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 Quadratic_Equations/363678: Need help with the problem below Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.1x^2-1.9x + 9.739, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?1 solutions Answer 259389 by ankor@dixie-net.com(15660)   on 2010-10-29 21:05:45 (Show Source): You can put this solution on YOUR website!Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.1x^2-1.9x + 9.739, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle : C(x)=0.1x^2-1.9x + 9.739 This is a quadratic equation, we can find the minimum by finding the axis of symmetry. x = -b/(2a); in this equation a=.1; b=-1.9 x = x = x = 9.5 which is 950 bicycles will give minimum cost : If you substitute 9.5 in the equation, you can find the cost per bicycle C(x) = .714, that's \$71.40 is the minimum cost
 Angles/363558: The measure of angle B is 5 times the measure of its supplement. Find the measure of angle B. Please Help me figure this out. -(christopher_pchc@yahoo.com) Thank you. 1 solutions Answer 259307 by ankor@dixie-net.com(15660)   on 2010-10-29 15:43:24 (Show Source): You can put this solution on YOUR website!The measure of angle B is 5 times the measure of its supplement. Find the measure of angle B. : The supplement of angle b = (180-b) therefore the equation: b = 5(180-b) b = 900 - 5b b + 5b = 900 6b = 900 b = b = 150 degrees
 Age_Word_Problems/363543: The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a skeleton that has lost 40% of its carbon-14? Note: Do not round any numbers during your calculation. 1 solutions Answer 259298 by ankor@dixie-net.com(15660)   on 2010-10-29 15:28:04 (Show Source): You can put this solution on YOUR website!The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a skeleton that has lost 40% of its carbon-14? Note: Do not round any numbers during your calculation. : Using the half-life formula: A = Ao*2^(-t/h) Where A = resulting amt after t yrs Ao = initial amt t = time h = half-life of substance : Assume the initial amt = 1, remaining amt after t yrs = .6 : 1*2^(-t/5750) = .6 using nat logs ln(2) = ln(.6) = ln(2) = -.736955942 t = -5750 * -.736955942 t = 4,237.55 yrs
 Numbers_Word_Problems/363308: solve. The larger of two consecutive integers is 10 more than 4 times the smaller. Fine the integers. i know the answer is possibly -3,-2, but i dont know how to work the problem out to get the answers, please explain,show your work...1 solutions Answer 259279 by ankor@dixie-net.com(15660)   on 2010-10-29 14:25:30 (Show Source): You can put this solution on YOUR website!The larger of two consecutive integers is 10 more than 4 times the smaller. Find the integers. : The two integers, x and (x+1) which is the larger x + 1 = 4x + 10 1 - 10 = 4x - x -9 = 3x x = x = -3, is the smaller and -2 is the larger : : Check -3 + 1 = 4(-3) + 10 -2 = -12 + 10
 Word_Problems_With_Coins/363305: A girl has nickels and quarters in her bank.She has four fewer nickels than quarters.she has \$3.70 in her bank . How many coins of each type does she have?1 solutions Answer 259277 by ankor@dixie-net.com(15660)   on 2010-10-29 14:17:26 (Show Source): You can put this solution on YOUR website!let n = no. of nickels let q = no. or quarters : Write an equation for each statement: : "She has four fewer nickels than quarters." n = q - 4 : "she has \$3.70 in her bank." .05n + .25q = 3.70 : Use substitution here, replace n with (q-4), find q .05(q-4) + .25q = 3.70 .05q - .20 + .25q = 3.70 .05q + .25q = 3.70 + .20 .30q = 3.90 q = q = 13 quarters then n = 13 - 4 n = 9 nickels : : Check: .05(9) + .25(13) = .45 + 3.25 = 3.70
 Volume/362722: I need help I have a square that is divided into 4 triangles one in each corner the triangles measure 12inches on each side and 17inches at the base I need to know the total area those 4 triangles make up. 1 solutions Answer 259273 by ankor@dixie-net.com(15660)   on 2010-10-29 14:08:39 (Show Source): You can put this solution on YOUR website!I need help I have a square that is divided into 4 triangles one in each corner the triangles measure 12inches on each side and 17inches at the base I need to know the total area those 4 triangles make up. : Wouldn't it just be the area of the square, 17^2 = 289 sq/inches
 Rational-functions/363229: Simplify 4 over x^2-5x+4 - 5 over x^2-11 solutions Answer 259259 by ankor@dixie-net.com(15660)   on 2010-10-29 12:28:32 (Show Source): You can put this solution on YOUR website!Simplify - we can factor both denominators - The common denominator will be (x-4)(x+1)(x-1), so we have = = ; about all we can do with it
 Radicals/363260: The diagram shows an isosceles right triangle. The two legs are "x," and the hypotenuse is x radical 2. A. If its perimeter is 10, find x. B. If its area is 12, find x.1 solutions Answer 259241 by ankor@dixie-net.com(15660)   on 2010-10-29 10:51:03 (Show Source): You can put this solution on YOUR website!The diagram shows an isosceles right triangle. The two legs are "x," and the hypotenuse is x radical 2. : A. If its perimeter is 10, find x. x + x + = 10 2x + = 10 = -2x + 10 Square both sides x^2(2) = (-2x+10)^2 FOIL (-2x+10)*(-2x+10) 2x^2 = 4x^2 - 20x - 20x + 100 2x^2 = 4x^2 - 40x + 100 : Combine on the right 0 = 4x^2 - 2x^2 - 40x + 100 : A quadratic equation 2x^2 - 40x + 100 = 0 : Simplify, divide by 2 x^2 - 20x + 50 = 0 Use the quadratic formula to find x, a=1; b=-20; c=50 Two solutions x = 17.06 and x = 2.93 is the only reasonable solution Check 2(2.93) + = 10.00 : : B. If its area is 12, find x. .5(x*x) = 12 multiply both sides by 2 x^2 = 24 x = x = 4.9 : Check .5 * 4.9 * 4.9 = 12.0
 Travel_Word_Problems/363303: Traveling downstream, a boat can go 54 miles in 3 hours. Going upstream, it makes only half this distance in four times as long. What is the rate of the boat in still water, and what is the rate of the current?1 solutions Answer 259203 by ankor@dixie-net.com(15660)   on 2010-10-29 09:11:10 (Show Source): You can put this solution on YOUR website!Traveling downstream, a boat can go 54 miles in 3 hours. Going upstream, it makes only half this distance in four times as long. What is the rate of the boat in still water, and what is the rate of the current? : Let s = boat rate in still water Let c = rate of the current then (s+c) = effective speed downstream and (s-c) = effective speed upstream : Write a distance equation based on the statement (dist = time * rate): "Traveling downstream, a boat can go 54 miles in 3 hours." 3(s+c) = 54 Simplify, divide both sides by 3 s + c = 18 s = (18-c); use this form for substitution : Write a distance equation based on the statement: "Going upstream, it makes only half this distance in four times as long." (Time: 4(3) = 12, half the distance 54/2 = 27 mi) 12(s-c) = 27 12s - 12c = 27 Substitute (18-c) for s 12(18-c) - 12c = 27 216 - 12c - 12c = 27 -24c = 27 - 216 -24c = -189 c = c = +7.875 mph is the current then s = 18 - 7.875 s = 10.125 mph is rate in still water : : Check solution in the down stream equation 3(10.125 + 7.875) = 3(18) = 54 : Confirm this in the upstream equation 12(10.125-7.875) = 12(2.25) = 27, half the distance : : How about this, did it make sense to you?
 Miscellaneous_Word_Problems/363327: A semi- truck travels 360 miles through flatline in the same amount of time it travels 180 miles through the mountains. The rate of the truck is 25 miles per hour slower in the mountains than in the flatland. Find both the flatline rate and mountain rate.1 solutions Answer 259189 by ankor@dixie-net.com(15660)   on 2010-10-29 08:15:11 (Show Source): You can put this solution on YOUR website!A semi-truck travels 360 miles through flatland in the same amount of time it travels 180 miles through the mountains. The rate of the truck is 25 miles per hour slower in the mountains than in the flatland. Find both the flatland rate and mountain rate. : Let r = the slow rate through the mountains then (r+25) = the faster rate through flat areas : Write a time equation; time = dist/rate : Flat time = Mountain time = Cross multiply 360r = 180(r+25) 360r = 180r + 4500 360r - 180r = 4500 180r = 4500 r = 4500/180 r = 25 mph through the mountains then 25 + 25 = 50 mph on the flat : : Check solution by finding the actual times, they should be equal 360/50 = 7.2 hrs 180/25 = 7.2 hrs also
 logarithm/363287: Solve for the indicated variable a.m = aP-w for a b.2x – 3 = ax for x 1 solutions Answer 259105 by ankor@dixie-net.com(15660)   on 2010-10-28 21:44:31 (Show Source): You can put this solution on YOUR website!a. m = aP-w for a Write it: aP - w = m add w to both sides aP = m + w divide both sides by P a = : b. 2x – 3 = ax for x Subtract ax from both sides 2x - ax - 3 = 0 add 3 to both sides 2x - ax = 3 Factor out x x(2-a) = 3 Divide both sides by (2-a) x =
 Linear_Equations_And_Systems_Word_Problems/363112: Help please! An ice cube that measures 5 centimeters on each side contains how many cubic centimeters of ice? Include units with solution. Find the exact value of the volume of a can of oil with a diameter 10 centimeters and height of 14 centimeters. Include units and use "pi" in the place of the pi symbol. 1 solutions Answer 259093 by ankor@dixie-net.com(15660)   on 2010-10-28 21:16:39 (Show Source): You can put this solution on YOUR website!An ice cube that measures 5 centimeters on each side contains how many cubic centimeters of ice? Include units with solution. 5 * 5 * 5 = 125 cu/cm of ice : Find the exact value of the volume of a can of oil with a diameter 10 centimeters and height of 14 centimeters. Vol = pi*r^2*h radius = 5 cm : V = pi * 5^2 * 14 V = pi * 25 * 14 V ~ 1099.557429 cu/cm is the volume of the can
 Linear_Algebra/363036: A line passes through the points (k=3,-2k) and (4,1) and has a y-intercept of 6. Find the value of k.1 solutions Answer 259082 by ankor@dixie-net.com(15660)   on 2010-10-28 21:00:46 (Show Source): You can put this solution on YOUR website!Assume the question is: A line passes through the points (k+3,-2k) and (4,1) and has a y-intercept of 6. Find the value of k. : Assign the given points as follows x1=(k+3); y1=-2k x2=4; y2=1 : Find the slope using these points: m = m = = is the slope : Write the slope intercept form y = x + 6 Substitute 4 for x and 1 for y; solve for k (4) + 6 = 1 = 1 - 6 = -5 multiply both sides by (1-k), results 4 + 8k = -5(1-k) 4 + 8k = -5 + 5k 8k - 5k = -4 - 4 3k = -9 k + k = -3 : Check solution find the value of the 1st pair as given: (k+3,-2k) -3+3, -2(-3) = 0, 6
 Travel_Word_Problems/363068: Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1070 m due east and then turns due north and travels another 1430 m before reaching the campground. The second cyclist starts out by heading due north for 1800 m and then turns and heads directly toward the campground. At the turning point, how far is the second cyclist from the campground? 1 solutions Answer 258924 by ankor@dixie-net.com(15660)   on 2010-10-28 15:21:57 (Show Source): You can put this solution on YOUR website!Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1070 m due east and then turns due north and travels another 1430 m before reaching the campground. The second cyclist starts out by heading due north for 1800 m and then turns and heads directly toward the campground. At the turning point, how far is the second cyclist from the campground? : Draw the diagram of this, it will be apparent that a right triangle is formed: side 1 = 1070 side 2: 1800 - 1430 = 370 Hypotenuse (h) = 2nd cyclist turning point to camp ground h = h = 1132.166 meter from turning point to camp ground
 Average/363024: if the average score of 20 students is 85 and 14 students got more than 85 then what is the lowest score that a student can achieve out of the remaining 6 students?1 solutions Answer 258881 by ankor@dixie-net.com(15660)   on 2010-10-28 13:51:36 (Show Source): You can put this solution on YOUR website!if the average score of 20 students is 85 and 14 students got more than 85 then what is the lowest score that a student can achieve out of the remaining 6 students? : = 85 multiply both sides by 20 14(86) + 6x = 20(85) 1204 + 6x = 1700 6x = 1700 - 1204 6x = 496 x = x = 82.67 is the average of the remaining 6 : The lowest 1 student can have to maintain this average Assume the other 5 students got 85 each = 82.76 multiply both sides by 6 5(85)+ x = 6(82.67) 425 + x = 496 x = 496 - 425 x = 71 is the lowest score for one student to have
 Numbers_Word_Problems/362684: Solve, Show your work to help me understand. The length of a rectangle is 3 times the width. if the length is increased by 4cm and the width is decreased by 1cm, the perimeter will be 102cm. Find the dimensions of the origional rectangle.1 solutions Answer 258870 by ankor@dixie-net.com(15660)   on 2010-10-28 13:04:20 (Show Source): You can put this solution on YOUR website!The length of a rectangle is 3 times the width. if the length is increased by 4cm and the width is decreased by 1cm, the perimeter will be 102cm. Find the dimensions of the original rectangle. : Let x = the width of the original rectangle It says, "length of a rectangle is 3 times the width."; so we have; 3x = the length of the original rectangle then (3x + 4) = length of the new rectangle and (x-1) = width of the new rectangle : Perimeter of the new rectangle: 2(3x+4) + 2(x-1) = 102 Simplify, divide by 2 and we have: 3x + 4 + x - 1 = 51 4x + 3 = 51 4x = 51 - 3 4x = 48 x = x = 12 cm is the original width then 3(12) = 36 cm is the original length : : Check the perimeter with these values 2(36+4) + 2(12-1) = 2(40) + 2(11) = 102, confirms our solutions
 Travel_Word_Problems/362933: The river boat Delta Duchess paddled upstream at 12 km/h, stopped for 2 h of sightseeing, and paddled back at 18 km/h. How far upstream did the boat travel if the total time for the trip, including the stop, was 7 h?1 solutions Answer 258864 by ankor@dixie-net.com(15660)   on 2010-10-28 12:34:36 (Show Source): You can put this solution on YOUR website!The river boat Delta Duchess paddled upstream at 12 km/h, stopped for 2 h of sightseeing, and paddled back at 18 km/h. How far upstream did the boat travel if the total time for the trip, including the stop, was 7 h? : We are only interested the in the actual travel time which is 5 hrs : Let d = distance traveled upstream (also return distance downstream) : Write a time equation; time = dist/speed : time up + time back = 5 hrs + = 5 Multiply by 36 to clear the denominators, results: 3d + 2d = 36(5) 5d = 180 d = 36 miles upstream : Check solution by finding the time for each way + = 3 + 2 = 5 hrs