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 Quadratic_Equations/160814: The speed of an airplane in still air is 168 mph. The plane travels 689 miles against the wind and 950 miles with the wind in a total time of 11 hours. What is the speed of the wind. I have tried everything with this question and I keep getting the wrong answer. I think I am screwing up distributing. 1 solutions Answer 118558 by ankor@dixie-net.com(15649)   on 2008-10-07 15:31:26 (Show Source): You can put this solution on YOUR website!The speed of an airplane in still air is 168 mph. The plane travels 689 miles against the wind and 950 miles with the wind in a total time of 11 hours. What is the speed of the wind. : Let x = speed of the wind then (168-x) = speed against the wind and (168+x) = speed with the wind : Write a time equation: Time = Against wind time + With wind time = 11 hr + = 11 : Multiply equation by (168+x)(168-x), results: 689(168+x) + 950(168-x) = 11(168+x)(168-x) : 115752 + 689x + 159600 - 950x = 11(28224 - x^2) : -261x + 275352 = 310464 - 11x^2 : Arrange as quadratic equation on the left +11x^2 - 261x + 275352 - 310464 = 0 : 11x^2 - 261x - 35112 = 0 : This nasty equation requires the quadratic formula; a=11; b=-261; c=-35112 You should get positive solution: x ~ 69.6 mph speed of the wind : : We can confirm that: 689/(268-69.6) = 7.00 hrs 950/(268+69.6) = 4.00 hrs --------------------------- total time = 11 hrs
 Linear_Algebra/160700: Use elimination method to solve the system. -4x+4y-2z=-8 -3x-y+4z=0 2x-2y+3z=-41 solutions Answer 118557 by ankor@dixie-net.com(15649)   on 2008-10-07 15:02:35 (Show Source): You can put this solution on YOUR website!-4x + 4y - 2z =-8 -3x - y + 4z = 0 +2x- 2y + 3z =-4 : The coefficients of the 1st and 3rd equations, will help us alot: : Multiply the 3rd equation by 2, and add to the 1st equation -4x + 4y - 2z = -8 +4x - 4y + 6z = -8 ---------------------adding eliminates x and y, find z 0x + 0y + 4z = -16 z = z = -4 : Substitute -4 for z in the 2nd equation -3x - y + 4(-4) = 0 -3x - y - 16 = 0 -3x - y = 16 : Substitute -4 for z in the 3rd equation: +2x - 2y + 3(-4) = -4 +2x - 2y - 12 = -4 +2x - 2y = -4 + 12 +2x - 2y = +8 : Multiply -3x - y = 16 by -2 and add to the above equaiton +6x + 2y = -32 +2x - 2y = 8 ---------------- addition eliminate y 8x = -24 x = x = -3 : Find y using the 2nd equation, substitute for x & z -3(-3) - y + 4(-4) = 0 +9 - y - 16 = 0 -y -7 = 0 -y = +7 y = -7 : Solutions: x=-3, y=-7; z=-4 : : Check solutions in the 3rd equation: +2x- 2y + 3z =-4 2(-3) - 2(-7) + 3(-4) = -4 -6 + 14 - 12 = -4 -18 + 14 = -4
 Radicals/160696: Solve: 10= ________ V 5m + 1 + 6 (10 equals the square root of 5m+1, plus 6) Please help with this problem!1 solutions Answer 118556 by ankor@dixie-net.com(15649)   on 2008-10-07 14:31:18 (Show Source): You can put this solution on YOUR website!Solve: 10= ________ V 5m + 1 + 6 (10 equals the square root of 5m+1, plus 6) : We can write it: 10 = : Subtract 6 from both sides; you have: 4 = : Square both sides, get rid of the radical 16 = 5m + 1 : Subtract 1 from both sides: 15 = 5m ; Divide both sides by 5 m = m = 3 : : Check solution in original equation: 10 = : 10 = : 10 = : 10 = 4 + 6
 Numbers_Word_Problems/160705: This question is from textbook In a certain triangle the measure of one angle is double the measure of a second angle but is 5 degrees less than the measure of the third angle. If the sum of the measures of the three interior angles of a triangle is always 180 degrees, form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the alegbraic expression.1 solutions Answer 118554 by ankor@dixie-net.com(15649)   on 2008-10-07 14:21:10 (Show Source): You can put this solution on YOUR website!In a certain triangle the measure of one angle is double the measure of a second angle but is 5 degrees less than the measure of the third angle. If the sum of the measures of the three interior angles of a triangle is always 180 degrees, form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the algebraic expression. : Let the angles be A, B, C : Write an equation for each statement: : "the measure of one angle is double the measure of a second angle" A = 2B or B = .5A : " but is 5 degrees less than the measure of the third angle." A = C-5 or C = (A+5) : "If the sum of the measures of the three interior angles of a triangle is always 180 degrees,": A + B + C = 180 : form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the algebraic expression. : Substitute for B and C A + .5A + (A+5) = 180 2.5A = 180 - 5 2.5A = 175 solve A = A = 70 degrees, B = 35, C = 75
 Linear-systems/160725: This question is from textbook Algebra 1 A migrating elephant herd started moving at a rate of 6 miles per hour. One stood still and was left behind. He got nervous and began running at 10 miles per hour. He caught up to the herd in 5 minutes. How far did he run? How long in hours did he run?1 solutions Answer 118549 by ankor@dixie-net.com(15649)   on 2008-10-07 14:01:18 (Show Source): You can put this solution on YOUR website!A migrating elephant herd started moving at a rate of 6 miles per hour. One stood still and was left behind. He got nervous and began running at 10 miles per hour. He caught up to the herd in 5 minutes. How far did he run? How long in hours did he run? : Change 5 min to hrs; = .083 hrs : Dist = time * speed .083 * 10 = .83 miles ran the lone elephant to catch up
 Money_Word_Problems/160728: The members of a flying club plan to share equally the cost of a \$200,000 airplane. The members want to 5 more people to join the club so that the cost per person will decrease by \$2,000. How many members are currently in the club?1 solutions Answer 118529 by ankor@dixie-net.com(15649)   on 2008-10-07 09:58:15 (Show Source): You can put this solution on YOUR website! (2008-10-06 21:30:37): The members of a flying club plan to share equally the cost of a \$200,000 airplane. The members want to 5 more people to join the club so that the cost per person will decrease by \$2,000. How many members are currently in the club? : We can deal with this in \$1000's Plane cost \$200, cost decrease is \$2 : Let x = no. members currently in the club then = cost per member now and = cost if 5 more members join : The equation: - 2 = : Multiply equation by x(x+5), results 200(x+5) - 2(x(x+5) = 200x 200x + 1000 - (2x^2 + 10x) = 200x : 200x + 1000 - 2x^2 - 10x - 200x = 0 : -2x^2 - 10x + 1000 = 0 : Simplify divide equation by -2 +x^2 + 5x - 500 = 0 Factor )x-20)(x+25) = 0 Positive solution x = 20 members currently : : Check solution find the actual costs 200000/20 = \$10000 200000/25 = \$8000
 Travel_Word_Problems/160643: A plane flew a distance of 1555 miles in 5 hours. During the first 3 hours of the flight, it flew with a wind a distance of 975 miles. During the remainder of the flight, the plane flew against a wind whose average was 5 mph less than what it had been during the first part of the flight. Find the rate of the plane in still air and the original speed of the wind. Some helpful equations: r= the rate in still air c= the rate of the air current r+c= rate traveling with the current r-c= rate traveling against the current1 solutions Answer 118495 by ankor@dixie-net.com(15649)   on 2008-10-06 21:44:10 (Show Source): You can put this solution on YOUR website!A plane flew a distance of 1555 miles in 5 hours. During the first 3 hours of the flight, it flew with a wind a distance of 975 miles. During the remainder of the flight, the plane flew against a wind whose average was 5 mph less than what it had been during the first part of the flight. Find the rate of the plane in still air and the original speed of the wind. : Some helpful equations: r= the rate in still air c= the rate of the air current r+c= rate traveling with the current r-c= rate traveling against the current : Summarizing what we know: : 1st part of the trip 975 mi in 3 hrs, at a speed (r+c) 2nd part of the trip: 1555-975 = 580 mi in 5-3 = 2 hrs at a speed (r - (c-5)) : Write a distance equation for each part of the trip: (Dist = time * speed) : 3(r+c) = 975 2(r- (c-5)) = 580; wind given as 5 mph less : Simplify: divide the 1st equation by 3, and the 2nd equation by 2 and you have; r + c = 325 and r - c + 5 = 290 r - c = 290 - 5 r - c = 285 : Use these two equation for elimination r + c = 325 r - c = 285 ----------------addition eliminate c, find r 2r = 610 r = 305 mph in still air : Find the original speed of the wind using r + c = 325 305 + c = 325 c = 20 mph is the wind on the 1st part of the trip : : Check solution by finding the distances 3(305+20) = 975 2(305-15) = 580 (wind is 5 mph less) ---------------- total dist 1555mi
 Numbers_Word_Problems/160673: The product of two numbers is 330. The smaller number is seven less than the larger number. What are the numbers?1 solutions Answer 118483 by ankor@dixie-net.com(15649)   on 2008-10-06 19:32:00 (Show Source): You can put this solution on YOUR website!The product of two numbers is 330. The smaller number is seven less than the larger number. What are the numbers? : Two numbers x, y : "The product of two numbers is 330." x*y = 330 : "The smaller number is seven less than the larger number." y = x-7 ; What are the numbers? : Substitute (x-7) for y in the 1st equation, solve for x x(x-7) = 330 x^2 - 7x = 330 x^2 - 7x - 330 = 0 Factor (x-22)(x+15) = 0 Two solutions x = +22 then y = +15 x = -15 then y = -22 : You can check them in the original equations
 Travel_Word_Problems/160682: In a horse race, Snail is 44 feet behind Cat. While Cat is racing at a steady spped of 48 feet per second. Snail has sped up to 56 feet per second. At these speeds how long will it take for snail to catch up to Cat? I Know "t*r=d" but how does it apply to this?1 solutions Answer 118480 by ankor@dixie-net.com(15649)   on 2008-10-06 19:19:57 (Show Source): You can put this solution on YOUR website!In a horse race, Snail is 44 feet behind Cat. While Cat is racing at a steady speed of 48 feet per second. Snail has sped up to 56 feet per second. At these speeds how long will it take for snail to catch up to Cat? : Time = : Use the relative speed to find out how long it will take to cover 44 ft : Time = = = 5.5 seconds
 Geometry_Word_Problems/160541: find the value of k so that the line through (4,k) and (-2,-1) is parallel to y=-2x+3/21 solutions Answer 118474 by ankor@dixie-net.com(15649)   on 2008-10-06 17:54:39 (Show Source): You can put this solution on YOUR website!find the value of k so that the line through (4,k) and (-2,-1) is parallel to y=-2x+3/2 : Parallel lines have the same slope, therefore the slope of the line: m= -2 : Use the slope formula m = : Assign the given coordinate as follows: x1 = 4; y1 = k x2 =-2; y2 = -1 m =-2 : = -2 : = -2 : Multiply both sides by -6, results -1 - k = -6(-2) : -1 - k = +12 : -k = 12 + 1 : -k = +13 or k = -13 ; Find the equation for this line, so we can check he given coordinates: y - (-13) = -2(x - 4) y + 13 = -2x + 8 y = -2x + 8 - 13 y = -2x - 5 If substitute the given values for x, we get the given value for y
 Travel_Word_Problems/160640: Jones can run around a 400-meter track in 65 seconds. How long does Smith take to run the 400 meters if he meets Jones in 35 seconds after they start together in a race around the track in opposite directions? Not sure how to set up the equation for this problem.1 solutions Answer 118460 by ankor@dixie-net.com(15649)   on 2008-10-06 16:28:59 (Show Source): You can put this solution on YOUR website!Jones can run around a 400-meter track in 65 seconds. How long does Smith take to run the 400 meters if he meets Jones in 35 seconds after they start together in a race around the track in opposite directions? : When they meet, they will have traveled a total of 400 meters in 35 seconds : Find Jone's speed in meters/sec: = 6.154 m/sec : Let s = Smith's speed in m/sec : Write a dist equation; Dist = time * speed : 35s + 35(6.154) = 400 : 35s + 215.39 = 400 : 35s = 400 - 215.39 : 35s = 184.61 s = s = 5.275 m/sec is Smith's speed : Find time for Smith to run 400 m: = 75.83 sec to run 400 m : : Check solution: 35 * 5.275 = 184.625 m 35 * 6.154 = 215.39 ------------------ Total dist = 400.0
 Word_Problems_With_Coins/160600: Sam found a number of nickels, dimes and quarters. He found 3 more dimes than nickels but twice as many quarter as dimes. The total value of the coins was \$5.05. How many coins of each type did Sam find? 1 solutions Answer 118456 by ankor@dixie-net.com(15649)   on 2008-10-06 15:56:01 (Show Source): You can put this solution on YOUR website!Sam found a number of nickels, dimes and quarters. He found 3 more dimes than nickels but twice as many quarter as dimes. The total value of the coins was \$5.05. How many coins of each type did Sam find? ; Let: n = no. of nickels d = no. of dime q = no. of quarters : Write an equation for each statement: ; "He found 3 more dimes than nickels" d = 3+n or n = (d-3) : " but twice as many quarter as dimes." q = 2d : "The total value of the coins was \$5.05." .05n + 10d + .25q = 5.05 : How many coins of each type did Sam find? : Substitute for q and n in the total\$ equation .05(d-3) + .10d + .25(2d) = 5.05 .05d - .15 + .10d + .50d = 5.05 .05d + .10d + .50d = 5.05 + .15 .65d = 5.20 d = d = 8 dimes then n = 8 - 3 n = 5 nickels and q = 2*8 q = 16 quarter : 8 + 5 + 16 = 29 coins total ; : Check solution in the total\$ equation .05(5) + .10(8) + .25(16) = .25 + .80 + 4.00 = 5.05; confirms our solutions
 Polynomials-and-rational-expressions/160577: 98.) Height difference. A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tosses is feet. a.) Find the polynomial D(t) that represents the difference in the height of the two balls. b.) How much higher is the red ball 2 seconds after the balls are tossed? c.) In reality, when does the difference in the heights stop increasing? 1 solutions Answer 118442 by ankor@dixie-net.com(15649)   on 2008-10-06 14:06:46 (Show Source): You can put this solution on YOUR website!Height difference. A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tosses is feet. : h = height ; Red Ball equation: h = -16t^2 + 96t : Green Ball equation h = -16t^2 + 80t : a.) Find the polynomial D(t) that represents the difference in the height of the two balls. ......Red ball height - green ball height D(t) = (-16t^2 + 96t) - (-16t^2 + 80t) D(t) = -16t^2 + 96t + 16t^2 - 80t; removing the brackets changes the signs D(t) = -16t^2 + 16t^2 +96t - 80t D(t) = 16t : b.) How much higher is the red ball 2 seconds after the balls are tossed? : Replace t with 2 sec: 16(2) = 32 ft ; c.) In reality, when does the difference in the heights stop increasing? : After 5 sec, Green ball hits the ground in 5 sec You can see this: h = -16(25) + 80(5) h = -400 + 400 h = 0 : : Here's a graphical representation of the two balls
 Rate-of-work-word-problems/160373: My question is on solving a word problem. I dont if you can help but this is the problem: aA vertical cylindrical storage tank, with diameter 20 feet, is filled with oil to a depth of 40 feet. Sometime later, the oil is drained, decreasing the deptht a rate of 8 inches per hour. Write an equation for the volume of oil (ft^3) remaining in the tank t hours later as a function of t. Draw a geometrically correct sketch, supporting your solution. The only thing i can pull out of this problem is that the volume of a cylinder is V = πr^2h. If you could help it would be greatly appreciated.1 solutions Answer 118412 by ankor@dixie-net.com(15649)   on 2008-10-06 09:43:52 (Show Source): You can put this solution on YOUR website!A vertical cylindrical storage tank, with diameter 20 feet, is filled with oil to a depth of 40 feet. Sometime later, the oil is drained, decreasing the depth a rate of 8 inches per hour. Write an equation for the volume of oil (ft^3) remaining in the tank t hours later as a function of t. Draw a geometrically correct sketch, supporting your solution. : This is a linear equation so we can find the slope using the time/volume : Find the volume at 40 ft, (radius = 10 ft) V = V = 12566 cu ft (rounded to nearest cu ft) : Therefore: t=0; v=12566 : Find out how many hours to empty the tank : At 8 in/hr how long to lower it 40 ft? t = = 60 hrs (vol = 0) Therefore: t=60; v=0 : Find the slope: m = = is the slope : An equation: V = t + 12566 : You can illustrate this with a graph. V = vertical axis; t = horizontal axis : You can prove this: t = 30 hr At 30 hrs the depth would be 30*8" = 240" = 20 feet (40-20) Find the volume at 20ft V = V = 6283 cu ft : Using the equation/graph v = (30) + 12566 v = 6283 cu ft : Did this sense to you? I am not sure what kind of sketch they have in mind, I'll leave that up to you.
 Distributive-associative-commutative-properties/160420: This question is from textbook saxon algebra 2 Write a function that represents the data set (-4, 9), (0, 1), (1, -1), (3, -5), (4, -7).1 solutions Answer 118359 by ankor@dixie-net.com(15649)   on 2008-10-05 15:55:38 (Show Source): You can put this solution on YOUR website!Write a function that represents the data set (-4, 9), (0, 1), (1, -1), (3, -5), (4, -7). Assuming this is linear, use the 1st and last coordinates to find the slope: x1=-4; y1=9 x2=+4; y2=-7 : The slope formula: m = Find the slope: m = = m = : m = = -2 : Use the slope intercept formula: y - y1 = m(x - x1) y - 9 = -2(x - (-4)) : y - 9 = -2(x + 4) : y - 9 = -2x - 8 : y = -2x - 8 + 9 : y = -2x + 1 or f(x) = -2x + 1 : You can check and see if this fits the data set
 Quadratic_Equations/160309: The speed of an airplane in still air is 243 mph. The plane travels 663 mi against the wind and 1735 mi with the wind in a total time of 10 hr. What is the speed of the wind?1 solutions Answer 118358 by ankor@dixie-net.com(15649)   on 2008-10-05 15:25:40 (Show Source): You can put this solution on YOUR website!The speed of an airplane in still air is 243 mph. The plane travels 663 mi against the wind and 1735 mi with the wind in a total time of 10 hr. What is the speed of the wind? : Let x = speed of the wind then (243-x) = speed against the wind and (243+x) = speed with the wind ; Write a time equation Time = : + = 10 : Multiply equation by (243-x)(234+x); results: 663(243+x) + 1735(243-x) = 10(243-x)(243+x) : 161109 + 663x + 421605 - 1735x = 10(59049 - x^2) : 582714 - 1072x = 590490 - 10x^2 Arrange as a quadratic equation on the left: +10x^2 - 1072x + 582714 - 590490 = 0 : 10x^2 - 1072x - 7776 = 0 : Have to use the quadratic formula for this nasty equation a=10; b= -1072; c=-7776 : The positive solution x ~ 114 mph is the speed of the wind : : Check solution by finding the total time: 663/(243-114) = 5.14 hr 1735/(243+114)= 4.86 hrs -------------------------- total time = 10.00 hrs
 Trigonometry-basics/160353: The hour hand of a clock is 4 inches long while the minute hand is 5 inches long. At some time between 12:15 PM and 12:30 PM, the tips of the hands are 8 inches apart. What time is it then? (Answer to the nearest second.)1 solutions Answer 118327 by ankor@dixie-net.com(15649)   on 2008-10-05 11:11:12 (Show Source): You can put this solution on YOUR website!The hour hand of a clock is 4 inches long while the minute hand is 5 inches long. At some time between 12:15 PM and 12:30 PM, the tips of the hands are 8 inches apart. What time is it then? (Answer to the nearest second.) : Find the angle (A) between the hands using the law of cosines: : b^2 + c^2 -2(bc)Cos(A) = a^2 Let a=8, b=4, c=5 : 4^2 + 5^2 - 2(4*5)Cos(A) = 8^2 16 + 25 - 2(20)Cos(A) = 64 41 - 40Cos(A) = 64 -40Cos(A) = 64-41 Cos(A) = A = 125.1 degrees is the angle between the hands : Let m = minutes hand position : 6m = degrees per min : Hour hand moves 360/12 = 30 degrees per hr : An equation Hrs degrees + 125.1 degrees = minutes degrees *30 = 125.1 = 6m : + 125.1 = 6m Multiply equation by 2 m + 250.2 = 12m : 250.2 = 12m - m : 250.2 = 11m m = m = 22.927 min or 22 min + .927(60) = 22 min 56 sec
 test/160346: hey, could you please solve the following question, thanks, The graph of function y= x^2 - kx + k + 8 touches the x-axis at one point. What is the value of k? I will be waiting for the solution, and thanks again, 1 solutions Answer 118307 by ankor@dixie-net.com(15649)   on 2008-10-04 21:17:49 (Show Source): You can put this solution on YOUR website!The graph of function y= x^2 - kx + k + 8 touches the x-axis at one point. What is the value of k? : we use the discriminant: b^2 - 4*a*c = 0; when it touches one point on the x axis (a double root) : in this equation a=1, b=k, c=(k+8) Substitute: k^2 - 4*1*(k+8) = 0 k^2 - 4k - 32 = 0 Factor (k-8)(k+4) = 0 Two solutions k = 8 k = -4 : for k=8 x^2 - 8x + 8 + 8 = 0 x^2 - 8x + 16 = 0; which is(x-4)^2 a double root at x=4 and for k=-4 x^2 -(-4)x + (-4) + 8 = 0 x^2 + 4x + 4 = 0; which is(x+2)^2 a double root at x=-2 : : Did that help?
 Travel_Word_Problems/159972: A boat heads upstream a distance of 30 miles on the Mississippi river, whose current is running at 5 miles per hour. If the trip back takes an hour less, what was the speed of the boat in still water?1 solutions Answer 118305 by ankor@dixie-net.com(15649)   on 2008-10-04 20:45:37 (Show Source): You can put this solution on YOUR website!A boat heads upstream a distance of 30 miles on the Mississippi river, whose current is running at 5 miles per hour. If the trip back takes an hour less, what was the speed of the boat in still water? : Let s = speed of the boat in still water then (s-5) = speed upstream and (s+5) = speed downstream : : Write a time equation: Time = : Time up = time down - 1 hr = + 1 : Multiply equation by (s+5)(s-5); results: 30(s+5) = 30(s-5) + (s+5)(s-5) : 30s + 150 = 30s - 150 + (s^2-25) : Combine like terms on the right 0 = s^2 + 30s - 30s - 25 - 150 - 150 : 0 = s^2 - 325 : s^2 = +325 s = s = 18 mph boat speed in still water : : Check solution by finding the time for each 30/13 = 2.3 hr 30/23 = 1.3 hr ---------------- differ = 1 hr
 Linear-systems/160343: -11x = 395 + y 14y = -634 - 10x I need to solve this system of linear equations using any method. I'd like to see the steps and the correct answer. I'm not sure which method would be the easiest and I'm just stuck. Thank you for all your help.1 solutions Answer 118301 by ankor@dixie-net.com(15649)   on 2008-10-04 20:12:10 (Show Source): You can put this solution on YOUR website!-11x = 395 + y 14y = -634 - 10x : Any method is tedious here, arrange the equations, thusly: -11x - y = 395 +10x +14y = -634 : Multiply the 1st equation by 14 -154x - 14y = 5530 + 10x + 14y = -634 ---------------------addition eliminates y, find x -144x + 0y = 4896 x = x = -34 : Find y using the 2nd original equation 14y = -634 - 10(-34) 14y = -634 + 340 14y = -294 y = y = -21 : : Check solutions in the 1st original equation: -11x = 395 + y -11(-34) = 395 + (-21) +374 = 395 - 21 374 = 374; equality reigns
 Polynomials-and-rational-expressions/160326: an open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determine the dimensions of the squares to be cut to create a box with a volume of 1040cm^31 solutions Answer 118266 by ankor@dixie-net.com(15649)   on 2008-10-04 16:29:58 (Show Source): You can put this solution on YOUR website!An open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determine the dimensions of the squares to be cut to create a box with a volume of 1040cm^3 : Let the side of the removed squares = x : The dimension of the box will be: (24-2x) by (30-2x) by x (height) : A volume equation, L * W * H (24-2x) * (30-2x) * x = 1040 FOIL (720 - 48x - 60x + 4x^2) * x = 1040 : Multiply by x; 720x - 108x^2 + 4x^3 = 1040 ; 4x^3 - 108x^2 + 720x - 1040 = 0 : Simplify; divide by 4: x^3 - 27x + 180x - 260 = 0 : Graphing this would be one way to solve this : ; x = 2 cm would work : L: 30-4 = 26 cm W: 24-4 = 20 cm H: 2 cm : Check the volume (26*20*2 = 1040 : You can see there is another solution on the graph: x ~ 7.4 The dimensions for that would be L: 30-14.8 = 15.2 W: 24-14.8 = 9.2 H: 7.4 cm : Check vol with this: 15.2*9.2*7.4 = 1035.8 (because not an integer)
 Complex_Numbers/160308: (10+i)^2 / 4-i thanks for the help!1 solutions Answer 118264 by ankor@dixie-net.com(15649)   on 2008-10-04 15:50:27 (Show Source): You can put this solution on YOUR website! ; Foil (10+i)(10+i) = = : Multiply by the conjugate of the denominator over itself * = = = : Minus a minus is a plus (denominator) = = +
 Functions/160322: How do you factor completely: 5x^2 - 10x? What's the answer?1 solutions Answer 118263 by ankor@dixie-net.com(15649)   on 2008-10-04 15:44:18 (Show Source): You can put this solution on YOUR website!How do you factor completely: 5x^2 - 10x? What's the answer? : you can factor out 5x 5x(x-2)
 Polynomials-and-rational-expressions/160302: This question is from textbook Algerbra and Trigonometry structure and method two ships leave port, one sailing east and the other south. Some time later they are 17 miles apart, with the eastbound ship 7 miles further from the port than the southbound ship. how far is each from port?1 solutions Answer 118254 by ankor@dixie-net.com(15649)   on 2008-10-04 14:09:44 (Show Source): You can put this solution on YOUR website!two ships leave port, one sailing east and the other south. Some time later they are 17 miles apart, with the eastbound ship 7 miles further from the port than the southbound ship. how far is each from port? : If you look at this, you can see that the hypotenuse of a right triangle is the distance between the ships. The two legs are the distance from the ships to port A rough diagram will make it easy to understand. : Let x = distance of the southbound ship from port then (x+7) = distance of the eastbound ship from port : Hypotenuse = 17 mi : x^2 + (x+7)^2 = 17^2 ; FOIL (x+7)(x+7) x^2 + (x^2 + 14x + 49) = 289 : Arrange as a quadratic equation which we can solve: x^2 + x^2 + 14x + 49 - 289 = 0 : 2x^2 + 14x - 240 = 0 : Simplify, divide by 2 x^2 + 7x - 120 = 0 : Factor (x - 8)(x + 15) = 0 : Positive solution x = 8 mi is southbound ship and 8 + 7 = 15 mi is the eastbound ship : : Check solution in pythag 8^2 + 15^2 = 17^2 64 + 225 = 298 : Did this make sense? Any questions? :
 Rate-of-work-word-problems/160276: One job. two power shovels excavate 20,000 cubic meters of earth, the larger shovel working for 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each move in 1 hour working alone? 1 solutions Answer 118248 by ankor@dixie-net.com(15649)   on 2008-10-04 13:13:50 (Show Source): You can put this solution on YOUR website!One job. two power shovels excavate 20,000 cubic meters of earth, the larger shovel working for 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each move in 1 hour working alone? : Let x = large shovel amt of earth moved in 1 hr Let y = small shovel amt in 1 hr ; Write an equation for each project: 40x + 35y = 20000 70x + 90y = 40000 : Simplify, divide the 1st equation by 5, and the 2nd equation by 10 8x + 7y = 4000 7x + 9y = 4000 : Multiply the 1st equation by 7 and the 2nd equation by 8 56x + 49y = 28000 56x + 72y = 32000 ----------------------subtraction eliminates x 0x - 23y = - 4000 y = y ~ 174 yds/hr, the small shovel : Find x using; 7x + 9y = 4000 7x + 9(174) = 4000 7x = 1566 = 4000 7x = 4000 - 1566 7x = 2434 x = x ~ 348 yds/hr, the large shovel : : Check solution in 1st original equation: 40x + 35y = 20000 40(348) + 35(174) = 13920 + 6090 = 200010 ~ 20000