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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^2-1 1 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

Graphs/360987: My home work ? is a firm produces both am and am/fm car radios. the am radios take 15 hours to produce and the am/fm radios take 20 hours to produce. the number of production hours is limited to 300 hours per week. the plant's capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 am radios and at least 3 am/fm radios br produced per week. Write a system of inequalities reppresenting the situation. In this case let x = am radios and y = am/fm radios. (use LTE for less than or equal to and GTE for greater than or equal to) I'm so lost. 1 solutions Answer 257572 by ankor@dixie-net.com(15660)   on 2010-10-24 21:45:45 (Show Source): You can put this solution on YOUR website! This same problem came up a few weeks ago. This is what I submitted then. Perhaps it will help you A small firm produces both AM and AM/FM car radios. The AM radios take 15 h to produce, and the AM/FM radios take 20 h. The number of production hours is limited to 300 h per week. The plant's capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 AM radios and at least 3 AM/FM radios be produced per week. Write a system of inequalities representing this situation. : Let x = number of AM radios; let y = number of AM/FM radios The production hour constraint: 15x + 20y =< 300 : Plant's capacity constraint: x + y =< 18 : Min AM radio production constraint: x => 4 Min AM/FM radio production constraint y => 3 : How about this, did it all make some sense to you?

Linear-equations/360818: Find a real number, n , such that the line containing the points (-6,3) and (-2,6) contains the point (n,5) 1 solutions Answer 257553 by ankor@dixie-net.com(15660)   on 2010-10-24 21:04:13 (Show Source): You can put this solution on YOUR website! Find a real number, n , such that the line containing the points (-6,3) and (-2,6) contains the point (n,5) ; Find the slope of the given points, where: x1=-6; y1=3 x2=-2; y2=6 : slope m = : m = = : Find the equation using the point/slope form y - 3 = (x - (-6)) y - 3 = (x + 6) y - 3 = x + 4.5 y = x + 4.5 + 3 y = x + 7.5 or y = .75x + 7.5 : Find n, .75n + 7.5 = 5 .75n = 5 - 7.5 .75n = -2.5 n = n = -3 when y = 5

Expressions-with-variables/360785: One race car travels at 200 miles per hour and has a 30 minute head start. The second race car travels at 763 milers per hour. At what distance with the faster car catch the slower car? 1 solutions Answer 257462 by ankor@dixie-net.com(15660)   on 2010-10-24 15:43:14 (Show Source): You can put this solution on YOUR website! One race car travels at 200 miles per hour and has a 30 minute head start. The second race car travels at 763 milers per hour. At what distance with the faster car catch the slower car? : Wow, 763 mph, isn't that about the speed of sound, anyway : Let t = time required for it to catch the slower car then (t + .5) - travel time of the slower car : When this happens the two cars will have traveled the same distance : Write a dist equation, dist = speed * time : 763t = 200(t+.5) 763t = 200t + 100 763t - 200t = 100 563t = 100 t = t = .1776 hrs : Find the dist: .1776*763 = 135.5 miles, the faster car catches the slower car. : confirm this using the slower car 200(.1776+.5) = 135.5 mi also

test/360684: John drove southeast from Albuquerque to Roswell and then south to Carlsbad. He averaged 75 mph along the route from Albuquerque to Roswell and averaged 70 mph from Roswell to Carlsbad. He covered the entire 220 miles in 3 hours. How long did he take to drive from Albuquerque to Roswell? 1 solutions Answer 257460 by ankor@dixie-net.com(15660)   on 2010-10-24 15:30:04 (Show Source): You can put this solution on YOUR website! John drove southeast from Albuquerque to Roswell and then south to Carlsbad. He averaged 75 mph along the route from Albuquerque to Roswell and averaged 70 mph from Roswell to Carlsbad. He covered the entire 220 miles in 3 hours. How long did he take to drive from Albuquerque to Roswell? : Let t = travel time from A to R then (3-t) = travel time from R to C : Write a distance equation; dist = speed * time : A-R dist + R-C dist = 220 miles 75t + 70(3-t) = 220 75t + 210 - 70t = 220 75t - 70t = 220 - 210 5t = 10 t = 2 hrs from A to R : : Check solution by finding the total dist R to C time 3 - 2 = 1 hr 2(75) + 1(70) = 220 mi

Rational-functions/360405: A rectangular garden, 21m^2 in area, will be fenced to keep out rabbits and skunks. Find the dimensions that will require the least amount of fencing if a barn already protects one side of the garden. 1 solutions Answer 257393 by ankor@dixie-net.com(15660)   on 2010-10-24 10:42:05 (Show Source): You can put this solution on YOUR website! A rectangular garden, 21m^2 in area, will be fenced Find the dimensions that will require the least amount of fencing if a barn already protects one side of the garden. : Let x = the width Let L = the length : since the barn is one side the perimeter: p = L + 2x : The given area: L * x = 21 L = : Replace L in the perimeter equation with p = + 2x : Graph this on a graphing calc, find the minimum (p = the y axis) min: x = 3.24 meters is the width L = L = 6.48 meters is the width : Sumarize, a garden of 6.48 by 3.24 meter gives 21 sq/m using minimum fencing. (About 13 meters of fencing) : : Check this, find the area with these dimensions 6.48 * 3.24 = 20.99 ~ 21

Linear-equations/360482: Find "k" if the line 3x+ky=5 is parallel to the line 2x-7y=4. 1 solutions Answer 257287 by ankor@dixie-net.com(15660)   on 2010-10-23 21:38:33 (Show Source): You can put this solution on YOUR website! Find "k" if the line 3x+ky=5 is parallel to the line 2x-7y=4. Find the slope of 2x - 7y = 4, put in the slope/intercept form -7y = -2x + 4 7y = 2x - 4; multiplied by -1 y = x - : slope = we know parallel lines have the same slope : put 3x + ky = 5 in the slope/intercept form ky = - 3x + 5 y = x + : slopes are equal therefore: = cross multiply 2k = -3 * 7 2k = -21 k =

Numeric_Fractions/360485: 2^(x)-2^(x-1)=32 x=? answ is x=6 but i want to know the solution? 1 solutions Answer 257271 by ankor@dixie-net.com(15660)   on 2010-10-23 20:06:22 (Show Source): You can put this solution on YOUR website! same as or just multiply by 2 to get rid of the denominator, results: now we have like terms so we can just subtract, results: therefore x = 6

Equations/360455: Hello, i'm working on algebra it's about this equation c=$535+4.50n and i don't get what this question is asking for in this For each equation, find the coordinates of a point that lies on the graph of the equation. what does that mean?? 1 solutions Answer 257229 by ankor@dixie-net.com(15660)   on 2010-10-23 18:20:27 (Show Source): You can put this solution on YOUR website! c = $535 + 4.50n In this equation, the cost (c) = $4.50 for each item (n) + a fixed cost of $535 : Say you want the cost for 10 items, then n = 10, substitute 10 for n in the given equation c = 535 + 4.50(10) c = 535 + 45.00 c = $580 is the total cost for 10 items : The coordinates would be 10, 985, on a graph x=10, y=985 : A graph of this equation, shows that when n = 10, cost = 580 : Did I shed some light on this for you here?

Exponential-and-logarithmic-functions/360521: Solve for x: log20x+log20(x+1)=1 x= ? x=? can i have exact details so i know how to do this later with other problems? please.. and thanks 1 solutions Answer 257221 by ankor@dixie-net.com(15660)   on 2010-10-23 17:49:25 (Show Source): You can put this solution on YOUR website! Solve for x: log20(x)+log20(x+1)=1 : adding logs means multiply so we can write it: log20(x(x+1)) = 1 : Which is log20(x^2+x) = 1 : Write the exponent equiv of logs 20^1 = (x^2 + x) 20 = x^2 + x 0 = x^2 + x - 20; a quadratic equation Factor to (x+5)(x-4) = 0 x= -5 x= +4, this is the only solution, can't have a log of a negative number : : Check solution x=4 in the original problem log20(4)+log20(4+1)=1 log20(4)+log20(5)=1 log20(4*5) log20(20) = 1, obviously

Graphs/360454: Hello, if you could help me with a problem I would be ever so grateful! I do not know where to start on this one. I have reviewed my notes but cannot seem to figure it out. Write an equation of the line containing a given point and perpendicular to the given line. (6,7); 4x + y =5 Thank you for any assistance you can give. 1 solutions Answer 257217 by ankor@dixie-net.com(15660)   on 2010-10-23 16:53:32 (Show Source): You can put this solution on YOUR website! Write an equation of the line containing a given point and perpendicular to the given line. (6,7); 4x + y = 5 : Find the slope of the given equation by putting it in the slope intercept form 4x + y = 5 y = -4x + 5 slope (m1) = -4 : The relationship of the slopes of perpendicular lines is m1*m2 = -1 We know m1, find m2 -4*m2 = -1 Divide both sides by -4 m2 = +, this is slope of the equation we are looking for : Use the point/slope form here: y - y1 = m(x-x1) Given: x1=6, y1=7 y - 7 = (x - 6) y - 7 = x - y = x - + 7 y = x - + y = x + let's just call it y = x + 5.5; is the equation (green) and passes thru 6.7 : : We can see this on a graph

Proportions/360415: It took Lance and Ivan 6 hours to travel 33 miles downstream by canoe.The next day the travelled upstream for 8 hours for 20 miles.What was the rate of the current? What was their average speed in still water? 1 solutions Answer 257206 by ankor@dixie-net.com(15660)   on 2010-10-23 16:05:25 (Show Source): You can put this solution on YOUR website! It took Lance and Ivan 6 hours to travel 33 miles downstream by canoe. The next day the traveled upstream for 8 hours for 20 miles. What was the rate of the current? What was their average speed in still water? : Let s = their speed in still water Let c = rate of the current then (s+c) = effective speed downstream and (s-c) = effective speed upstream : Write two distance equations, dist = time * speed : 6(s+c) = 33 8(s-c) = 20 which is 6s + 6c = 33 8s - 8c = 20 : Use elimination here, multiply the 1st equation by 8, the 2nd equation by 6 48s + 48c = 264 48s - 48c = 120 -------------------addition eliminates c, find s 96s = 384 s = s = 4 mph in still water : Find s: using: 6s + 6c = 33 6(4) + 6c = 33 6c = 33 - 24 6c = 9 c = c = 1.5 mph is the current : : Check these solutions in the 2nd equation 8(s-c) = 20 8(4 - 1.5) = 8 * 2.5 = 20; confirms our solutions

Radicals/360439: Hello, I need help with solving a problem. I am doing rational and radical exponents. The problem is (-27x^9)^1/3. Whoever help me I thank you very much. Because I have tried figuring this problem out since yesterday and no luck. Thanks again so much for your help and time. 1 solutions Answer 257190 by ankor@dixie-net.com(15660)   on 2010-10-23 13:57:17 (Show Source): You can put this solution on YOUR website! To get rid of the brackets, multiply both term's exponents inside the brackets by the exponent outside the brackets. -27 is understood to have an exponent of 1 = = we know the cube root of -27 = -3, therefore is the answer

Square-cubic-other-roots/360436: How to work out (-5-√-100)^2 Answer -75+100i How to get the answer without calculator 1 solutions Answer 257187 by ankor@dixie-net.com(15660)   on 2010-10-23 13:46:07 (Show Source): You can put this solution on YOUR website! (-5-√-100)^2 FOIL (-5-√-100)*(-5-√-100) = which is = = -75 + 10i*10 = -75 + 100i

Travel_Word_Problems/360337: In a diagram, a man is in a rowboat at point A, which is located 3 miles from point B, the closest point to A on a straight shoreline. The man needs to get to point C, on the same shoreline, 10 miles from B. If the man travels on water at a rate of 1/2 miles per hour and travels on land at a rate of 3/2 miles per hour, where should he land the boat in order to arrive at point C in the SHORTEST amount of time? 1 solutions Answer 257182 by ankor@dixie-net.com(15660)   on 2010-10-23 13:15:02 (Show Source): You can put this solution on YOUR website! In a diagram, a man is in a rowboat at point A, which is located 3 miles from point B, the closest point to A on a straight shoreline. The man needs to get to point C, on the same shoreline, 10 miles from B. If the man travels on water at a rate of 1/2 miles per hour and travels on land at a rate of 3/2 miles per hour, where should he land the boat in order to arrive at point C in the SHORTEST amount of time? : Let x = the distance from point B where the boat lands on the shore then (10-x) = the walking distance to point C : The rowing distance will be the hypotenuse, with sides x and 3 Rowing distance = : A time equation, Time = dist/speed Use .5 mph for rowing speed and 1.5 mph for walking speed : Total time = rowing time + walking time t = + : Graph the above equation, time on the y axis Using a graphing calc, min: x=1.06, y=12.32 hrs : He should land the boat and walk 1.06 mi from A, for shortest travel time (12.32 hrs)