You can.You are given that that first (the faster) pump works as effectively as three slower pumps.Therefore, you may think that 4 = 3+1 slower pumps, actually, work, and these 4 pumps fill the tank in 12 minutes.Hence, one single slower pump can fill the tank in 4.12 = 48 minutes, working alone.Next, since the faster pump is 3 times as fast, it needs only 48/3 = 16 minutes to fill the tank, working alone.Solved.-It is a standard and typical joint work problem.There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons-Read them and get be trained in solving joint-work problems.Also, you have this free of charge online textbook in ALGEBRA-I in this site-.The referred lessons are the part of this textbook under the topic' Rate of work and joint work problems' of the section ' Word problems'.Save the link to this online textbook together with its descriptionFree of charge online textbook in ALGEBRA-Iyour archive and use it when it is needed.Answer by. You canSince the faster pump works 3 times as fast as the slower, in filling the tank the faster pump does 3/4 of the work and the slower pump does 1/4.The faster pump fills 3/4 of the tank in 12 minutes; the time it would take that pump alone to fill the tank is 12.(4/3) = 16 minutes.The slower pump fills 1/4 of the tank in 12 minutes; the time it would take that pump alone to fill the tank is 12.4 = 48 minutes.ANSWERS:Faster pump alone: 16 minutesSlower pump alone: 48 minutesAnswer by. You canThis problem may seem puzzling at first since the actual rate of filling, and the actual capacity of the tank are not given. However it can be solved as follows.Let vol of tank be X litresLet rate of P1 be y litres/minThen rate of P2 is litres/minIf they work together, rate is litres /minand it takes 12 min.So capacity of tank = litresSo if P1 alone is used, time taken=If P2 alone is used, time taken=Solved.: HiA plane took off 1 hour later for its destination 3000km away. In order to reach the destination on time the pilot increased speed by 500km per hour.What is the new speed of the plane.ThanksAnswer by. You can.Let x be the new speed, in km/h.Then the regular speed is (x-500) km/h.The regular flight time is hours.The new time flight is hours.The difference is one hour (1 hour), which gives you THIS 'time equation'- = 1 hour.To solve the equation, multiply both sides by x.(x-500).
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You will get3000x - 3000.(x-500) = x.(x-500)300.500 = x.(x-500)x^2 - 500x - 1500000 = 0= = =.Only positive root makes sense x = = 1500.ANSWER. The new speed is 1500 km/h.CHECK. The regular speed is then 500 km/h lover, i.e. 1000 km/h.Check the 'time equation' - = 3 - 2 = 1 hour.!
Precisely correct!Solved.: She is going to buy a scarf for $12.50 and some nail polish for $3. At the register she finds out that the scarf is 5% off. The store charges her a 9% tax.The sale price for the scarf is $. (do not round)The subtotal (scarf and nail polish before tax) is $. (do not round)The total (including tax) is $. (round to the nearest hundredth)Answer by. You canBefore going to the register:Scarf price = $12.50Nail polish price = $3At the register:Since the scarf price is 5% off so the selling price of the scarf is:= $= $= $= $ 11.875Hence:Selling price of scarf is $11.875The subtotal (scarf and nail polish before tax ) is $(11.875+3) or $14.875Now:If 9% tax is applied on the subtotal then the total price including tax will be:= $= $= $ 16.21375Hence:The subtotal after applying tax is approximately $16.21: Cynthia Besch wants to buy a rug for a room that is 22 ft wide and 32 ft long.
She wants to leave a uniform strip of floor around the rug. She can afford to buy 264 square feet of carpeting.
What dimensions should the rug have?Answer by. You canu, the size of uniform strip around the carpetand the dimensions are 18-2u and 27-2u.Note that you may want to look for the two factors of 322 which differ by 9.Dimensions for the rug:14 feet and 23 feet-23 and 14?Otherwise, the two factors of 322 and differ by 9.: Graph the function f(x)=x^3-2x^2+x by finding its zeros. Use the graph to estimate where the instantaneous rate of change is positive, negative, and zero.ThanksFound 2 solutions by greenestamps, josgarithmetic:Answer by. You canNote the factorization and the graph shown in the response from the other tutor are fine; but they have listed the roots incorrectly.There is a single root at x=0 and a double root at x=1; the graph shows that clearly.For finding where the instantaneous rate of change is positive, negative, or zero, we can first tell that the rate is 0 at exactly x=1 because of the double root.
And the graph shows that the rate of change is positive for x 1 and negative just to the left of x=1.The graph clearly shows that the rate of change is also zero somewhere between 0 and 1. Since the instructions are to estimate, it looks like the rate is 0 at about x = 1/3. (And calculus would tell us that is exactly right.)And the rate of change is clearly positive to the left of that point, and negative between that point and x=1.Answer by.
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You canA very different way of solving the problem, which I find much easier and faster.Since one of the bulldozers works twice as fast as the other, when working together one bulldozer does 2/3 of the work and the other does 1/3.So the slower bulldozer does 1/3 of the job in 3 days, which means it will take it 9 days to do the job alone.And the faster bulldozer works twice as fast, so it will take it half as long as the other to do the job alone - 4.5 days.ANSWERS:4.5 days alone for the faster bulldozer9 days alone for the slowerAnswer by. You canCall the clearing of 20 acres 1 jobLet = time in days for the faster worker todo the job working alone= time in days for the slower worker to dothe job working alone- 1 job / 3 days = their rate of woking togetherAdd their rates working alone to get their rate working togetherMultiply both sides byand-The faster worker takes 4.5 days working aloneThe slower worker takes 9 days working alone-check:Multiply both sides byOK: An inlet pipe on a swimming pool can be used to fill a pool in 36 hours. The drain pipe can be used to empty the pool in 40 hours. If the pool is 2/3 filled using the inlet pipe and then the drain pipe is accidentally opened, how long from that time will it take to fill the pool?Answer by. You canFind the value of x for which the tangent line to will be parallel to the tangent line to?Is @Alan3354 blind? Can't he see that @ MATHLOVER has plagiarized someone else's work (see MiscellaneousWordProblems/1153638/Answers 775890 and 775891).I wish I had the authority to jail people who STEAL other people's work and present it as their own. I would give them MAXIMUM IMPRISONMENTand ISOLATE them from others.A word to the person who CLAIMS to love math:What do you gain by PLAGIARIZING someone's work?
If you want to use someone's else's work, DON'T present it as your own. Let the reader know thatyou're using someone else's work by CITING the AUTHOR of the work you're copying and presenting. Did you even notice that when you PLAGIARIZEDthis particular person's work, you also presented his ERROR also.You need to STOP!! This is not the 1st time I've seen you do it!
STOP!!!I understand, @ALAN. Ha, ha, ha, ha!Answer by. You can.Let x be the rate of the slower train, in miles per hour.Then the rate of the faster train is (x+15) mph, according to the condition.The full distance equation is8x + 8.(x+15) = 1000.Simplify and solve for x8x + 8x + 120 = 100016x = 1000 - 12016x = 880x = = 55.ANSWER. The slower train rate is 55 mph. The faster train rate is 55+15 = 70 mph.Solved.-See introductory lessons on Travel and Distance problems-in this site.They are written specially for you.You will find the solutions of many similar problems there.Read them and learn once and for all from these lessons on how to solve simple Travel and Distance problems.Become an expert in this area.: work out the fraction halfway between 1/2 and 1 1/4Answer by. You canHiA person has 1500 dollars to buy a computer. The end of year sale gives an 15 percent discount followed by a 3 percent discount if the person pays cash.What is the maximum value the person can pay if he pays by cash.ThanksIf you're asking for the MAXIMUM price of the computer before the discounts are factored in, then it's.However, this amount is based on a 1st discount of 15%, followed by a further 3% discount on the 15% discounted price.If it's a TOTAL DISCOUNT of 18% (15% + 3%), based on a cash payment, then that MAXIMUM price, before the 18% discount is:.Answer by.
You can-A person has 1500 dollars to buy a computer. The end of year sale gives an 15 percent discount followed by a 3 percent discount if the person pays cash.What is the maximum value the person can pay if he pays by cash.-What is the MAXIMUM amount he pays?If he purchases the computer before the sale and also does not have either of the other two discounts then the maximum he pays is 1500 dollars (plus tax).: HiThis is exactly as it appears in the textbook. Josie needs a new computer and has saved $1500.00. She decided to wait for the end of year sale where she was promised a 15 percent discount and a further 3 percent off if she paid cash.What is the maximum value to the dollar of a full priced computer she can afford if she pays cash.What is the difference between the full price computer she can afford with cash and of a computer she paid by card.ThanksFound 3 solutions by greenestamps, ikleyn, josgarithmetic:Answer by. You can.Let x be the maximum value of the full priced computer she can afford if she pays cash(i.e. Exactly the unknown value under the question).Then the equation for x, from the given condition, is0.97.(0.85x) = 1500 dollars, (1)where 0.85 = 1-0.15 and 0.97 = 1-0.03.From equation (1)x = = 1819.28 dollars. ANSWER to Q1The answer to the second question isdifference = 1819.28 - = 1819.28 - 1764.71 = 54.57 dollars.
You canlog(x) + log(x+3) = 9Using log(a)+log(b) = log(ab)log(x(x+3)) = 9Raise 10 to both sidesx(x+3) =Expand and simplify:Use quadratic formula:Discard negative solution (approx)Check:log(31621.28) + log(3+31621.28) = 4.49998 + 4.50002 = 9 (ok, to within 5 decimal places)EDIT: Added leading 1/2 which was omitted from typing only, not from the calculations: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+217t+185.Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?The rocket splashes down after seconds.How high above sea-level does the rocket get at its peak?The rocket peaks at meters above sea-level.Found 2 solutions by ikleyn, MathLover1:Answer by. You can.In my post, I only want to explain to the visitor, that the given equation DOES NOT describe the flight of a real rocket.It describe the flight of a PROJECTILE, i.e.
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An object launched with the initial velocity of 217 m/s,but then falling freely under the Earth's gravitation force.The drag force, which provides vertical acceleration of a real rocket, ABSENTS in the given equation (!)So, it is not a real rocket (!) (!)Such object has a common name 'a projectile' in Physics.Answer by. You canNASA launches a rocket at seconds. You canIf the interest is compounded continuously for years at a rate of per year, then the compounded amount is given by:given:$% =yearsanswer: $=: A bacteria culture starts with 560 bacteria and grows at a rate proportional to its size. After 2 hours there will be 1120 bacteria.(a) Express the population P after t hours as a function of t.P(t)=(b) What will be the population after 8 hours? bacteria(c) How long will it take for the population to reach 2490? Give your answer accurate to at least 2 decimal places.
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hoursAnswer by. You canLet x = number of grams of soybean mealLet y = number of grams of meat byproductsLet z = number of grams of grainWe are to minimize:subject to the constraints:We use the simplex method.We form the initial matrixSince this is a minimizing problem, we form the dualmaximizing problem. We form the transpose of theabove matrix:The dual maximizing problem:Maximize:subject to the constraints:We form the initial tableau:The most negative number on the bottom row is -66.It is in column 2, so we call column 2 'the pivot column'.We divide each positive number above the pivot element INTO the numberat the right to see which gives the smallest positive answer.1.4 3 1.15)7.0 3)9 10)11.0We get the smallest value when we divide 10 into the number at the farright, so 10 is the pivot element.Now we make the pivot element become 1, by dividing the pivot rowthrough by 10. Then we make 0's elsewhere in the pivot column, usingthe pivot row. Making an element of a column become 1 and all the otherelements in the column become 0 is called 'pivoting' on the elementthat we caused to become 1.Now the only negative number on the bottom row is -27.
It is incolumn 1, so now column 1 is the pivot column. We divide eachpositive number above the pivot element INTO the numberat the right to see which gives the smallest positive answer.1.9 2.23)5.7 0.5)1.1We get the smallest value when we divide 3 into the number at the farright, so 3 is the pivot element.Now we make the pivot element become 1, by dividing the pivot rowthrough by 3.
Then we use it to make 0's elsewhere in the pivot column,using the pivot row.There are no more negative numbers on the bottom row, sowe have reached the final tableau:So the minimum cost is 123.9, or $123.90 and this occurs whenx 1 = 0, the number at the bottom of the s 1 column. X 2 = 9,the number at the bottom of the s 2 column. X 3 = 3.9the number at the bottom of the s 3 column.Note this is the same answer that Ikleyn got using a different technique.EdwinAnswer by. You can.Let X = the mass of soybean meal consumed (in grams);Y = the mass of meat;Z = the mass of grain.The objective function to minimize is the costC(X,Y,Z) = 7.X + 9.Y + 11.Z cents. (1)The constraints are2.5.X + 4.5.Y + 5.Z = 60 units of vitamins, (2)5.X + 3.Y + 10.Z = 66 calories. (3)Other constraints are X = 0; Y= 0, and Z = 0.
(4)Now, a remarkable fact is that the solution to this 3D minimax problem can be obtained ANALYTICALLY.Constraints (2) and (3) represent two planes in 3D:2.5.X + 4.5.Y + 5.Z = 60 (5)5.X + 3.Y + 10.Z = 66 (6)These planes are not parallel - hence, their intersection is a straight line.The idea is to present this straight line in a parametric form - then the solution of the minimax problemon this straight line will be easy.Multiply equation (5) by 2 (both sides) and then subtract equation (6) from the obtained equation.You will get3Y - 9Y = 66 - 2.60, or -6Y = -54.Hence,Y = 9. (7)Thus we found that the intersection of two planes (5) and (6) is a straight line, which lies on the plane Y = 9.Subctitute Y =9 into equations (5) and (6). You will get then2.5.X + 4.5.9 + 5Z = 60 (5')5.X + 3.9 + 10Z = 66, (6')or, collecting all constant terms on the right side2.5.X + 5Z = 19.5, (5')5.X + 10.Z = 39, (6')Equations (5') and (6') are DEPENDENT (which is OBVIOUS).Hence, two equations (5') and (6') represent THE SAME plane.So, our straight line is the intersection of planes (7) and (6').Now, from equation (6'),X = 7.8 - 2Z.Thus our stright line in parametric form isX = 7.8 - 2Z, Y = 9. (8)Substitute (8) into the objective function (1). You will getC(X,Y,Z) = 7.X + 9.Y + 11.Z = 7.(7.8 - 2Z) + 9.9 + 11.Z = 54.6 - 14Z + 81 + 11Z = -3Z + 135.6. (9)Thus, on our line the objective function is presented as the linear function (9) of Z.We see that when Z increases from 0 to positive values, the function (9) decreases.But Z can increase only till X = 7.8 - 2Z is = 0 (is non-negative).Hence, the linear function (9) has the minimum at Z = 7.8/2 = 3.9.Then X = 7.8 - 2.3.9 = 0, according to (8).Thus we just obtained the solution to our minimax problem:The minimum solution point is X= 0; Y= 9 and Z= 3.9and the mimimum cost is -3.Z + 135.6 = -3.3.9 + 135.6 = 123.9.ANSWER. The minimum cost is 123.90 cents (or, after rounding, $1.24) and it is achieved at this diet:0 gram of soybean meal; 9 gram of meat, and 3.9 gram of grain.Solved.: Jason has 4 pairs of socks.
They are colored brown, black, white, and blue. Ifhe picks two socks out of his drawer at a time, what are all of the combinationshe may have?Answer by. You canJason has 4 pairs of socks. They are colored brown, black, white, and blue. Ifhe picks two socks out of his drawer at a time, what are all of the combinationshe may have?Case 1.
The socks match.There are 4 matching pairs-Case 2. The socks don't match.4 colors CHOOSE 2 = 4C2 = 6-Total for both cases:4 + 6 = 10 combinations.Edwin: A patient takes vitamin pills. Each day he must have at least 150 IU of vitamin A, 3 mg of vitamin Upper B 1, and 30 mg of vitamin C.
He can choose between pill 1, which contains 90 IU of vitamin A, 1 mg of vitamin Upper B 1, and 5 mg of vitamin C, and pill 2, which contains 30 IU of vitamin A, 1 mg of vitamin Upper B 1, and 20 mg of vitamin C. Pill 1 costs 25cents, and pill 2 costs 75cents. How many of Pill 1 and pill 2 should he buy? What is the minimum cost?Answer by. You can.The need vitamin A Vitamin B1 Vitamin C150 IU 3 mg 30 mgPill 1 90 IU 1 mg 5 mgPill 2 30 IU 1 mg 20 mgThere are not so many configurations n.Pill1 + m.Pill2, so we can easily analyse all potential variants.Cost, in cents1.Pill1+2.Pill2 150 IU 3 mg 45 mg 1756.Pill1+0.Pill2 540 IU 6 mg 30 mg 1500.Pill1+5.Pill2 150IU 5 mg 100 mg 375All other variants EITHER do not provide the required parameters OR are farther from the goal, regarding the price, obviously.So, there are only these 3 variants, of them variant 6 Pills 1 + 0 Pills 2 is the most cheaper.ANSWER.
Version (6 Pills 1 + 0 Pills 2) provides the required parameters and is the most cheap. It costs $1.50.Solved.: The number of visitors to a website in the first week is 40. The number of visitors each week is double the number of visitors the previous week.
What is the total number of visitors to the website in the first 10 weeks? Show all your work!!!Answer by. You canRefer to the diagram below.We start at a height of 120 feet.
Then the ball is dropped to bounce back up again to a peak height of 60 feet (half that of 120). The diagram shows this with the use of arrows. Blue arrows point down while red point up. I've also marked in a lighter blue color each time there is a bounce point.
This process keeps going until we reach the green point in the diagram, which is after the 4th bounce. The height of this green point is 7.5 feet.We then add up the lengths of each arrow in the diagram120 + 60+60 + 30+30 + 15+15 + 7.5 = 337.5Answer: 337.5 feet-Alternative MethodRefer to the diagram above. The sequence of blue arrow lengths120, 60, 30, 15is a geometric sequence with a = 120 as the first term and r = 0.5 as the common ratioCompute the partial sum S4Sn = a.(1-r^n)/(1-r)S4 = 120.(1-0.5^4)/(1-0.5)S4 = 225The blue arrows have their lengths add to 225 feet.As confirmation: 120+60+30+15 = 225Do the same for the sequence: 60, 30, 15, 7.5This is the lengths of the red arrowsThis time, a = 60 is the first term.
The common ratio stays the same.Sn = a.(1-r^n)/(1-r)S4 = 60.(1-0.5^4)/(1-0.5)S4 = 112.5The red arrows have their lengths add to 112.5 feet.As confirmation: 60+30+15+7.5 = 112.5Now add the two subtotals225+112.5 = 337.5We get the same answer of 337.5 feet: Find the dimensions of a rectangular Persian rug whose perimeter is 24 ft and whose area is 35f. t ^ 2Answer by.
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