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 Quadratic_Equations/322751: A rectangular field is to be enclosed by a fence and then divded into two small plots by a fence parallel to one of the sides. If thre is 1800 m of fencing available, find the dimensions of the field that will give the maximum area.1 solutions Answer 231104 by ankor@dixie-net.com(15660)   on 2010-07-15 19:46:08 (Show Source): You can put this solution on YOUR website!A rectangular field is to be enclosed by a fence and Ithen divided into two small plots by a fence parallel to one of the sides. If there is 1800 m of fencing available, find the dimensions of the field that will give the maximum area. : 2L + 3W = 1800 2L = 1800-3W Divide both sides by 2 L = (900-1.5W) : Area = L * W Replace L with (900-1.5W) A = W(900-1.5W) A = -1.5W^2 + 900W Find the axis of symmetry, x=-b/(2a); in this equation: a=-1.5, b=900 W = W = W = +300 m is the width for max area then L = 900 - 1.5(300) L = 450 m is the length and 300 * 450 = 135,000 sq/m is max area
 Miscellaneous_Word_Problems/322806: Find a number which is decreased by 54 and is 5 times its opposite?1 solutions Answer 231094 by ankor@dixie-net.com(15660)   on 2010-07-15 19:06:58 (Show Source): You can put this solution on YOUR website!Find a number which is decreased by 54 and is 5 times its opposite? : Let x = "a number then -x = it's opposite : x - 54 = 5(-x) x - 54 = -5x x + 5x = +54 6x = 54 x = x = 9 ; ; Check solution in original statement 9 - 54 = 5(-9) -45 = -45
 Linear_Equations_And_Systems_Word_Problems/322644: 1n 2005,a father was 4 times as old as his son.in the year 2015,thrice the son's age will exceed the father's age by ten years,in which year was the son born?1 solutions Answer 231093 by ankor@dixie-net.com(15660)   on 2010-07-15 18:59:24 (Show Source): You can put this solution on YOUR website!1n 2005, a father was 4 times as old as his son. In the year 2015,thrice the son's age will exceed the father's age by ten years, in which year was the son born? : In 2005, let; f = father's age, s = son's age: f = 4s : In 2015: f + 10 = 3(s+10) - 10 f + 10 = 3s + 30 - 10 f + 10 = 3s + 20 f = 3s + 20 - 10 f = 3s + 10 Replace f with 4s, find s: 4s = 3s + 10 4s - 3s = 10 s = 10 yrs old in 2005 Son was born in 1995 : : Check solution, fathers age in 2005, 4(10) = 40 In 10 yrs 40 + 10 = 3(10+10) - 10 50 = 3(20) - 10
 Linear-systems/322627: why is it that in diff places you do not reciprocate the values that you need to eliminate?for example 1x+2y=3 2x+1y=3 then if youre trying to eliminate y or get it it becomes 1(1x+2y=3) 2(2x+1y=3)then becomes x+2=3 4x+2y=61 solutions Answer 231077 by ankor@dixie-net.com(15660)   on 2010-07-15 17:52:47 (Show Source): You can put this solution on YOUR website!why is it that in diff places you do not reciprocate the values that you need to eliminate?for example 1x+2y=3 2x+1y=3 then if youre trying to eliminate y or get it it becomes 1(1x+2y=3) 2(2x+1y=3)then becomes x+2=3 4x+2y=6 : I am not sure what you are trying to say here, but if you want to solve the following by eliminating y: : 1x + 2y = 3 2x + 1y = 3 Multiply the 2nd equation by 2 and you have 1x + 2y = 3 4x + 2y = 6 -------------subtracting eliminates y, find x -3x = -3 x = x = +1 : Find y using the 1st equation 1 + 2y = 3 2y = 3 - 1 2y = 2 y = y = +1 : Check solution in the 2nd original equation 2(1) + 1 = 3
 Problems-with-consecutive-odd-even-integers/322593: The product of four different positive integers is 360. what is the maximum possible sum of these four integers ?1 solutions Answer 231061 by ankor@dixie-net.com(15660)   on 2010-07-15 17:06:14 (Show Source): You can put this solution on YOUR website!The product of four different positive integers is 360. what is the maximum possible sum of these four integers ? : Find the 4th root of 360 = 4.35....... integers above and below this value 3 * 4 * 5 * 6 = 360 : 3 + 4 + 5 + 6 = 18 is max
 Quadratic_Equations/322752: Ethan cuts half a rectangular lawn 40 m by 30 m by mowing a strip of equal width around the perimeter. Julia cuts the small rectangle left. How wide a strip does Ethan cut so that they share the work equally?1 solutions Answer 231059 by ankor@dixie-net.com(15660)   on 2010-07-15 16:56:23 (Show Source): You can put this solution on YOUR website!Ethan cuts half a rectangular lawn 40 m by 30 m by mowing a strip of equal width around the perimeter. Julia cuts the small rectangle left. How wide a strip does Ethan cut so that they share the work equally? : Let x = the width of the strip cut by E : Find the total area of the lawn; 40 * 30 = 1200 sq/m Each will mow an area of 600 sq/m : Dimension of the small rectangle which is 600 sq/ft: (40-2x) by (30-2x) ; Write an area equation of this rectangle. find x, which is the width of the strip (40-2x)(30-2x) = 600 FOIL 1200 - 80x - 60x + 4x^2 = 600 Arrange as a quadratic equation 4x^2 - 140x + 1200 - 600 = 0 4x^2 - 140x + 600 = 0 Simplify divide by 4 x^2 - 35x + 150 0 = Factor (x - 5)(x - 30) = 0 The reasonable solution x = 5 ft is the width of the strip : : Check solution by finding the area of the inside rectangle (40-10)*(30-10) = 600
 Geometry_Word_Problems/321933: triangle has a perimeter of 36 centimeters. If the length of each side is increased by 50%1 solutions Answer 230655 by ankor@dixie-net.com(15660)   on 2010-07-13 19:25:47 (Show Source): You can put this solution on YOUR website!triangle has a perimeter of 36 centimeters. If the length of each side is increased by 50% : Assume it is an equilateral triangle, each side 36/3 = 12 Increase each side by 50%, 18 cm, new perimeter, 3*18 = 54 cm
 Miscellaneous_Word_Problems/321711: Phone was thrown from top of a building. The height h(t) of the cell phone at time (t) is described by the function h(t) = -16tsquared +96t+112. When will the phone be at a height of 192 feet and how many seconds will it take to hit the ground? I have tried putting the numbers in and just cannot figure this out. Can you help please? Thanks1 solutions Answer 230425 by ankor@dixie-net.com(15660)   on 2010-07-12 19:54:32 (Show Source): You can put this solution on YOUR website!Phone was thrown from top of a building. The height h(t) of the cell phone at time (t) is described by the function h(t) = -16tsquared +96t+112. When will the phone be at a height of 192 feet and how many seconds will it take to hit the ground? : -16t^2 + 96t + 112 = h(t) The phone will be at 192 ft when h(t) = 192 -16t^2 + 96t + 112 = 192 Subtract 192 from both sides -16t^2 + 96t + 112 - 192 -16t^2 + 96t - 80 = 0; a quadratic equation Simplify, and change the signs, divide each term by -16 t^2 - 6t + 5 = 0 Factors to (t - 5)(t + 1) = 0 The positive solution t = 5 sec , tel at 192 ft : Phone will hit the ground when h(t) = 0 -16t^2 + 96t + 112 = 0 Simplify again, divide by -16 t^2 - 6t - 7 = 0 Factors to (t - 7)(t + 1) = 0 positive solution t = 7 sec, phone strikes the ground
 Linear_Equations_And_Systems_Word_Problems/321836: Bob received \$14,000 inheritance and divided it between a mutual fund that yielded a yearly return of 5% and a 1-year CD that paid 3.5% annually. If his total earnings for the year on this investment was \$640, how much did he invest in each of these two funds?1 solutions Answer 230414 by ankor@dixie-net.com(15660)   on 2010-07-12 19:03:23 (Show Source): You can put this solution on YOUR website!Bob received \$14,000 inheritance and divided it between a mutual fund that yielded a yearly return of 5% and a 1-year CD that paid 3.5% annually. If his total earnings for the year on this investment was \$640, how much did he invest in each of these two funds? : Let x = amt invested at 5% The total was given as 14000, therefore (14000-x) = amt invested at 3.5% : Write a total interest equation in decimal form .05x + .035(14000-x) = 640 : .05x + 490 - .035x = 640 : .05x - .035x = 640 - 490 : .015x = 150 x = x = \$10,000 amt invested at 5% : I'll let you find out the amt invested a 3.5% : Check solution by finding the total interest using the two values
 Quadratic_Equations/321789: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0 Problem: Solution: 2, (only solution) Thank you!!1 solutions Answer 230405 by ankor@dixie-net.com(15660)   on 2010-07-12 18:11:07 (Show Source): You can put this solution on YOUR website!Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0 Problem: Solution: 2, (only solution) : A solution of 2 will come from factors: (x-2), (x-2) FOIL (x-2)(x-2) = x^2 - 4x + 4 = 0
 Linear_Equations_And_Systems_Word_Problems/321698: . Suppose you have a lemonade stand, and when you charge \$1 per cup of lemonade you sell 60 cups. But when you raise your price to \$1.50 you only sell 30 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.1 solutions Answer 230400 by ankor@dixie-net.com(15660)   on 2010-07-12 17:20:14 (Show Source): You can put this solution on YOUR website!you charge \$1 per cup of lemonade you sell 60 cups. But when you raise your price to \$1.50 you only sell 30 cups Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge : the slope of the equation: m = Assign the given values as follows: x1=1.00, y1=60 x2=1.50, y2=30 Find the slope m = = = -60 is the slope : Use the point/slope formula: y - y1 - m(x - x1) y - 60 = -60(x - 1) y - 60 = -60x + 60 y = -60x + 60 + 60 y = -60x + 120 : c = -60p + 120, is the equation
 Numbers_Word_Problems/321696: Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number1 solutions Answer 230399 by ankor@dixie-net.com(15660)   on 2010-07-12 17:08:00 (Show Source): You can put this solution on YOUR website!Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number: There is no unique solution : let x = the middle number then (x-1) = the 1st number and (x+1) = the 3rd number : x^2 = ((x-1)*(x+1)) + 1 FOIL x^2 = x^2 - 1 + 1 : x^2 = x^2 Which means this is true for any 3 consecutive numbers even, -1, 0 +1 : Try a few like; 142, 143, 144: 143^2 = 20449, 142*144 = 20448
 Travel_Word_Problems/321686: how long does it take a train to travel 27 feet at 4 mph1 solutions Answer 230378 by ankor@dixie-net.com(15660)   on 2010-07-12 15:11:53 (Show Source): You can put this solution on YOUR website!how long does it take a train to travel 27 feet at 4 mph : t = 27 5.867t = 27 t = t = 4.6 seconds
 Angles/321619: what are the measures of two complementary angles if the difference in their measures is 101 solutions Answer 230374 by ankor@dixie-net.com(15660)   on 2010-07-12 15:02:31 (Show Source): You can put this solution on YOUR website!x + y = 90 x - y = 10 ------------Adding eliminates y, find x 2x = 100 x = 50, then y = 40
 Age_Word_Problems/321555: The son is 23 years younger than the mother. In seven years, the mother will be twice as old as the daughter. How old is each now?1 solutions Answer 230361 by ankor@dixie-net.com(15660)   on 2010-07-12 14:02:51 (Show Source): You can put this solution on YOUR website!The son is 23 years younger than the mother. In seven years, the mother will be twice as old as the daughter. How old is each now? : Not much information here, let's assume Mommy is 31 then son is 8 yrs old and 31 + 7 = 2(d + 7) 31 + 7 = 2d + 14 31 + 7 - 14 = 2d 31 - 7 = 2d 24 = 2d d = 24/2 d = 12 yrs is the daughter : There are many possibilities that are reasonable, and will give an integer value for the daughter's age Mommy's age could be 27, 29, 31, 33, all odd numbers up to 89 and even beyond For example when Mom is 89, son will be 66, daughter will be 41 :
 Rate-of-work-word-problems/321410: 1) A silversmith has two alloys, one containing 30% silver and the other,55%. How much of each should be melted and combined to obtain 100 grams containing 45% silver? 2) A cellular phone company charges customers a certain amount for the first minute of a long distance call and an additional amount for each suceeding ...minute. A customer makes two calls to the same city, a 33-minute call for Php 269 and a 19-minute for Php 157. How much does the cellular phone company charge for the first minute? for each succeding minute? 3) A swimming pool can be filled by three water pipes, A,B and C. Pipe C alone can fill the pool in 8 hours. If pipes B and C are used together, the pool can be filled in 6 hours. If pipes A and B are used together, it takes 10 hours. How long does it take to fill the pool if all three pipes are used? i need ur help!1 solutions Answer 230343 by ankor@dixie-net.com(15660)   on 2010-07-12 11:31:22 (Show Source): You can put this solution on YOUR website!1.A silversmith has two alloys, one containing 30% silver and the other, 55%. How much of each should be melted and combined to obtain 100 grams containing 45% silver? : Let x = amt of 55% alloy Total amt will be 100 gr, therefore (100-x) = amt of 30% alloy required A typical mixture equation, using decimals .55x + .30(100-x) = .45(100) .55x + 30 - .30x = 45 .55x - .30x = 45 - 30 .25x = 15 x = x = 60 gr of 55% alloy then 100 - 60 = 40 gr of 30% alloy : : 2) A cellular phone company charges customers a certain amount for the first minute of a long distance call and an additional amount for each succeeding minute. A customer makes two calls to the same city, a 33-minute call for Php 269 and a 19-minute for Php 157. How much does the cellular phone company charge for the first minute? for each succeeding minute? : Let x = amt charged for 1st min Let y = amt charged for each succeeding min : Call 1: x + 32y = 269 Call 2: x + 18y = 157 -----------------------Subtraction eliminates x, find y " "0x + 14y = 112 y = y = 8 cents for each succeeding min I'll let you find the value of x, the first minute cost : : 3) A swimming pool can be filled by three water pipes, A,B and C. Pipe C alone can fill the pool in 8 hours. If pipes B and C are used together, the pool can be filled in 6 hours. If pipes A and B are used together, it takes 10 hours. How long does it take to fill the pool if all three pipes are used? : Let the completed job = 1 (a full pool) : "pipes B and C are used together, the pool can be filled in 6 hours." + = 1 It tells us pipe C can do it in 8 hrs, therefore: + = 1 multiply by 8B 8(6) + 6B = 8B 48 = 8B - 6B 48 = 2B B = B = 24 hrs for B alone : "If pipes A and B are used together, it takes 10 hours." we know B, therefore + = 1 Multiply by 24A 24(10) + 10A = 24A : 240 = 24A - 10A 240 = 14A A = A = 17.143 hrs for A alone : :
 Miscellaneous_Word_Problems/321337: URGENT! 1. Mr. Honda anf Mr. Toyota arrange to meet on the highway connecting their hometown. Mr Honda drives at 45 kph and Mr. Toyoya at 35 kph.They leave their homes w/c are 120 kilometers apart at the same time. In how many hours will they meet? 2. There are two trains. The rabbit heads North on the expressway at 4 kph. Exactly 2 hours after, the Panther follows at a steady speed of 54 kph. How long does it tAke the panther overtake the rabbit?1 solutions Answer 230207 by ankor@dixie-net.com(15660)   on 2010-07-11 15:32:14 (Show Source): You can put this solution on YOUR website!1. Mr. Honda and Mr. Toyota arrange to meet on the highway connecting their hometown. Mr Honda drives at 45 kph and Mr. Toyoya at 35 kph. They leave their homes w/c are 120 kilometers apart at the same time. In how many hours will they meet? : Let t = travel time when they meet when they meet, the total distance they travel will equal 120 km write a dist equation, dist = speed * time : H's dist + T's dist = 120 km 45t + 35t = 120 80t = 120 t = t = 1.5 hrs to mee : ; 2. There are two trains. The rabbit heads North on the expressway at 4 kph. Exactly 2 hours after, the Panther follows at a steady speed of 54 kph. How long does it tAke the panther overtake the rabbit? : Let t = the panther's travel time then (t+2) = the rabbit's travel time : When p overtakes r, they will have traveled the same distance Write a distance equation, dist = speed * time ; P's dist = r's dist 54t = 4(t+2) : 54t = 4t + 8 : 54t - 4t = 8 : 50t = 8 t = t = .16 hrs which is: .16*60 = 9.6 min to catch the unfortunate rabbit ; But what about the train? Did the rabbit jump on the train and escape?
 Equations/321406: can you help me with how to solve this? 5x^2-4x=33 ? (the ^2 means squared) thanks!1 solutions Answer 230204 by ankor@dixie-net.com(15660)   on 2010-07-11 15:16:10 (Show Source): You can put this solution on YOUR website!5x^2-4x=33 ? Subtract 33 from both sides 5x^2 - 4x - 33 = 0 Factor this by using the factors of 33 and adding the correct signs to satisfy the middle term, (5x + 11)(x - 3) = 0 x = 3 and 5x = -11 x =
 Surface-area/321359: A rectangular swimming pool has a diagonal of 40 meters and makes a 30 degree angle with the length of the pool. What is the area of the pool? Okay, I drew the shape and I immediately found out that the diagonal seperates the rectangle into two 30-60-90 degree triangles, and the Area is equal to length times width, and the pythagorean theorem must be used, but I got stuck, I mean how am I supposed to find the length and width here? Am I supposed to use the trigonometric equations here? (eg: sin theta = hypotenuse/opposite) Thank you in advance!1 solutions Answer 230202 by ankor@dixie-net.com(15660)   on 2010-07-11 14:48:09 (Show Source): You can put this solution on YOUR website!A rectangular swimming pool has a diagonal of 40 meters and makes a 30 degree angle with the length of the pool. What is the area of the pool? : Find the width using the sine of 30 sin(30) = W/40 : Find the length using the cos of 30 cos(30) = L/40
 Permutations/321348: how many 6 digit numbers we have in all?1 solutions Answer 230194 by ankor@dixie-net.com(15660)   on 2010-07-11 14:26:17 (Show Source): You can put this solution on YOUR website!how many 6 digit numbers we have in all?: : How about 999,999 - 99,999 = 900,000?
 Polynomials-and-rational-expressions/321341: Hi, I am having a problem with two variables on a dividend when dividing polynomials. My exact problem is: 2x^3-9x^2y-12^y+17xy^2 divided by 2x-3y I know the usual process and I have gotten to the second equation involving getting a difference of -6x^2y but now I am stuck, because when I divide -6x^2y to the first term of the divisor, I have to multiply that quotient (which is -3xy) to the brought-down -12y^3, and as far as I remember I can't multiply it because -12y^3 has no x variable. Can you please help? Thanks.1 solutions Answer 230193 by ankor@dixie-net.com(15660)   on 2010-07-11 14:03:27 (Show Source): You can put this solution on YOUR website!My exact problem is: 2x^3-9x^2y-12^y+17xy^2 divided by 2x-3y : Rearrange the number divided, then the long division procedure will work : .................______________________________ (2x-3y)|2x^3 - 9x^2y + 17xy^2 - 12y^3 : : I got a quotient of: x^2 - 3xy - y^2, remainder -15y^3
 Miscellaneous_Word_Problems/321344: URGENT! 1.While waiting for a train, alvin takes a bus ride at 60 kph to a certain point and then take walks back leisurely at 10 kph. The bus takes 1/4 hour less than his walking. How far does he walk and how long. 1 solutions Answer 230163 by ankor@dixie-net.com(15660)   on 2010-07-11 10:07:33 (Show Source): You can put this solution on YOUR website!.While waiting for a train, alvin takes a bus ride at 60 kph to a certain point and then take walks back leisurely at 10 kph. The bus takes 1/4 hour less than his walking. How far does he walk and how long. : Let t = time he walked then (t-.25) = time rode; (changed 1/4 to .25) : Write a distance equation; dist = speed * time : riding dist = walking dist 60(t-.25) = 10t 60t - 15 = 10t 60t - 10t = 15 50t = 15 t = t = .3 hrs, which is .3*60 = 18, min is time he walked : Find the dist 10 * .3 = 3 km he walked, (and rode) : : Confirm our solutions by finding the dist he rode (.3-.25) * 60 = .05 * 60 = 3 km also
 Linear_Algebra/321027: The estimated masses of a proton and an electron are 1.67 x 10-24 grams and 9.11 x 10-28 grams, respectively. Find the ratio to three significant digits of the mass of the proton to the mass of the electron.1 solutions Answer 230124 by ankor@dixie-net.com(15660)   on 2010-07-10 22:01:48 (Show Source): You can put this solution on YOUR website!The estimated masses of a proton and an electron are 1.67 x 10-24 grams and 9.11 x 10-28 grams, respectively. Find the ratio to three significant digits of the mass of the proton to the mass of the electron. : = = .183315(10^4) = 1833.15 : Proton mass is about 1833 times an electron mass
 Linear-equations/321310: Find the x-intercept of the line that has an equation of -3x + 6y = 9. 1 solutions Answer 230123 by ankor@dixie-net.com(15660)   on 2010-07-10 21:50:15 (Show Source): You can put this solution on YOUR website!Find the x-intercept of the line that has an equation of –3x + 6y = 9. : The x intercept occurs when y=0, therefore: -3x + 6(0) = 9 -3x = 9 divide both sides by -3 x = x = -3