^2+3m/15m^2+9m1 solutions Answer 237636 by mananth(12270)   on 2010-08-13 09:37:56 (Show Source): You can put this solution on YOUR website!m^2+3m/15m^2+9m
 Travel_Word_Problems/331523: The speed of a passenger train is 6 mph faster than the speed of a freight train. The passenger train travels 280 miles in the same time it takes the freight train to travel 250 miles.Find the speed of each train1 solutions Answer 237597 by mananth(12270)   on 2010-08-13 06:17:01 (Show Source): You can put this solution on YOUR website!let speed of freight train be x speed of passenger train = x+6 .. Passenger train distance = 280 miles freight train 250 miles .. the times taken for these distances is the same 280/(x+6)=250/x 280x=250(x+6) 280x=250x+1500 30x = 1500 x= 50 mph the speed of freight train. x+6= 50+6 = 56mph = speed of passenger train.
 Travel_Word_Problems/331475: Bob will rent a car for the weekend. He can chooose one of two payment plans. The first plan costs \$51.98 for two days plus .14 cents per mile. The second plan cost \$43.98 for two days plus .18 cents per mile. How many miles does Bob need to drive for the two plans to cost the same?1 solutions Answer 237592 by mananth(12270)   on 2010-08-13 04:37:40 (Show Source): You can put this solution on YOUR website!let the number of miles Bob does be x so that both plans are same. plan a = 51.98+0.14x plan b = 43.98+0.18x .. 51.98+0.14x= 43.98+0.18x 0.04x =51.98-43.98 0.04x=8 x= 8/0.04 x=200 miles ..
 Quadratic_Equations/331444: please solve the quadratic equation 1 solutions Answer 237591 by mananth(12270)   on 2010-08-13 04:33:23 (Show Source): You can put this solution on YOUR website! x^2-6x+9+3x^2-5x-12=0 4x^2-11x-3=0 4x^2-12x+x-3=0 4x(x-3)+1(x-3)=0 (x-3)(4x+1)=0 x=3 OR x=-1/4
 test/331524: a man's age is 3 times the sum of the ages of his two sons.after 5years his age will be twice the sum of the ages of his two sons.find the age of the man. 1 solutions Answer 237589 by mananth(12270)   on 2010-08-13 03:11:15 (Show Source): You can put this solution on YOUR website!let age of sons be x & y & father's age =z z = 3(x+y) z/3 = (x+y) .. after 5 years their ages will be x+5, y+5, z+5 z+5=2(x+5+y+5) z+5=2x+2y+20 z+5=2(x+y)+20 z+5-20=2(x+y)+20-20 z-15=2(x+y) But (x+y)= z/3 z-15=2*z/3 multiply 3 3*(z-15)=2z 3z-45=2z 3z-2z=45 z=45 father's age
 Geometry_Word_Problems/331525: The surface area of two cups are in the ratio 9:64 .if the smaller cup has a height of 25 cm and a volume of 2400 cm^3 calculate a)the height of larger cup. b)the volume of larger cup.1 solutions Answer 237588 by mananth(12270)   on 2010-08-13 02:32:05 (Show Source): You can put this solution on YOUR website!volume of cylinder = pir^2h smaller cup volume = 2400= pi*r^2*25 r^2=2400/(pi*25) r=sqrt(2400/(pi*25) r=5.3 cm .. surface area of smaller cup = 2*pi*r*h S=2*pi*5.3*25 S= 832.5 sq. cm .. Ratio of surface area = 9/64 9/64= 832.5/x x=64*832.5/9 = 5920 sq. cm is the surface area of larger cup