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# Recent problems solved by 'venugopalramana'

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 Polynomials-and-rational-expressions/22646: Fully factor the third-order polynomial H(s) if it is known that one of the factors is (s+2). H(s)= 2s^3-7s^2-43s-42 I need help.... 1 solutions Answer 11278 by venugopalramana(3286)   on 2005-12-18 05:25:42 (Show Source): You can put this solution on YOUR website!H(s)= 2s^3-7s^2-43s-42 try s=0,1,2,-1,-2 etc.. we find that at s=2 ....H=0...HENCE S+2 IS A FACTOR DIVIDING WITH S+2 WE GET -2...|...2......-7.........-43.........-42 .....|...0......-4..........22..........42 .............................................. .........2......-11.........-21..........0 HENCE WE GET 2S^2-11S-21 =2S^2-14S+3S-21=2S(S-7)+3(S-7)=(2S+3)(S-7)..HENCE H(S)=(S+2)(2S+3)(S-7)
 Equations/22878: Please help me with this An inlet pipe can fill a pool in 10 hours, while the drain can empty it in 12 hours if the pool is empty and both the intel pipe and the drain are open, how long will it take to fill the pool?1 solutions Answer 11277 by venugopalramana(3286)   on 2005-12-18 05:15:47 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY.IF YOU HAVE DIFFICULTY ,I SHALL WORK OUT FOR YOU.KEY IS TO FIND HOW MUCH WILL BE FILLED OR DRAINED IN 1 HOUR BY EACH PIPE AND THEN ESTIMATR FOR THE COMBINATION IN 1 HOUR AND THEN TAKE RECIPROCAL TO FIND THE HOURS NEEDED TO FILL OR EMPTY THE FULL TANK OR WHATEVER IS NEEDED Mixture_Word_Problems/18599: Need help with this, The inlet pipe of an oil tank can fill the tank in 1 hour, 30 minutes. The outlet pipe can empty the tank in 1 hour. How long does it take to empty the tank if both pipes are open?1 solutions Answer 9051 by venugopalramana(345) on 2005-11-08 02:05:51 (Show Source): The inlet pipe of an oil tank can fill the tank in 1 hour, 30 minutes. The outlet pipe can empty the tank in 1 hour. How long does it take to empty the tank if both pipes are open?inlet pipe fills 1 tank in 1hr 30 mts =1.5=3/2 hrs.or inlet pipe fills ...1/(3/2)=2/3 tank in 1 hr.out let pipe empties 1 tank in 1 hr....so assuming the tank is full at the start water to be emptied =1 tank and in 1 hr inlet fills 2/3 tank and out let empties 1 tank ..so net out flow is 1-2/3=(3-2)/3=1/3 tank in 1 hour.so 1/3 tank emptying needs .....1 hrthen 1 tank emptying needs ......? hrs...= 1*1/(1/3)=3 hrs.
 Rate-of-work-word-problems/22699: Pipe A can fill a tank in 4 hours, and pipe B can fill the tnk in half hte time required pipe C, a drain pipe, to empty the tank. When all three pipes are open, the tank can be filled in 2.4 hours.How much time is required for pipe C to empty the tank?1 solutions Answer 11275 by venugopalramana(3286)   on 2005-12-18 04:38:20 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY.IF YOU HAVE DIFFICULTY ,I SHALL WORK OUT FOR YOU.KEY IS TO FIND HOW MUCH WILL BE FILLED OR DRAINED IN 1 HOUR BY EACH PIPE AND THEN ESTIMATR FOR THE COMBINATION IN 1 HOUR AND THEN TAKE RECIPROCAL TO FIND THE HOURS NEEDED TO FILL OR EMPTY THE FULL TANK OR WHATEVER IS NEEDED Mixture_Word_Problems/18599: Need help with this, The inlet pipe of an oil tank can fill the tank in 1 hour, 30 minutes. The outlet pipe can empty the tank in 1 hour. How long does it take to empty the tank if both pipes are open?1 solutions Answer 9051 by venugopalramana(345) on 2005-11-08 02:05:51 (Show Source): The inlet pipe of an oil tank can fill the tank in 1 hour, 30 minutes. The outlet pipe can empty the tank in 1 hour. How long does it take to empty the tank if both pipes are open?inlet pipe fills 1 tank in 1hr 30 mts =1.5=3/2 hrs.or inlet pipe fills ...1/(3/2)=2/3 tank in 1 hr.out let pipe empties 1 tank in 1 hr....so assuming the tank is full at the start water to be emptied =1 tank and in 1 hr inlet fills 2/3 tank and out let empties 1 tank ..so net out flow is 1-2/3=(3-2)/3=1/3 tank in 1 hour.so 1/3 tank emptying needs .....1 hrthen 1 tank emptying needs ......? hrs...= 1*1/(1/3)=3 hrs.
 Linear-systems/22838: I was doing a test in algebra and I wanted to know how to slove this, it takes 1/2 a gallon of paint to fill 530 square feet of a wall and 3/4 of a gallon to fill up 735 sqaure feet of a wall it also says write an equation to find out how many gallons you need to fill up a certain amount of space in a wall let g be gallons, s for square feet.1 solutions Answer 11239 by venugopalramana(3286)   on 2005-12-17 07:33:00 (Show Source): You can put this solution on YOUR website!I was doing a test in algebra and I wanted to know how to slove this, it takes 1/2 a gallon of paint to fill 530 square feet of a wall and 3/4 of a gallon to fill up 735 sqaure feet of a wall it also says write an equation to find out how many gallons you need to fill up a certain amount of space in a wall let g be gallons, s for square feet. THE DATA IS SUPERFLUOUS AND ERRONEUS.IF IT TAKES 1/2 GALLON TO PAINT 530 SQ.FT.,IT SHOULD MAKE 3/4 GALLON SUFFICIENT TO PAINT 795 SQ.FT.SO LET US TAKE ONLY THE FIRST PART LET THE SPACE TO BE FILLED =S SQ.FT. LET THE PAINT REQD. = G GALLONS BUT 1/2 GALLON CAN PAINT 530 SQ.FT SO 1 GALLON CAN PAINT 530*2=1060 SQ.FT SO G GALLONS CAN PAINT 1060*G SQ.FT = S SQ.FT. WE CALLED SO THE EQN.IS S=1060G ................. CHECK BACK YOUR QUESTION AND WRITE BACK PROPERLY IF THERE IS A MISTAKE FOR US TO UPDATE THE ANSWER.
 Functions/22842: the quotient when 3 more than a number is divided by 3 less than that same number1 solutions Answer 11238 by venugopalramana(3286)   on 2005-12-17 07:21:52 (Show Source): You can put this solution on YOUR website!LET THE NUMBER BE X 3 MORE THAN IT =X+3...THIS IS DIVIDED BY.. 3 LESS THAN THE ORIGINAL NUMBER = X-3...HENCE QUOTIENT IS (X+3)/(X-3)
 Equations/22847: x^2-16 x^2-6x+8 these are two different Questions x^2-10x+25 x-51 solutions Answer 11237 by venugopalramana(3286)   on 2005-12-17 07:18:33 (Show Source): You can put this solution on YOUR website!WHAT DO YOU WANT FACTORISATION?PLEAE WRITE QUESTION CORRECTLY x^2-16 =(X)^2-(4)^2=(X+4)(X-4)...USING FORMULA A^2-B^2=(A+B)(A-B) x^2-6x+8 =X^2-4X-2X+8=X(X-4)-2(X-4)=(X-4)(X-2) these are two different Questions x^2-10x+25=X^2-2*X*5+5^2=(X-5)^2...USING FORMULA A^2-2*A*B+B^2=(A-B)^2 x-5=X-5 ONLY ...IF YOU WANT DIVISION THEN x^2-10x+25.....X^2-2*X*5+5^2...............(X-5)^2......X-5 --------- = -------------...............=--------- = ---- IS THE ANSWER x-5.................X-5......................X-5..........1
 Rate-of-work-word-problems/22848: It takes Billy 2 hours longer than Reena to do a certain job. They worked together for 2 hours; then Reena left and Billy finished the job in 1 hour. How long would it take each of them to do the job alone ? (this is from Intermediate Algebra, 7th ed. Jerome Kaufmann/Karen Schwitters, pg 330, problem 42, Quadratic Equations and Inequalities...only one I couldn't get)1 solutions Answer 11236 by venugopalramana(3286)   on 2005-12-17 07:07:33 (Show Source): You can put this solution on YOUR website!LET TIME TAKEN BY REENA ALONE TO DO 1 JOB =X HRS BILLY ALONE TAKES 2 HRS. MORE =X+2 SO REENA CAN DO ALONE IN 1 HOUR =1/X JOB BILLY CAN DO ALONE IN 1 HOUR =1/(X+2) JOB TOGETHER THEY CAN DO IN 1 HR.=(1/X)+(1/(X+2)) JOB IN 2 HRS TOGETHER THEY CAN DO =2*{(1/X)+(1/(X+2))} JOB NOW REENA LEFT AND BILL ONLY WORKED FOR 1 HOUR = BILLY ALONE DOES 1/(X+2) JOB IN 1 HOUR SO TOTAL JOB DONE =2*{(1/X)+(1/(X+2))}+(1/(X+2)) JOB..BUT THIS COMPLETED THE 1 JOB .SO 2*{(1/X)+(1/(X+2))}+(1/(X+2)) =1 2/(X)+2/(X+2)+1/(X+2)=1..L.C.M IS (X)(X+2) {2(X+2)+2(X)+1(X)}/(X)(X+2)=1 MULTIPLYING BY LCM (X)(X+2) BOTH SIDES WE GET 2X+4+2X+X=(X)(X+2)=X^2+2X 5X+4=X^2+2X X^2+2X-5X-4=0 X^2-3X-4=0 X^2-4X+X-4=0 X(X-4)+(X-4)=0 (X+1)(X-4)=0 X-4=0 X=4 SO REENA CAN DO THE JOB IN 4 HRS AND BILL CAN DO IN X+2=4+2=6 HRS THE JOB.
 logarithm/22742: What is the value of X in the equation log(3x+10) = logX^2 I appreciate all your help!!1 solutions Answer 11185 by venugopalramana(3286)   on 2005-12-15 23:21:47 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING PROBLEM WHICH IS SIMILAR TO YOURS AND SOLVE YOUR PROBLEM.IN CASE OF DIFFICULTY COME BACK log(x+1) + log(x-5) = 4 USING THE FORMULA LOG A TO BASE X = LOG A/LOG X TO A COMMON BASE OR STANDARD BASE.HENCE WE HAVE {LOG (X+1)/LOG 2} + {LOG (X-5)/LOG 2}=4 LOG(X+1)+LOG(X-5)=4*LOG 2=LOG 2^4=LOG 16 (SINCE LOG X^N=N*LOG X) LOG(X+1)(X-5)=LOG 16 (SINCE LOG X + LOG Y =LOG(X*Y)) TAKING ANTILOGS (X+1)(X-5)=16 X^2-5X+X-5=16 X^2-4X-5-16=0 X^2-7X+3X-21=0 X(X-7)+3(X-7)=0 (X-7)(X+3)=0 HENCE X=7 OR X=-3 AS X=-3 LEADS TO LOG OF NEGATIVE NUMBERS WHICH DO NOT EXIT , THE ANSWER IS X=7
 logarithm/22743: What is the value of X in the equation: log(x+1) + log(x-5) = 4 THANK YOU VERY MUCH!!!!!1 solutions Answer 11184 by venugopalramana(3286)   on 2005-12-15 23:18:18 (Show Source): You can put this solution on YOUR website!log(x+1) + log(x-5) = 4 USING THE FORMULA LOG A TO BASE X = LOG A/LOG X TO A COMMON BASE OR STANDARD BASE.HENCE WE HAVE {LOG (X+1)/LOG 2} + {LOG (X-5)/LOG 2}=4 LOG(X+1)+LOG(X-5)=4*LOG 2=LOG 2^4=LOG 16 (SINCE LOG X^N=N*LOG X) LOG(X+1)(X-5)=LOG 16 (SINCE LOG X + LOG Y =LOG(X*Y)) TAKING ANTILOGS (X+1)(X-5)=16 X^2-5X+X-5=16 X^2-4X-5-16=0 X^2-7X+3X-21=0 X(X-7)+3(X-7)=0 (X-7)(X+3)=0 HENCE X=7 OR X=-3 AS X=-3 LEADS TO LOG OF NEGATIVE NUMBERS WHICH DO NOT EXIT , THE ANSWER IS X=7
 Linear-systems/22717: Somebody please explain to me if the perimeter of a rectangle is 30 inches, how do you write an equation for the perimeter in standard form.and then graph it. Thanx!!1 solutions Answer 11121 by venugopalramana(3286)   on 2005-12-15 11:52:00 (Show Source): You can put this solution on YOUR website!PERIMETER =2(L+B)=30 L+B=30/2=15 L=-B+15 GIVE DIFFERENT VALUES TO B ,FIND CORRESPONDING VALUES OF L FROM THE ABOVE FORMULA,TABULATE AS BELOW AND PLOT THEM TO GET THE GRAPH AS SHOWN BELOW B....1....4.....8....12..... L....14...11....7.....3....
 logarithm/22276: Simplify the following expression. Your answer should not contain logarithms. 25^log5(x) (that's log base 5 then x)1 solutions Answer 10801 by venugopalramana(3286)   on 2005-12-11 11:09:34 (Show Source): You can put this solution on YOUR website!LET Y=25^(LOG X TO BASE 5) USE FORMULA LOG X TO BASE 5 = LOG X/LOG 5 TO COMMON BASE Y=25^(LOG X/LOG 5) TAKING LOGS BOTH SIDES LOG Y ={(LOG X)/(LOG 5)}*LOG 25 =LOG X*LOG 5^2/LOG 5=LOG X*(2*LOG 5)/LOG 5(SINCE LOG X^N=N*LOG X) =2LOG X=LOG X^2 HENCE LOG Y = LOG X^2 TAKING ANTILOGS Y=X^2 HENCE Y=25^(LOG X TO BASE 5)=X^2
 Complex_Numbers/22161: 3. Sometimes, we can take a weighted approach to calculating the mean. Take our example of high temperatures in July. Suppose it was 98°F on 7 days, 96°F on 14 days, 88°F on 1 day, 100°F on 6 days and 102°F on 3 days. Rather than adding up 31 numbers, we can find the mean by doing the following: Mean = ( 1 x 88 + 14 x 96 + 7 x 98 + 6 x 100 + 3 x 102) / 31 …where 1, 14, 7, 6, and 3 are the weights or frequency of a particular temperature’s occurrence. Then we divide by the total of number of occurrences. Suppose we are tracking the number of home runs hit by the Boston Red Sox during the month of August: Number of Games HRs Hit each Day 2 3 5 2 6 1 7 0 Using the weighted approach, calculate the average number of home runs per game hit by the Sox. 1 solutions Answer 10709 by venugopalramana(3286)   on 2005-12-09 10:59:56 (Show Source): You can put this solution on YOUR website!2 3 5 2 6 1 7 0 WHY DOUBT FOLLOW SAME PROCEDURE (2*3+5*2+6*1+7*0)/(2+5+6+7)=19/20
 Complex_Numbers/22163: 4. When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over. Why will some numbers come up more frequently than others? Each die has six sides numbered from 1 to 6. How many possible ways can a number be rolled? In other words, we can roll (2,3) or (3,2) or (6,1) and so on. What are the total (x,y) outcomes that can occur? How might you then estimate the percentage of the time a particular number will come up if the dice are rolled over and over? Once these percentages have been calculated, how might the mean value of the all the numbers thrown be determined? 1 solutions Answer 10708 by venugopalramana(3286)   on 2005-12-09 10:55:27 (Show Source): You can put this solution on YOUR website!SEE MY COMMENTS IN CAPITAL LETTERS --------------------------------------------------- 4. When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6)....OK It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over. ....YA Why will some numbers come up more frequently than others? BECAUSE OF 2 DICE AND TOTAL OF TWO NUMBERS SHOWING UP ON 2 DICE BEING TAKEN.SEE THE TABLE BELOW.IT WONT HAPPEN WITH 1 DICE THROW.ALL NUMBERS FROM 1 TO 6 IN THAT CASE ARE EQUALLY LIKELY. DICE 1 DICE 2 TOTAL DICE 1 DICE 2 TOTAL total FREQ. % 1 1 2 4 1 5 1 0 2.8 1 2 3 4 2 6 2 1 5.6 1 3 4 4 3 7 3 2 8.3 1 4 5 4 4 8 4 3 11.1 1 5 6 4 5 9 5 4 13.9 1 6 7 4 6 10 6 5 16.7 2 1 3 5 1 6 7 6 19.4 2 2 4 5 2 7 8 5 22.2 2 3 5 5 3 8 9 4 25.0 2 4 6 5 4 9 10 3 27.8 2 5 7 5 5 10 11 2 30.6 2 6 8 5 6 11 12 1 33.3 3 1 4 6 1 7 3 2 5 6 2 8 3 3 6 6 3 9 3 4 7 6 4 10 3 5 8 6 5 11 3 6 9 6 6 12 Each die has six sides numbered from 1 to 6. How many possible ways can a number be rolled? In other words, we can roll (2,3) or (3,2) or (6,1) and so on. What are the total (x,y) outcomes that can occur? SEE TABLE ABOVE How might you then estimate the percentage of the time a particular number will come up if the dice are rolled over and over? SEE TABLE ABOVE FOR PERCENT Once these percentages have been calculated, how might the mean value of the all the numbers thrown be determined? BY TAKING WEIGHTED AVERAGE OF THE VALUE MULTIPLIED BY FREQUENCY..THAT IS (1*0+2*1+3*2+4*3+5*4+6*5+7*6+8*5+9*4+10*3+11*2+12*1)/36=7
 Sequences-and-series/22134: form a sequence that has two arithmetic means between -2 and 58. 1 solutions Answer 10702 by venugopalramana(3286)   on 2005-12-09 07:20:38 (Show Source): You can put this solution on YOUR website!LET THE 2 A.M.S BE X,Y...HENCE -2,X,Y,58 ARE IN A.P.WE FIND THAT 58 IS THE FOURTH TERM OR N=4 , A=-2 AND D=?...USING TN=A+(N-1)D,WE GET.... T4=A+(4-1)D 58=-2+3D 3D=58+2=60 D=20 SO X=-2+1D=-2+20=18 Y=-2+2D=-2+2*20=38 SO THE 2 A.MS ARE 18 AND 38
 Complex_Numbers/22150: factor the polynomial: 1 solutions Answer 10700 by venugopalramana(3286)   on 2005-12-09 07:13:40 (Show Source): You can put this solution on YOUR website!216x^3+1...use the formula a^3+b^3=(a+b)(a^2-ab+b^2) 216x^3+1=(6x)^3+1^3=(6x+1){(6x)^2-(6x)*1+1^2} =(6x+1)(36x^2-6x+1)