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# Recent problems solved by 'venugopalramana'

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 Miscellaneous_Word_Problems/55225: Travis made 44 and 72 on the first two tests in algebra and has one test remaining. The average on the three tests must be at least 60 for Travis to pass the course. Let s represent his score on the last test. Write an inequality to describe each situation.1 solutions Answer 37482 by venugopalramana(3286)   on 2006-10-09 05:42:00 (Show Source): You can put this solution on YOUR website!Travis made 44 and 72 on the first two tests in algebra and has one test remaining. The average on the three tests must be at least 60 for Travis to pass the course. Let s represent his score on the last test. Write an inequality to describe each situation. total score in 3 tests = 44+72+s = 116+s average = (116+s)/3...this should be atleast 60..so (116+s)/3 >=60 116+s>=180 s>=180-116=64 s>=64
 Numeric_Fractions/55228: Please show me how to factor completly 4a^4-26a^2+301 solutions Answer 37481 by venugopalramana(3286)   on 2006-10-09 05:37:50 (Show Source): You can put this solution on YOUR website!Please show me how to factor completly 4a^4-26a^2+30 2[2a^4-13a^2+15]=2[2a^4-10a^2-3a^2+15]=2[2a^2(a^2-5)-3(a^2-5)] =2(a^2-5)(2a^2-3)
 Numeric_Fractions/55230: please factor completly x^5-7x^4+12x^31 solutions Answer 37480 by venugopalramana(3286)   on 2006-10-09 05:33:30 (Show Source): You can put this solution on YOUR website!please factor completly x^5-7x^4+12x^3 = x^3(x^2-7x+12)=x^3{x^2-3x-4x+12}=x^3[x(x-3)-4(x-3)] =x^3(x-3)(x-4)
 Numeric_Fractions/55232: Please solve 6x^2+x=151 solutions Answer 37479 by venugopalramana(3286)   on 2006-10-09 04:30:51 (Show Source): You can put this solution on YOUR website!Please solve 6x^2+x=15 6x^2 +x-15=0 6x^2+10x-9x-15=0 2x(3x+5)-3(3x+5)=0 (3x+5)(2x-3)=0 3x+5=0.......that is 3x=-5......x=-5/3....or 2x-3=0......2x=3......x=3/2
 Graphs/55215: Solve the system by graphing, addition and substitution methods. 3x – y = 1 3x – y = 21 solutions Answer 37478 by venugopalramana(3286)   on 2006-10-09 04:26:42 (Show Source): You can put this solution on YOUR website!Solve the system by graphing, addition and substitution methods. 3x – y = 1 ..........1 3x – y = 2................2 eqn.1 - eqn.2 0=1-2=-1...not possible..hence no solution..they are in consistent eqns. x...............0.......................2..............4......etc y=3x-1.........-1.......................5..............11.....etc y=3x-2.........-2.......................4...............10.....etc the 2 graphs are parallel and do not intersect hence there is no solution.
 Graphs/55216: Solve the system by graphing, addition and substitution methods. –4x + 7y = –10 x – 5y = 91 solutions Answer 37477 by venugopalramana(3286)   on 2006-10-09 04:20:26 (Show Source): You can put this solution on YOUR website!Solve the system by graphing, addition and substitution methods. –4x + 7y = –10 ...............1 x – 5y = 9................2 x=9+5y putting in eqn.1 -4(9+5y)+7y=-10 -36-20y+7y=-10 -13y=-10+36=26 y= -26/13 =-2 x=9+5*(-2)=9-10=-1 x=............0...................1.....................2....etc y=(x-9)/5....-1.8................-1.6..................-1.4.. etc Y=(4X-10)/7..-10/7................-6/7.................-2/7...ETC the 2 graphs intersect at x=-1 and y=-2
 Equations/55168: Express 2x^2+2y^2-12x+16y=-32 in standard form for a circle. Identify the radius and center of the circle.1 solutions Answer 37475 by venugopalramana(3286)   on 2006-10-08 23:55:08 (Show Source): You can put this solution on YOUR website!Express 2x^2+2y^2-12x+16y=-32.DIVIDING BY 2 x^2+y^2-6x+8y=-16 [X^2-2(X)(3)+3^2]-3^2+[Y^2+2(Y)(4)+4^2]-4^2=-16 (X-3)^2+(Y+2)^2=9=3^2 THIS IS IN THE STD.FORM OF (X-H)^2+(Y-K)^2=R^2 HENCE CENTRE = (H,K) = (3,-2) RADIUS = R =3 in standard form for a circle. Identify the radius and center of the circle.
 Linear_Equations_And_Systems_Word_Problems/55212: This question is from textbook Applied College Algebra 24. The owner of a highway construction company knows that the maximum load a cylindrical column of a circular cross section can support varies directly as the fourth power of the diameter and inversely as the square of the height. If a column 2 feet in diameter and 10 feet high supports up to 6 tons, how much of a load can a column 3 feet in diameter and 14 feet high support?1 solutions Answer 37471 by venugopalramana(3286)   on 2006-10-08 23:03:27 (Show Source): You can put this solution on YOUR website!The owner of a highway construction company knows that the maximum load (L SAY)a cylindrical column of circular cross section can support varies directly as the fourth power of the diameter(D SAY) and inversely as the square of the height(H SAY). If a column 2 feet in diameter and 10 feet high supports up to 6 tons, how much of a load can a column 3 feet in diameter and 14 feet high support? L = K*D^4*1/H^2...WHERE K IS A CONSTANT CASE 1.. 6=K*2^4/10^2=16K/100 K=6*100/16=75/2=37.5 CASE 2 L=37.5*3^4/14^2 = 37.5*81/196 = 15.5 T.
 Coordinate-system/55186: What is the area defined by the following graphs: |x|+|y| is greater than or equal to 2 and |x|+|y| is less than or equal to 51 solutions Answer 37469 by venugopalramana(3286)   on 2006-10-08 22:56:33 (Show Source): You can put this solution on YOUR website!What is the area defined by the following graphs: |x|+|y| is greater than or equal to 2 CASE 1 ..X AND Y POSITIVE..WE GET...X+Y>=2 CASE 2...X + VE Y - VE.....WE GET ..X-Y>=2 CASE 3...X -VE..Y -VE......WE GET ..-X-Y>=2 CASE 4...X - VE..Y..+ VE...WE GET ...-X+Y>=2 and |x|+|y| is less than or equal to 5 SAME WAY WE GET HERE X+Y<=5......X-Y<=5......-X-Y<=5.......-X+Y<=5 GRAPH LOOKS LIKE THIS it is the area of square with side of 5sqrt(2) - area os square with side of 2sqrt(2) = 5*sqrt(2)*5*sqrt(2)-2*sqrt(2)*2*sqrt(2) =50-8=42
 Coordinate-system/55199: Find the center and the radius of the circle whose equation is given: x^2+y^2+6x+8=0 Center = (_,_) Radius = _1 solutions Answer 37462 by venugopalramana(3286)   on 2006-10-08 22:32:01 (Show Source): You can put this solution on YOUR website!Find the center and the radius of the circle whose equation is given: x^2+y^2+6x+8=0 [X^2+2(X)(3)+3^2]-3^2+Y^2+8=0 (X+3)^2+Y^2=1 COMPARING WITH STD EQN. (X-H)^2+(Y-K)^2 =R^2 CENTRE = (H,K) = (-3,0) RADIUS =R =1 Center = (_,_) Radius = _
 logarithm/55009: This question is from textbook College Algebra Solve and find exact solutions. 4^(2x-1)=1/2 book answer: 1/41 solutions Answer 37232 by venugopalramana(3286)   on 2006-10-07 08:32:15 (Show Source): You can put this solution on YOUR website!Solve and find exact solutions. 4^(2x-1)=1/2 =2^(-1) [2^2]^(2x-1)=2^(-1) 2^{2(2x-1)}=2^(-1) 2(2x-1)=-1 4x-2=-1 4x=1 x=1/4 book answer: 1/4
 Linear_Equations_And_Systems_Word_Problems/54923: This question is from textbook Applied College Algebra 24. The owner of a highway construction company knows that the maximum load a cylindrical column of circular cross section can support varies directly as the fourth power of the diameter and inversely as the square of the height. If a column 2 feet in diameter and 10 feet high supports up to 6 tons, how much of a load can a column 3 feet in diameter and 14 feet high support?1 solutions Answer 37145 by venugopalramana(3286)   on 2006-10-06 11:56:27 (Show Source): You can put this solution on YOUR website!24. The owner of a highway construction company knows that the maximum load (L SAY)a cylindrical column of circular cross section can support varies directly as the fourth power of the diameter(D SAY) and inversely as the square of the height(H SAY). If a column 2 feet in diameter and 10 feet high supports up to 6 tons, how much of a load can a column 3 feet in diameter and 14 feet high support? L = K*D^4*1/H^2...WHERE K IS A CONSTANT CASE 1.. 6=K*2^4/10^2=16K/100 K=6*100/16=75/2=37.5 CASE 2 L=37.5*3^4/14^2 = 37.5*81/196 = 15.5 T.
 Angles/54924: One angle of a triangle has a measure of 70 degrees. The other two angles have degree measures in a ratio of 5 to 6. What is the sum of the measures, in degrees, of the two largest angles? I first tried 50 +60=110+70=180. Then I realized that 180 is the sum of all of the angles in a triangle, so it couldn't be right. Thanks if you can help!1 solutions Answer 37144 by venugopalramana(3286)   on 2006-10-06 11:51:13 (Show Source): You can put this solution on YOUR website!One angle of a triangle has a measure of 70 degrees. The other two angles have degree measures in a ratio of 5 to 6. What is the sum of the measures, in degrees, of the two largest angles? I first tried 50 +60=110+70=180. ONE ANGLE =70 HENCE SUM OF OTHER 2 ANGLES = 180-70=110...YOU ARE CORRECT!WHY DOUBT? SINCE ANGLES ARE IN 5:6 RATIO...TAKE THEM AS 5X,6X 5X+6X=11X=110...HENCE X=110/11=10 SO THE 2 ANGLES ARE 50,60.. Then I realized that 180 is the sum of all of the angles in a triangle, so it couldn't be right. WHY IT IS RIGHT ..SUM OF 3 ANGLES 50,60,70 IS 180 Thanks if you can help!
 Linear-equations/54781: a) write the slope-y-intercept equation form of line which passes through the 2 points: (-3,1), (0,6) b) wrie the slope-y-intercept equation form of the line which has slop 2/3 and passes through the point: (-3,3) c) write the point-slope equation form of the line which passes through the 2 points: (9,0), (-5,3) d) write the general equation form of the line which passes through the 2 points: (1,2), (6,7)1 solutions Answer 37007 by venugopalramana(3286)   on 2006-10-05 12:11:12 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY FOR SLOPE AND A POINT PROBLEM FOR THE 2 POINT PROBLEM SOLUTION IS AS FOLLOWS. ------------------------------------------------------------------ a) Write the slope-y-intercept equation form of the line which passes through the 2 points: X1,Y1=(-3,1), (0,6)=X2,Y2 FORMULA IS Y= (Y2-Y1)(X-X1)/(X2-X1)+Y1 Y=(6-1)(X+3)/((0+3) + 1 Y=5(X+3)/3 +1 Y=(5X/3)+ 6.................M=5/3=SLOPE.........6=Y INTERCEPT ---------------------------------------------------------------- use the given conditions to write an equation in the point-slope form and the slope-intercept form...thank you slope=-2 = M , passing through (0, -3) = X1,Y1 FORMULA IS Y=M(X-X1)+Y1 Y=-2(X-0)+(-3)= -2X-3
 Inequalities/54784: solve each of the following inequalities. express answers in interval notation. a) 2y^2+5y-63<0 b) 4y^2+10y-14<0 c) x^2+x-30<01 solutions Answer 37006 by venugopalramana(3286)   on 2006-10-05 12:08:42 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK ------------------------------- PLEASE HELP ME WITH THIS PROBLEM; For f(x)=1 over x62-2x-8 find the intervals where f(x)<0. HOPE YOU MEAN Y = F(X)=1/ X^2-2X-8.....ASSUMING SO Y= 1/X^2-4X+2X-8=1/[X(X-4)+2(X-4)]=1/[(X+2)(X-4)] THE ROOTS ARE X=-2 AND X=4 FOR F(X) TO BE <0,X SHOULD LIE BETWEEN THE 2 ROOTS ..THAT IS ..BETWEEN -2 & 4 . -2 ------------------------------------------------------- ANSWERS ARE a) 2y^2+5y-63<0 ...(2Y-9)(Y+7)<0....Y LIES BETWEEN -7 AND 9/2...(-7,9/2) b) 4y^2+10y-14<0 ...2(2Y+7)(Y-1)<0...Y LIES BETWEEN -7/2 AND 1 ...(-7/2,1) c) x^2+x-30<0....(X+6)(X-5)<0....X LIES BETWEEN -6 AND 5......(-6,5)
 Inequalities/54633: solve each of the following quadratic inequalities. express your answers in interval notation. a) 2y^2+5y-63<0 b) 4y^2+10y-14<0 c) x^2+x-30<01 solutions Answer 37005 by venugopalramana(3286)   on 2006-10-05 12:07:20 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK ------------------------------- PLEASE HELP ME WITH THIS PROBLEM; For f(x)=1 over x62-2x-8 find the intervals where f(x)<0. HOPE YOU MEAN Y = F(X)=1/ X^2-2X-8.....ASSUMING SO Y= 1/X^2-4X+2X-8=1/[X(X-4)+2(X-4)]=1/[(X+2)(X-4)] THE ROOTS ARE X=-2 AND X=4 FOR F(X) TO BE <0,X SHOULD LIE BETWEEN THE 2 ROOTS ..THAT IS ..BETWEEN -2 & 4 . -2 ------------------------------------------------------- ANSWERS ARE a) 2y^2+5y-63<0 ...(2Y-9)(Y+7)<0....Y LIES BETWEEN -7 AND 9/2...(-7,9/2) b) 4y^2+10y-14<0 ...2(2Y+7)(Y-1)<0...Y LIES BETWEEN -7/2 AND 1 ...(-7/2,1) c) x^2+x-30<0....(X+6)(X-5)<0....X LIES BETWEEN -6 AND 5......(-6,5) You may edit the question. M
 Functions/54624: This question is from textbook ALGEBRA AND TRIGONOMETRY PLEASE HELP ME WITH THIS PROBLEM; For f(x)=1 over x62-2x-8 find the intervals where f(x)<0.1 solutions Answer 37004 by venugopalramana(3286)   on 2006-10-05 11:58:11 (Show Source): You can put this solution on YOUR website!PLEASE HELP ME WITH THIS PROBLEM; For f(x)=1 over x62-2x-8 find the intervals where f(x)<0. HOPE YOU MEAN Y = F(X)= X^2-2X-8.....ASSUMING SO Y= X^2-4X+2X-8=X(X-4)+2(X-4)=(X+2)(X-4) THE ROOTS ARE X=-2 AND X=4 FOR F(X) TO BE <0,X SHOULD LIE BETWEEN THE 2 ROOTS ..THAT IS ..BETWEEN -2 & 4 . -2
 real-numbers/54626: Write an expression for the area of an isosceles triangle and simplify. The base is 1/2Y and the height is 2/5y + 41 solutions Answer 37003 by venugopalramana(3286)   on 2006-10-05 11:53:33 (Show Source): You can put this solution on YOUR website!Write an expression for the area of an isosceles triangle and simplify. The base is 1/2Y and the height is 2/5y + 4 AREA=BASE*HT/2=(Y/2)(2Y/5 +4)/2=Y(2Y+5)/(2*2)=(2Y^2+5Y)/4
 Linear-equations/54630: a) Write the slope-y-intercept equation form of the line which passes through the 2 points: (-3,1), (0,6) b) write the slope-y-intercept equation form of the line which has a slope 2/3 and passes through the point : (-3,3) c)write the point-slope equation form of the line which passes through the 2 points: (9,0), (-5,3) d)write the general equation form of the line which passes through the 2 points: (1,2), (6,7)1 solutions Answer 37002 by venugopalramana(3286)   on 2006-10-05 11:45:56 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY FOR SLOPE AND A POINT PROBLEM FOR THE 2 POINT PROBLEM SOLUTION IS AS FOLLOWS. ------------------------------------------------------------------ a) Write the slope-y-intercept equation form of the line which passes through the 2 points: X1,Y1=(-3,1), (0,6)=X2,Y2 FORMULA IS Y= (Y2-Y1)(X-X1)/(X2-X1)+Y1 Y=(6-1)(X+3)/((0+3) + 1 Y=5(X+3)/3 +1 Y=(5X/3)+ 6.................M=5/3=SLOPE.........6=Y INTERCEPT ---------------------------------------------------------------- use the given conditions to write an equation in the point-slope form and the slope-intercept form...thank you slope=-2 = M , passing through (0, -3) = X1,Y1 FORMULA IS Y=M(X-X1)+Y1 Y=-2(X-0)+(-3)= -2X-3
 Linear-equations/54653: What is the equation of the line having slope 4/7 and passing through the point (-3,1) in standard form?1 solutions Answer 37001 by venugopalramana(3286)   on 2006-10-05 11:39:54 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING AND TRY use the given conditions to write an equation in the point-slope form and the slope-intercept form...thank you slope=-2 = M , passing through (0, -3) = X1,Y1 FORMULA IS Y=M(X-X1)+Y1 Y=-2(X-0)+(-3)= -2X-3
 Functions/54668: use the given conditions to write an equation in the point-slope form and the slope-intercept form slope=-5, passing through (-4, -2)1 solutions Answer 37000 by venugopalramana(3286)   on 2006-10-05 11:37:02 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING AND TRY ------------------------------------------ use the given conditions to write an equation in the point-slope form and the slope-intercept form...thank you slope=-2 = M , passing through (0, -3) = X1,Y1 FORMULA IS Y=M(X-X1)+Y1 Y=-2(X-0)+(-3)= -2X-3
 Functions/54669: use the given conditions to write an equation in the point-slope form and the slope-intercept form...thank you slope=-2, passing through (0, -3)1 solutions Answer 36999 by venugopalramana(3286)   on 2006-10-05 11:35:42 (Show Source): You can put this solution on YOUR website!use the given conditions to write an equation in the point-slope form and the slope-intercept form...thank you slope=-2 = M , passing through (0, -3) = X1,Y1 FORMULA IS Y=M(X-X1)+Y1 Y=-2(X-0)+(-3)= -2X-3
 Mixture_Word_Problems/54768: A 25% SOLUTION OF ALCOHOL IS TO BE MIXED WITH A 40% SOLUTION TO GET 50l OF A FINAL MIXTURE THAT IS 30% alcohol. How much of each of the original solution should be used?1 solutions Answer 36997 by venugopalramana(3286)   on 2006-10-05 11:32:02 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY ------------------------------------------------------------------ PLEASE HELP ASAP: Ziggy's famous yogurt blends regular yogurt that is 3% fat with its no fat yogurt to obtain low fat yogurt that is 1% fat. How many pounds of regular and how many pounds of non-fat yogurt should be mixed to obtain 60 pounds of lowfat yogurt. PLEASE HELP ASAP. thank you THESE ARE MATERIAL BALANCE PROBLEMS.THE PRINCIPLE IS TO APPLY TOTAL OF ALL INPUTS =TOTAL OF ALL OUTPUTS.. THIS PRINCIPLE CAN BE APPLIED TO TOTAL MIXTURE AS A WHOLE AS WELL AS INDIVIDUAL COMPONENTS OF THE MIXTURE.LET US SEE THE APPLICATION USING YOUR PROBLEM. HERE THE MIXTURE COMPRISES 2 INPUTS-REGULAR YOGURT (RY) & NO FAT YOGURT (NFY) AND ONE OUT PUT-LOW FAT YOGURT (LFY).THE COMPONENT OF IMPORTANCE IN THE MIXTURE IS FAT CONTENT.SO WE TAKE 2 BALANCES HERE ..ONE FOR THE TOTAL MIXTURE AND ANOTHER FOR COMPONENT OF FAT IN THE MIXTURE. I..TOTAL BALANCE... INPUTS 1.QTY.OF.RY=X POUNDS 2.QTY OF NFY=Y POUNDS OUT PUT 1.QTY.OF LFY=60 POUNDS SO APPLYING TOTAL OF ALL INPUTS =TOTAL OF ALL OUTPUTS.....WE GET X+Y=60.............................I II..COMPONENT BALANCE..HERE IT IS FAT . INPUTS 1.QTY.OF FAT IN RY=X*3/100=3X/100 POUNDS 2.QTY OF FAT IN NFY=Y*0/100=0 POUNDS OUT PUT 1.QTY.OF FAT IN LFY=60*1/100=60/100 POUNDS SO APPLYING TOTAL OF ALL INPUTS =TOTAL OF ALL OUTPUTS.....WE GET 3X/100 + 0=60/100.............................II 3X=60 X=20 POUNDS. OF REGULAR YOGURT Y=60-20=40 POUNDS OF NO FAT YOGURT.