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 Radicals/118406: Word Problem: The insulation comes in 40cm wide rolls that are cut to fit between the rafters in the attic. The roof is 7m from peak to eave and the attic space is 3m high at the peak, how long does each piece of insulation need to be? Round to the nearest tenth. 40^2=7^2+3^2 Am I using the right formula in order to solve this problem?1 solutions Answer 86595 by ankor@dixie-net.com(15624)   on 2008-01-02 19:32:00 (Show Source): You can put this solution on YOUR website!The insulation comes in 40cm wide rolls that are cut to fit between the rafters in the attic. The roof is 7m from peak to eave and the attic space is 3m high at the peak, how long does each piece of insulation need to be? Round to the nearest tenth. : you sort of have the right idea, however: : The width of the insulation (40 cm) has no bearing on the problem : The roof consists of two right triangles, back-to-back /|\. : We want to find the base of one of the triangles then double it : The height is given as 3 m "|"; call it b The hypotenuse is given as 7 m; "/" or "\"; call it c : Find the base (a) using the pythagorean theorem: a^2 + b^2 = c^2 a^2 + 3^2 = 7^2 a^2 + 9 = 49 a^2 = 40 - 9 a^2 = 40 a = a = 6.32455 double this: 12.6 meters is the length of the insulation : Did this help?
 Age_Word_Problems/118411: The monkey’s mother is half as old as the monkey will be when it is three times as old as its mother was when she was half as old as the monkey will be when it is twice as old as it is now. The combined ages of the monkey and its mother are thirty years.1 solutions Answer 86594 by ankor@dixie-net.com(15624)   on 2008-01-02 18:46:58 (Show Source): You can put this solution on YOUR website!Let x = mother's age now. Let y = offspring's age now : The monkey’s mother is half as old as the monkey will be when it is three times as old as its mother was when she was half as old as the monkey will be when it is twice as old as it is now. : The last phrase:"when she was half as old as the monkey will be when it is twice as old as it is now." just means: .5(2y) = y : Replacing that phrase with y: mother is half as old as the monkey will be when it is three times as old as its mother was y : x = .5(3y) x = 1.5y : "The combined ages of the monkey and its mother are thirty years." x + y = 30 1.5y + y = 30; substituted 1.5y for x 2.5y = 30 y = 30/2.5 y = 12 yrs old Then x = 18 yrs old : Check solution in: mother is half as old as the monkey will be when it is three times as old as its mother was when y 18 = .5(3(12) 18 = .5(36) : I'm never sure of these tormentors, but no one seemed to want it, hence my effort. Hope it's useful to you.
 Travel_Word_Problems/118454: ok, its a project. the problem is: asafa powell is the worlds fastest man. in the 100meter he currently broke the world record by a time of 9.74 secounds, i run the 100 meter sprint in 10.9 secoounds. what i would like to know is if we race nd we take off at the same time what would be the distance between me and him, right when he crosses the finish line. hard isnt it? well i tried but i cant seem to sole it, however i think i am on the right track i think ration plays a role in this. well ty for your time and i hope you can solve this and show me how to solve it please thankyou arthur1 solutions Answer 86579 by ankor@dixie-net.com(15624)   on 2008-01-02 15:11:47 (Show Source): You can put this solution on YOUR website!Powell is the world's fastest man. In the 100 meters, he currently broke the world record by a time of 9.74 seconds, I run the 100 meter sprint in 10.9 seconds. If we race, and we take off at the same time, what would be the distance between me and him, when he crosses the finish line. : All you have to find out is, how far can you travel in 9.74 sec at the speed of 10.9 sec for 100 meters. : Find your speed in meters per seconds (speed = distance/time): = 9.1743 meters/sec : In 9.74 seconds 9.74 * 9.1743 = 89.3578 meters : Powell is at 100 meter at that time, therefore 100 - 89.3578 = 10.6422 meters behind him. if
 Equations/118453: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together. I know that Sally can paint a house 2/3 faster than John. 1 solutions Answer 86570 by ankor@dixie-net.com(15624)   on 2008-01-02 13:41:48 (Show Source): You can put this solution on YOUR website!If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together. : Let t = time required when painting together : Let the completed job = 1 : A simple equation: + = 1 ; Multiply equation by 12 to get rid of the denominators: 12* + 12* = 12(1) : Cancel out the denominators and you have: 3t + 2t = 12 : 5t = 12 : t = 12/5 : t = 2.4 hrs working together (and not fooling around) : : Check our solution in the original equation: + = .6 + .4 = 1, confirms out solution
 Linear-systems/118448: This question is from textbook structure and method book 1 I AM WORKING ON THE aMERICAN SCHOOL CIRICULUM AND I AM DOING A HOME TEST. I HAVE THE FOLLOWING WORD PROBLEM AND I CAN'T UNDERSTAND HOW TO GET THE TWO ANSWERS ASKED FOR. A SAILBOAT TRAVELS 20 MILES DOWNSTREAM IN 3 HOURS.IT RETURNS IN 4 HOURS.FIND THE SPEED OF THE SAILBOAT IN STILL WATERAND THE RATE OF THE CURRENT. I CAN FIGURE OUT THAT THE RATE OF THE BOAT GOING DOWN STREAM WOULD TRAVEL 6.23 MPH AND COMMING BACK IT WOULD TRAVEL 5 MPH. I CAN'T FIGURE OUT HOW THAT WILL HELP ME.1 solutions Answer 86568 by ankor@dixie-net.com(15624)   on 2008-01-02 13:32:14 (Show Source): You can put this solution on YOUR website!A SAILBOAT TRAVELS 20 MILES DOWNSTREAM IN 3 HOURS.IT RETURNS IN 4 HOURS. FIND THE SPEED OF THE SAILBOAT IN STILL WATER AND THE RATE OF THE CURRENT. I CAN FIGURE OUT THAT THE RATE OF THE BOAT GOING DOWN STREAM WOULD TRAVEL 6.23 MPH AND COMING BACK IT WOULD TRAVEL 5 MPH. : One way is to use two unknowns and use the elimination method : Let x = speed of the boat in still water Let y = speed of the current then: (x+y) = speed downstream (x-y) = speed upstream : Write two distance equations: Distance = speed * time Down stream: 3(x+y) = 20 Upstream: 4(x-y) = 20 : 3x + 3y = 20 4x - 4y = 20 : Multiply the 1st equation by 4 and the 2nd equation by 3 12x + 12y = 80 12x - 12y = 60 ---------------adding eliminates y, find x 24x + 0y = 140 x = 140/24 x = 5.83 mph speed of the boat in still water : Find y 3(5.833) + 3y = 20 17.5 + 3y = 20 3y = 20 - 17.5 3y = 2.5 y = 2.5/3 y = .833 mph is the speed of the current : : Check solutions in the 2nd equation 4(5.833) - 4(.833) = 23.33 - 3.33 = 20 confirms our solution
 Quadratic_Equations/118447: Find three consecutive integers such that the product of the first and second is 36 less than the product of the second and third. I tried x x+1 x+2 but did not get any further :(1 solutions Answer 86564 by ankor@dixie-net.com(15624)   on 2008-01-02 12:52:14 (Show Source): You can put this solution on YOUR website!: You have your 3 consecutive integers: x, (x+1), (x+2) : Find three consecutive integers such that the product of the first and second is 36 less than the product of the second and third. : The product of the 1st and 2nd would be: x(x+1) : The product of the 2nd and 3rd would be: (x+1)(x+2) : Write an equation for what it says: : Product of 1st & 2nd = Product of 2nd & 3rd - 36 x(x+1) = (x+1)(x+2) - 36 : FOIL x^2 + x = x^2 + 3x + 2 - 36 : Combine all the x's on the left x^2 - x^2 + x - 3x = 2 - 36 : -2x = -34 : x = -34/-2 : x = +17, our 1st integer : I'll let you take it from there. Check your solutions in the equation
 Quadratic_Equations/118446: It takes a local train 30 minutes longer than the express to travel 216km.The local averages 6km/h less than the express.What is a possible equation which could be used to determine the speed of each train? I said 216/x-6 - 216/x = 30 but I was marked wrong :(1 solutions Answer 86563 by ankor@dixie-net.com(15624)   on 2008-01-02 12:20:25 (Show Source): You can put this solution on YOUR website!It takes a local train 30 minutes longer than the express to travel 216km.The local averages 6km/h less than the express.What is a possible equation which could be used to determine the speed of each train? I said 216/x-6 - 216/x = 30 but I was marked wrong :( : You have to convert 30 min to hrs + = : If you solve this you will get speeds of 48 and 54 km/hr :
 Travel_Word_Problems/118440: A person riding a motorcycle leaves 1 hr after a person riding a bicycle. Both travel the same road. If the person riding the bicycle is traveling at 10mpr and the person riding the motorcycle is traveling at 30mpr, how long will it take the motorcycle to overtake the bicycle? The answer I think is 30min but what is the equation to that?1 solutions Answer 86554 by ankor@dixie-net.com(15624)   on 2008-01-02 08:39:48 (Show Source): You can put this solution on YOUR website!A person riding a motorcycle leaves 1 hr after a person riding a bicycle. Both travel the same road. If the person riding the bicycle is traveling at 10mpr and the person riding the motorcycle is traveling at 30mpr, how long will it take the motorcycle to overtake the bicycle? : That's the right answer but here is a step-by-step method to construct an equation. : Let t = time required for the motorcycle to overtake the bike : Since the bike left an hour earlier: (t+1) = travel time of the bike : We know when the motorcycle overtakes the bike the will have traveled the same distance. We can make a simple distance equation from this fact: distance = speed * time : Motorcycle dist = bike distance 30t = 10(t+1) : 30t = 10t + 10 30t - 10t = 10 20t = 10 t = t = half an hour like you said
 Miscellaneous_Word_Problems/118387: a graduated cylinder was filled with water to the 15.0 ml mark and weighed on a balnace. It mass was27.35g. An object made of silver was [placed in the cylinder and completely submerged in the water. The water level rose to 18.3ml. When reweighed the cylinder,water and silver object had a total mass of 62.0g. Calculate the density of silver1 solutions Answer 86512 by ankor@dixie-net.com(15624)   on 2008-01-01 12:40:44 (Show Source): You can put this solution on YOUR website!A graduated cylinder was filled with water to the 15.0 ml mark and weighed on a balance. It's mass was 27.35 g. An object made of silver was placed in the cylinder and completely submerged in the water. The water level rose to 18.3ml. When reweighed the cylinder,water and silver object had a total mass of 62.0g. Calculate the density of silver. : Mass of the silver: 62 - 27.35 = 34.65 g : Volume of the silver: 18.3 - 15.0 = 3.3 ml of water displaced by the silver : Convert ml to cu/cm; we know that; 1 liter = 10^3 cu/cm 1 ml = 1 cm^3 therefore: 3.3 ml = 3.3 cm^3 : Density is defined as the ratio of Mass to Volume often given as, grams/cm^3: D = D = 10.5 is the density of silver : Did this help?
 Mixture_Word_Problems/118357: The population denstity in Tustin Foothills is about 3589 people per square mile. the population density in Orange is about 5719 people per square mile. how many more people would there be in a square region 3 miles on each side in Orange than in an equivalent region in Tustin Foothills (assume uniform, distribution of people)?1 solutions Answer 86507 by ankor@dixie-net.com(15624)   on 2008-01-01 11:31:08 (Show Source): You can put this solution on YOUR website!The population denstity in Tustin Foothills is about 3589 people per square mile. the population density in Orange is about 5719 people per square mile. how many more people would there be in a square region 3 miles on each side in Orange than in an equivalent region in Tustin Foothills (assume uniform, distribution of people) : 3^2(5719) - 3^2(3589) = 9(5719) - 9(3589) = 51471 - 32301 = 19,170
 Quadratic_Equations/118365: A fountain in the town square sprays water in a parabolic arc. The water spray starts at 1/2 metre above the ground and reaches a maximum height of 5 metres after 3 seconds. Determine the quadratic function that models the path followed by the water in the fountain and use it to determime the height of the water at 1&3/4 seconds . Round your answer to the nearest tenth of a metre .1 solutions Answer 86480 by ankor@dixie-net.com(15624)   on 2007-12-31 13:35:49 (Show Source): You can put this solution on YOUR website!A fountain in the town square sprays water in a parabolic arc. The water spray starts at 1/2 metre above the ground and reaches a maximum height of 5 metres after 3 seconds. Determine the quadratic function that models the path followed by the water in the fountain and use it to determine the height of the water at 1&3/4 seconds . Round your answer to the nearest tenth of a metre. : Using the form: y = ax^2 + bx + c : y = .5 when x = 0; c = .5 : Using the vertex, x = 3; y = 5 9a + 3b + .5 = 5 9a + 3b = 5 - .5 9a + 3b = 4.5 : Using the symmetry of a parabola we know that 3 sec after the vertex, y = .5 again x = 6; y = .5 36a + 6b + .5 = .5 36a + 6b = .5 - .5 36a + 6b = 0 : Multiply the vertex equation by 2 and subtract from the above equation: 36a + 6b = 0 18a + 6b = 9 -------------subtracting eliminates b, find a 18a + 0b = -9 a = -9/18 a = -.5 : Find b using 9a + 3b = 4.5 9(-.5) + 3b = 4.5 -4.5 + 3b = 4.5 3b = 4.5 + 4.5 3b = 9 b = 3 : Our equation: y = -.5x^2 + 3x + .5 : Illustrated by the graph: : Find the height after 1.75 seconds: h = -.5(1.75^2) + 3(1.75) -.5 h = -1.53125 + 5.25 + .5 h = 4.2 meters after 1.75 seconds
 Inequalities/118343: A wealthy old man is criticized for marrying a woman for he is three times her age. He wittily replies, "Oh, but in 20 years time 2 shall only be twice her age." How old is the man and his wife?1 solutions Answer 86462 by ankor@dixie-net.com(15624)   on 2007-12-31 08:07:46 (Show Source): You can put this solution on YOUR website!A wealthy old man is criticized for marrying a woman for he is three times her age. He wittily replies, "Oh, but in 20 years time I shall only be twice her age." How old is the man and his wife? : Let m = old man's age Let g = girl's age : "he is three times her age." m = 3g : "In 20 years time I shall only be twice her age." (m+20) = 2(g+20) m + 20 = 2g + 40 m = 2g + 40 - 20 m = 2g + 20 : "How old are they?" Substitute 3g for m, find g 3g = 2g + 20 3g - 2g = 20 g = 20 yrs is the girls age 60 yrs is the old fart's age : : Check solution: in 20 yrs he will be 80 and she will be 40
 Inequalities/118342: The sum of the ages of Dorothy and Dorileen is 41. In 5 years, Dorothy will be twice as old as Dorileen. Find their age 3 years ago.1 solutions Answer 86461 by ankor@dixie-net.com(15624)   on 2007-12-31 07:55:00 (Show Source): You can put this solution on YOUR website!Let x = Dorthy's age 3 yrs ago Let y = Dorileen's age 3 yrs ago : There present age will be: (x+3) and (y+3) : "The sum of the ages of Dorothy and Dorileen is 41." (x+3) + (y+3) = 41 x + y + 6 = 41 x + y = 41 - 6 x + y = 35 x = (35 - y) : " In 5 years, Dorothy will be twice as old as Dorileen." (That will be 8 yrs from 3 yrs ago) x + 8 = 2(y + 8) x + 8 = 2y + 16 x = 2y + 16 - 8 x = 2y + 8 : "Find their ages 3 yrs ago" Substitute (35-y) for x and find y 35 - y = 2y + 8 35 - 8 = 2y + y 3y = 27 y = 27/3 y = 9 yrs old is Dorileen's age 3 yrs ago : 35 - 9 = 26 yrs is Dorthy's age 3 yrs ago : : Check solution using the statement: "The sum of the ages of Dorothy and Dorileen is 41." (26+3) + (9+3) = 29 + 12 = 41 :
 Rational-functions/118161: simplify (2x to the power of -2 times y to the power of 3 over x to the power of 2 times y to the power of -3) to the power of -1 a. 2 b. 2x to the power of 4 over y to the power of 6 c. 1 over 2 d. x to the power of 4 over 2y to the power of 61 solutions Answer 86438 by ankor@dixie-net.com(15624)   on 2007-12-30 19:50:50 (Show Source): You can put this solution on YOUR website!simplify (2x to the power of -2 times y to the power of 3 over x to the power of 2 times y to the power of -3) to the power of -1 : Assume that you mean: : You can get rid of the outside exponent of -1 by inverting the fraction: : Add the like term exponents so they will be positive: = : Remember when you divide, the exponents are subtracted, but if it's a negative exponent, you have a minus a minus, which is a plus : Looks like the answer is d, doesn't it
 Rational-functions/118319: how do u graph and what would the graph look like for 2y is greater than -11 solutions Answer 86434 by ankor@dixie-net.com(15624)   on 2007-12-30 19:33:20 (Show Source): You can put this solution on YOUR website!how do u graph and what would the graph look like for 2y is greater than -1 : 2y > -1 y > : If you plotted this graph, it would look like this Shade the area above (but not at) the horizontal line
 Age_Word_Problems/118288: Dan is 5 times as old as mike. in 7 years dan will be 2 more than 3 times as old as mike. find their present ages.1 solutions Answer 86417 by ankor@dixie-net.com(15624)   on 2007-12-30 18:18:33 (Show Source): You can put this solution on YOUR website!Let d = Dan's; present age Let m = Mike's present age : Just write an equation for what it says: "Dan is 5 times as old as mike. " d = 5m : In 7 years we have: (d+7) and (m+7) : "in 7 years dan will be 2 more than 3 times as old as mike." d + 7 = 3(m+7) + 2 d + 7 = 3m + 21 + 2 d + 7 = 3m + 23 d = 3m + 23 - 7 d = 3m + 16 : We know that d = 5m; substitute 5m for d and solve for m 5m = 3M + 16 5m - 3m = 16 2m = 16 m = 16/2 m = 8 therefore d = 5(8) = 40 : : Check solution in the statement: "in 7 years dan will be 2 more than 3 times as old as mike." 40 + 7 = 3(8+7) + 2 47 = 3(15) +2; confirms out solution
 Miscellaneous_Word_Problems/118276: 14a2-15a+41 solutions Answer 86403 by ankor@dixie-net.com(15624)   on 2007-12-30 12:52:48 (Show Source): You can put this solution on YOUR website!A ball is thrown directly upward from ground level with an initial speed of 80 ft/s. How high will it go and when will it return to the ground? : There are two forces at work on the ball, Force of gravity pulling downward: -16t^2 Initial speed upward: + 80t : h = -16t^2 + 80t : When the ball hits the ground; h= 0 -16t^2 + 80t = 0 : Simplify and change the signs, factor out -16t -16t(t - 5) = 0 Two solutions -16t = 0 t = 0; when the ball is thrown from ground level and t = +5 seconds elapse when the ball hits the ground : A graph of this shows time in seconds as x and height in feet as y: : You can see that the axis of symmetry is 2.5 sec The max height occurs at the vertex: : Substitute 2.5 in the original equation h = -16(2.5^2) + 80(2.5) h = -16(6.25) + 200 h = -100 + 200 h = +100 ft is the max height : : Did this help
 Geometry_Word_Problems/118270: This question is from textbook In triangle ABC, the measure of angle C=90, the measure of angle B=30, AC=6x^2-4x, and AB=2x. Find the value of x.1 solutions Answer 86388 by ankor@dixie-net.com(15624)   on 2007-12-29 21:29:40 (Show Source): You can put this solution on YOUR website!In triangle ABC, the measure of angle C=90, the measure of angle B=30, AC=6x^2-4x, and AB=2x. Find the value of x. : After drawing this triangle out it was apparent that we are given the sin of 30: : Side opposite: AC = 6x^2-4x and hypotenuse: AB = 2x ; = sin(30) = Cancel out the 2x and you have: 3x - 2 = 3x = + 2 3x = + x = * x = : : Check solution using the decimal of (5/6); x = .8333 = = = .500, the sine of 30 degrees
 Rational-functions/118230: (4x +12) * x^2 ÷2 _____________ 2x-6 x-3 Help do I do the (4x +12) first then the others?1 solutions Answer 86383 by ankor@dixie-net.com(15624)   on 2007-12-29 19:01:48 (Show Source): You can put this solution on YOUR website!(4x +12) * x^2 ÷2 _____________ 2x-6 x-3 : Trying to sort this out, I came up with: (4x + 12) * / : Invert the dividing fraction and multiply; (4x + 12) * * : Do some factoring here 4(x + 3) * * : Cancel (x-3) 4(x + 3) * * : 4(x + 3) * : Cancel 4, leaving us with: : If this is not what you meant, well, what can I say?
 Linear-equations/118258: The stabilization ratio (births/deaths) for south and central america can be modeled by the formula: y= -0.0012x2 + 0.074x + 2.69 where y is the number of births divided by the number of deaths in the year 1950 + x. a)Use the graph to estimate the year in which the stabilization ratio was at its maximum. b)Use the formula to find the year in which the stabilization ratio was at its maximum. c)what was the maximum stabilization ratio from bart (b)? d)what is the significance of a stabilization ratio of 1?1 solutions Answer 86369 by ankor@dixie-net.com(15624)   on 2007-12-29 17:08:11 (Show Source): You can put this solution on YOUR website!The stabilization ratio (births/deaths) for south and central america can be modeled by the formula: y= -0.0012x2 + 0.074x + 2.69 where y is the number of births divided by the number of deaths in the year 1950 + x. : : a)Use the graph to estimate the year in which the stabilization ratio was at its maximum. : Maximum looks to be around 30: 1950 + 30 = 1980 : : b)Use the formula to find the year in which the stabilization ratio was at its maximum. : Find the axis of symmetry: x = -b/(2a); a=-.0012; b=+.074 x = = 30.8333 ~ 31 1950 + 31 = 1981 year of max stabilization ratio : : c)what was the maximum stabilization ratio from part (b)? : Substitute 30.83 for x, in the original equation; You should get y ~ 3.83 : : d)what is the significance of a stabilization ratio of 1? : I would imagine that means that deaths and births are equal : Did this help?
 Volume/118232: How many 80 pound cement bags can I fit in a 40 foot shipping container?1 solutions Answer 86365 by ankor@dixie-net.com(15624)   on 2007-12-29 16:06:14 (Show Source): You can put this solution on YOUR website!You need to know a couple other things. : The cubic feet of the shipping container The cubic feet of a sack of cement Probably the weight limitations of the shipping container, also
 Complex_Numbers/118256: write a quadratic function in standard form that goes through the given points (1,3) (2,1) (-2,-15)1 solutions Answer 86364 by ankor@dixie-net.com(15624)   on 2007-12-29 16:01:35 (Show Source): You can put this solution on YOUR website!If you can't don't want to use the matrix method, you also use the elimination method : write a quadratic function in standard form that goes through the given points (1,3) (2,1) (-2,-15) : In form ax^2 + bx + c = y; solve for a, b, c : 1,3: eq1: a + b + c = 3 2,1: eq2: 4a + 2b + c = 1 -2,-15: eq3: 4a - 2b + c = -15 : Using equation 2 & 3 we can find b: 4a + 2b + c = 1 4a - 2b + c = -15 ------------------subtracting eliminates a and c 0a + 4b + 0x = 16 4b = 16 b = 16/4 b = 4 : Substitute 4 for b in eq1 & 2 a + 4 + c = 3 a + c = 3 - 4 a + c = -1 and 4a + 2(4) + c = 1 4a + 8 + c = 1 4a + c = 1 - 8 4a + c = -7 : Using these two equations: 4a + c = -7 a + c = -1 -------------subtracting eliminates c 3a + 0c = -6 3a = -6 a = -6/3 a = -2 : Find c, by substituting for a & b in a + b + c = 3 -2 + 4 + c = 3 c + 2 = 3 c = 3 - 2 c = 1 : Therefore we have y = -2x^2 + 4x + 1 ; Is this what you had in mind?
 Complex_Numbers/118255: 5/1+i write expression as complex number in standard form1 solutions Answer 86359 by ankor@dixie-net.com(15624)   on 2007-12-29 15:00:21 (Show Source): You can put this solution on YOUR website!5/1+i write expression as complex number in standard form : Multiply by the conjugate of the denominator over itself * = = = = or - i
 Linear-equations/118250: A parachutist is 800 feet above the ground when she opens her parachute. She then falls at a constant rate of 5 feet per second. How do I write this out as an equation?1 solutions Answer 86356 by ankor@dixie-net.com(15624)   on 2007-12-29 14:44:31 (Show Source): You can put this solution on YOUR website!A parachutist is 800 feet above the ground when she opens her parachute. She then falls at a constant rate of 5 feet per second. How do I write this out as an equation? : You want x = time in seconds and y = feet above the ground : Since it falls 5 ft every second, we have -5x feet from 800 ft y = -5x + 800 : The graph: : You can see that when x = 160 seconds, the height (y) = 0; (160*5 = 800)
 Travel_Word_Problems/118242: At the beginning of the Alay Lakad, Rizza and Angel are 30 km apart. If they leave at the same time and walk in the same direction, Rizza overtakes Angels in 60 hours. If they walk towards each other, they meet in 5 hours. What are their speeds? 1 solutions Answer 86345 by ankor@dixie-net.com(15624)   on 2007-12-29 11:39:55 (Show Source): You can put this solution on YOUR website!Rizza and Angel are 30 km apart. If they leave at the same time and walk in the same direction, Rizza overtakes Angels in 60 hours. If they walk towards each other, they meet in 5 hours. What are their speeds? : Let x = R's walking speed Let y = A's walking speed : Walking the same direction equation; write a distance equation Dist = time * speed : R's dist - 30 km = A's distance 60x - 30 = 60y 60x - 60y = 30 Simplify divide equation by 30 2x - 2y = 1 : Walking towards each other equation (they are 30 km apart): Write another distance equation: Dist = time * speed R's dist + A's dist = 30 km 5x + 5y = 30 Simplify, divide equation by 5 x + y = 6 : Use elimination, mult above equation by 2 add to equation: 2x - 2y = 1: 2x + 2y = 12 2x - 2y = 1 ------------ adding eliminates y 4x = 13 x = 13/4 x = 3.25 km/hr is R's speed : Find y using equation x + y = 6 3.25 + y = 6 y = 6 - 3.25 y = 2.75 km/hr is A's speed : : Check using the 1st equation: 60x - 30 = 60y 60(3.25) - 30 = 60(2.75) 195 - 30 = 165 and using the 5x + 5y = 30 equation 5(3.25) + 5(2.75) = 16.25 + 13.75 = 30; confirms our solutions
 Quadratic_Equations/118245: a> Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its lenght and breadth. b> The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Determine their present ages. c> Is it possible to design a rectangular park of perimeter 80 m and 400 m2? If so, find its lenght and breadth. 1 solutions Answer 86343 by ankor@dixie-net.com(15624)   on 2007-12-29 11:08:08 (Show Source): You can put this solution on YOUR website!Is it possible to design a rectangular mango grove whose length is twice it's breadth, and the area is 800 m2? If so, find its length and breadth. : It's possible. Let x = width of the grove Then 2x = length : Area = L * W: x(2x) = 800 2x^2 = 800 x^2 = 800/2 x^2 = 400 x = Sqrt(400) x = 20 m by 40 m : : b> The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Determine their present ages. : It would simply things if we let x and y be the ages 4 years ago Then (x+4) and (y+4) = ages now : Present age sum = 20: (x+4) + (y+4) = 20 x + y + 8 = 20 x + y = 20 - 8 x + y = 12 y = 12-x : Product of age 4 yrs ago x*y = 48 y = 48/x Replace y with 12-x 12-x = 48/x 12x - x^2 = 48 -x^2 + 12x - 48 = 0 This equation has no real roots, (discriminant less than 0) There is no solution If we plot these equations, you can see they don't intersect y = 12-x and y = 48/x : : : c> Is it possible to design a rectangular park of perimeter 80 m and 400 m2? If so, find its length and breadth. : It is: let the sides = x and y Perimeter: 2x + 2y = 80 Simplify, divide by 2 x + y = 40 y = (40-x) : Area: x * y = 400 Replace y with (40-x) x(40-x) = 400 40x - x^2 = 400 -x^2 + 40x - 400 = 0 Easier to factor if we multiply by -1 x^2 - 40x + 400 = 0 Factor (x-20)(x-20) = 0 x = 20, : The park will be a square; 20 by 20