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# Recent problems solved by 'fractalier'

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 Volume/38271: If the circumference of a right circular cylinder is 18pi(don't have pi on the keyboard) and the height of the cylinder is 8, then find the volume to the nearest tenth. I found the radius of the circle to be 9, but when i find the volume of the cylinder i get 2287.1, which isn't one of my choices.1 solutions Answer 23747 by fractalier(2101)   on 2006-05-17 17:18:29 (Show Source): You can put this solution on YOUR website!The volume of a right circular cylinder is V = (pi)(r^2)h If the circumference is 18(pi), then yes, the radius is 9. Plug in what we know and get... V = (pi)(9^2)(8) V = 648(pi) V = 2035.8 You must have calculated incorrectly.
 Linear_Equations_And_Systems_Word_Problems/38274: Doug can deliver his pspers in 45 minutes. If Meg helps, they can finish in 20 minutes. How long will it take Meg to work alone?1 solutions Answer 23745 by fractalier(2101)   on 2006-05-17 17:13:36 (Show Source): You can put this solution on YOUR website!The normal equation for this kind of equation is t/A + t/B = 1 where t is the time working together A is the time it takes the first person working alone B is the time it takes the second person working alone and the 1 represents one whole job to do... Now plug in and solve for B 20/45 + 20/B = 1 multiply all by 45B to clear fractions 20B + 900 = 45B 900 = 25B B = 36 minutes
 Polynomials-and-rational-expressions/38275: The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. a) Write h as a function of r. b) What is the measurement of the height if the radius of the cylinder is 3 centimeters?1 solutions Answer 23744 by fractalier(2101)   on 2006-05-17 17:10:24 (Show Source): You can put this solution on YOUR website!Solved this exact problem earlier today...please scroll thru my answers amd you will find it...
 Linear_Equations_And_Systems_Word_Problems/38276: A dentisit can schedule 15 patients in a day if she allows 24 minutes per patient. How many can she schedule if she allows 30 minutes per patient and works the same number of hours?1 solutions Answer 23743 by fractalier(2101)   on 2006-05-17 17:09:30 (Show Source): You can put this solution on YOUR website!Here we can express the work done by the dentist in patient-minutes and can write a working equation as 15 * 24 = x * 30 or 30x = 360 and x = 12 patients
 Linear-equations/38277: Helen's Health Foods usually sells 400 cans of ProPac Muscle Punch per week when the price is \$5 per can. After experimenting with prices for some time, Helen has determined that the weekly demand can be found using the equation d=600 - 40p where d is the number of cans and p is the price per can. a) Will Helen sell mores or less Muscle Punch if she raises her prices from \$5? b) What happens to her sales every time she raises her price by \$1?1 solutions Answer 23742 by fractalier(2101)   on 2006-05-17 17:07:28 (Show Source): You can put this solution on YOUR website!If you examine the demand equation d = 600 - 40p you see that the demand goes DOWN (she sells less punch) as p goes UP We can rewrite it as d = -40p + 600 to put it into slope-intercept form. Here you can see the slope is -40. That means that for every increase of \$1 in p, the demand goes down 40.
 Triangles/38257: if the midpoints of the sides of a triangle are joined, is the area of the determined triangle half the area of the original trianle? i worked it for an isosceles triangle and it didn't come to half the area, but i dont know if it works for the other triangles1 solutions Answer 23740 by fractalier(2101)   on 2006-05-17 16:07:01 (Show Source): You can put this solution on YOUR website!The determined triangle is actually equal to 1/4 the area of the larger triangle...if you join the midpoints of two sides, it is called the median of triangle and equal to 1/2 the parallel and opposite side...since it is half as high and half as wide, it is 1/4 the area...
 Parallelograms/38258: if a rhombus is inscribed in a circle, would that make the diagonals congruent?1 solutions Answer 23734 by fractalier(2101)   on 2006-05-17 15:57:48 (Show Source): You can put this solution on YOUR website!Please see my earlier solution to this...the conclusion is that the rhombus would have to be a square, and squares have congruent diagonals...
 Equations/38219: Multiply. and write the answer in simplest form: 4 1/5 x 10/21 x 9/201 solutions Answer 23709 by fractalier(2101)   on 2006-05-17 12:56:16 (Show Source): You can put this solution on YOUR website!Make all of the fractions improper and cancel where you can...thus 4 1/5 x 10/21 x 9/20 = 21/5 x 10/21 x 9/20 = 1/5 x 10/1 x 9/20 = 18/20 = 9/10
 Quadratic_Equations/38221: Gail is a srever at a restaurant. ON saturday Gail gets up at 6.30.a.m, atrats work at x a.m & finishes at x p.m. How long does Gail work on saturday?1 solutions Answer 23708 by fractalier(2101)   on 2006-05-17 12:53:34 (Show Source): You can put this solution on YOUR website!Seems to me there's twelve hours between any time that a.m. and the same time that's p.m.
 Money_Word_Problems/38220: Paul invested \$5000 in a time deposit. What interest will he earn for 1 year if the interest rate is 6.5%?1 solutions Answer 23707 by fractalier(2101)   on 2006-05-17 12:51:35 (Show Source): You can put this solution on YOUR website!The formula is I = PRT, Interest = principal x rate x time, so I = \$5000(.065)(1) = \$325
 Numeric_Fractions/38218: Please help me solve for A: 2A/3=8+4A? Thanks1 solutions Answer 23706 by fractalier(2101)   on 2006-05-17 12:43:20 (Show Source): You can put this solution on YOUR website!Okay, from 2A/3 = 8 + 4A let us multiply both sides by 3 to clear the fractions 2A = 24 + 12A now subtract 12A from both sides -10A = 24 now divide both sides by -10 and reduce A = 24/-10 = -12/5
 Rational-functions/36949: Simplify using factoring and cancellation (y^3-19y-30)/(y+2)1 solutions Answer 23705 by fractalier(2101)   on 2006-05-17 12:40:29 (Show Source): You can put this solution on YOUR website!Though it is not easy to see, (y^3 - 19y - 30) / (y + 2) = (y + 2)(y^2 - 2y - 15)/ (y + 2) = y^2 - 2y - 15
 Polynomials-and-rational-expressions/37211: What is the degree of the polynomial 12xy^3-7y^2z^5+5x^6y-2X^2y^21 solutions Answer 23704 by fractalier(2101)   on 2006-05-17 12:32:13 (Show Source): You can put this solution on YOUR website!The degree of a polynomial is the the highest degree of any single term in the polynomial...thus for 12xy^3 - 7y^2z^5 + 5x^6y - 2x^2y^2 notice that both the second and third terms are of degree seven, so the polynomial is also of degree seven...
 Linear_Equations_And_Systems_Word_Problems/37658: This question is from textbook Tyrone is twice as old as his daughter. In six years Tyrone's age will be three times what his daughter's age was six years ago. How old are they present?1 solutions Answer 23703 by fractalier(2101)   on 2006-05-17 12:20:43 (Show Source): You can put this solution on YOUR website!Always set up variables for age problems NOW. That is, let T = Tyrone's age NOW and let D = his daughter's age NOW. Thus T = 2D and T + 6 = 3(D - 6) Substituting 2D + 6 = 3D - 18 D = 24 T = 48
 Triangles/38133: In triangle ABC if segment BC is one inch shoter than segment AB, segment AC is 10 inches shorter than the sum of segment BC and segment AB, and the perimeter of triangle ABC is 72 inches, find the length of segment BC. A) 20 in. B) 21 in. C) 31 in. D) 32 in.1 solutions Answer 23702 by fractalier(2101)   on 2006-05-17 12:15:52 (Show Source): You can put this solution on YOUR website!Let's call the length of AB, x. Thus the length of BC is x - 1. And the length of AC is x + (x - 1) - 10. Now if we add all the sides we get 72...so x + (x - 1) + (x + (x - 1) - 10) = 72 and 4x - 12 = 72 4x = 84 x = 21 and x - 1 = 20 is side BC Choice A.
 Quadratic-relations-and-conic-sections/38194: m^2 + 3n^2 = 11 m - n = 2 Conic - systems of two non-linear equations (two solutions) second question: y = x^2 and 7x = y + 12 (one solotion from these equations)1 solutions Answer 23701 by fractalier(2101)   on 2006-05-17 12:10:40 (Show Source): You can put this solution on YOUR website!These are both solved the same way. We solve the linear equation and substitute for it into the curve...thus from m^2 + 3n^2 = 11 m - n = 2 we have m = n + 2 now substituting we get (n + 2)^2 + 3n^2 = 11 n^2 + 4n + 4 + 3n^2 = 11 4n^2 + 4n - 7 = 0 This doesn't factor so use the quadratic and get n = (-4 ± sqrt(128)) / 8 n = (-4 ± 8sqrt(2)) / 8 n = (-1 ± 2sqrt(2)) / 2 This gives you 2 values for n. To find each corresponding value of m, merely plug into m = n + 2 and you'll have your points of intersection. The second problem is done the same way.
 Numeric_Fractions/38217: No real question, just a comment: I need to complete college algebra to get my B.A. degree, which I should have gotten years ago. I think I was mostly just scared off by the subject -- I had a terrible high school algebra teacher (mean, sexist, a lech). This site has been an ENORMOUS help to me, and to others, I'm sure. Thank you. I am attempting the easiest stuff first -- repeatedly -- to increase my comfort level and relearn the subject. It may take awhile but I finally feel I'll get there. I can tell this is second nature to you tutors, so I appreciate your patience in helping and explaining what seems to be very basic. Thanks again!1 solutions Answer 23700 by fractalier(2101)   on 2006-05-17 12:03:45 (Show Source): You can put this solution on YOUR website!Be glad to help you when I can. There are quite a few (hundreds, actually) sites where you can avail yourself of all kinds of assistance in algebra...this being a nice LIVE one...I make my students find 25 places online they can get help as one of their first homework assignments, no matter what math class I teach... I would suggest that you, too, make such a "favorites" list...
 Systems-of-equations/38205: 1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Answer: b) Graph this function and show the graph over the valid range of the variable x.. Show Graph here. c) Using the graph, what is the value of x that will produce the maximum volume? Answer. 1 solutions Answer 23699 by fractalier(2101)   on 2006-05-17 11:59:36 (Show Source): You can put this solution on YOUR website!Again, If we cut out x from all four corners, the new length will be 6 - 2x and the new width will be 4 - 2x, with the height of the box being just x. Now Volume V = lwh, so we have V = x(6 - 2x)(4 - 2x) I cannot graph it for you, but you can see that x must be more than zero and less than 2. Using early calculus I can show you how to find the maximum area, but without a way to show you it's graph, that's the best I can do... We need to maximize the function V(x) = x(6 - 2x)(4 - 2x) We do that by taking its derivative and setting it equal to zero, then solving for x...here goes... V(x) = x(6 - 2x)(4 - 2x) V(x) = 24x - 20x^2 + 4x^3 V'(x) = 24 - 40x + 12x^2 thus 12x^2 - 40x + 24 = 0 3x^2 - 10x + 6 = 0 This isn't factorable so we use the quadratic formula and get x = (10 ± 2sqrt(7)) / 6 = (5 ± sqrt(7)) / 3 The positive root is too big, so x must be x = (5 - sqrt(7)) / 3 or about .785 Now plug that in to V(x) to get the maximum volume... V(.785) = .785(6 - 2(.785))(4 - 2(.785)) = 8.45 cubic feet
 Polynomials-and-rational-expressions/38214: An open-top box is to be constructed from a 4 by 6 foot rectangulare cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x b) Graph this function and show the graph over the valid range of the variable x c) Using the graph, what is the value of x that will produce the maximum volume?1 solutions Answer 23698 by fractalier(2101)   on 2006-05-17 11:58:46 (Show Source): You can put this solution on YOUR website!I solved this one last week but here goes again... If we cut out x from all four corners, the new length will be 6 - 2x and the new width will be 4 - 2x, with the height of the box being just x. Now Volume V = lwh, so we have V = x(6 - 2x)(4 - 2x) I cannot graph it for you, but you can see that x must be more than zero and less than 2. Using early calculus I can show you how to find the maximum area, but without a way to show you it's graph, that's the best I can do... We need to maximize the function V(x) = x(6 - 2x)(4 - 2x) We do that by taking its derivative and setting it equal to zero, then solving for x...here goes... V(x) = x(6 - 2x)(4 - 2x) V(x) = 24x - 20x^2 + 4x^3 V'(x) = 24 - 40x + 12x^2 thus 12x^2 - 40x + 24 = 0 3x^2 - 10x + 6 = 0 This isn't factorable so we use the quadratic formula and get x = (10 ± 2sqrt(7)) / 6 = (5 ± sqrt(7)) / 3 The positive root is too big, so x must be x = (5 - sqrt(7)) / 3 or about .785 Now plug that in to V(x) to get the maximum volume... V(.785) = .785(6 - 2(.785))(4 - 2(.785)) = 8.45 cubic feet
 Proportions/37432: Please help me solve this problem: The ratio of the weight of an object on Jupiter to its weight on Earth is 8 to 3. How much would a 100 pound person weigh on Jupiter?1 solutions Answer 23697 by fractalier(2101)   on 2006-05-17 11:47:31 (Show Source): You can put this solution on YOUR website!use a proportion for this... Jupiter/Earth = 8/3 = x/100 Now cross multiply and get 3x = 800 and x = 800/3 = 266 2/3 lbs
 Systems-of-equations/38206: Need Help badly. I don't understand at all. 2) The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. a) Write h as a function of r. Answer: Show work in this space. b) What is the measurement of the height if the radius of the cylinder is 3 centimeters? Answer: Show work in this space. c) Graph this function. Show graph here. 1 solutions Answer 23696 by fractalier(2101)   on 2006-05-17 11:41:36 (Show Source): You can put this solution on YOUR website!Just posted this solution...scroll down to find it...
 Expressions-with-variables/38215: This question is from textbook 3n/12 + 7n/121 solutions Answer 23695 by fractalier(2101)   on 2006-05-17 11:40:36 (Show Source): You can put this solution on YOUR website!3n/12 + 7n/12 = 10n/12 = 5n/6 You can add numerators if the denominators are alike.
 Systems-of-equations/38216: I can't seem to figure this one out. Any help is appreciated. Thank you! The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. a)Write h as a function of r. b)What is the measurement of the height if the radius of the cylinder is 3 centimeters? c)Graph this function. 1 solutions Answer 23694 by fractalier(2101)   on 2006-05-17 11:39:30 (Show Source): You can put this solution on YOUR website!If V = 121 = (pi)(r^2)h and we need to write h as a function of r, merely solve for h...thus 121 = (pi)(r^2)h h = 121 / (pi)(r^2) If r = 3 cm, just plug it in and get h = 121 / 9(pi) I cannot graph it here due to the limitations of this interface, but you can start by plotting points, (r, h)...it will be hyperbolic in nature...
 Geometry_Word_Problems/38213: Okay this is a function of a right triangle where side a is equal to 16 and its corresponding angle is 45 degrees side b and the hypoteneous are unknown. Is there a way to solve for the two missing sides?1 solutions Answer 23693 by fractalier(2101)   on 2006-05-17 11:34:40 (Show Source): You can put this solution on YOUR website!Sure. If it is a right triangle and one angle is 45 degrees, the other must also be 45 degrees (all angles in a triangle add to 180, right?)... Now if the base angles are equal, the sides must also be...we have an isosceles right triangle... So side b is also 16. We can use the Pythagorean Theorem to find the hypotenuse... a^2 + b^2 = c^2 16^2 + 16^2 = c^2 c^2 = 512 c = sqrt(512) = 16sqrt(2)
 Polynomials-and-rational-expressions/37672: This question is from textbook Elementary Algebra Please help, factor by grouping, if possible and check: 1 solutions Answer 23692 by fractalier(2101)   on 2006-05-17 11:31:13 (Show Source): You can put this solution on YOUR website!Yes, let me show you how...from 10x^3 - 25x^2 + 2x - 5 let us group the terms this way (10x^3 - 25x^2) + (2x - 5) Now from the first group we can factor out 5x^2 and get 5x^2(2x - 5) + (2x - 5) Now we factor out 2x - 5 from both and get the final answer (2x - 5)(5x^2 + 1)
 Linear_Equations_And_Systems_Word_Problems/37666: This question is from textbook Sunshine Car Rentals rents a basic car at a daily rate of \$17.99 plus .18 per mile. City Reantals rents a basic car at \$18.95 plus .16 per mile. For what mileage is the cost be the same?1 solutions Answer 23691 by fractalier(2101)   on 2006-05-17 11:20:14 (Show Source): You can put this solution on YOUR website!Let x be the number of miles driven. Then change the English into algebra giving us the equation 17.99 + .18x = 18.95 + .16x Now multiply everything by 100 to clear the decimals 1799 + 18x = 1895 + 16x Now subtract 16x and 1799 from both sides 1799 + 2x = 1895 2x = 96 so that x = 48 miles
 Surface-area/38212: I am having trouble finding the volume and surface area of a cone. The lateral side is 10 ft and the base is 9ft.. This is a right cone,don't know if it makes a difference.1 solutions Answer 23690 by fractalier(2101)   on 2006-05-17 11:16:07 (Show Source): You can put this solution on YOUR website!For a right circular cone, the volume is V = (1/3)(pi)(r^2)h and the surface area (in terms of the lateral side s) is A = (pi)r^2 + (pi)rs You haven't specified whether the 9 ft is the radius or diameter, but given these formulas and the one relating height to radius and lateral side, s^2 = r^2 + h^2, you can plug everything in and go...
 Linear_Equations_And_Systems_Word_Problems/37670: This question is from textbook Susan wants to have business cards printed. One style will cost \$25 plus 2 cents per card. Another style will cost \$10 plus 5 cents per card. For how many cards will the cost be the same for both styles?1 solutions Answer 23689 by fractalier(2101)   on 2006-05-17 11:11:44 (Show Source): You can put this solution on YOUR website!Let x be the number of cards to be printed. Then change the facts in the problem into an algebraic equation... 25 + .02x = 10 + .05x Now multiply all by 100 to clear the decimals... 2500 + 2x = 1000 + 5x Subtract 1000 from both sides 1500 + 2x = 5x Now subtract 2x and then divide by 3... 1500 = 3x x = 500 cards
 Radicals/38211: Looking for some help. Solve the following radical equation x=1+6 sqrt x-9 thank you for your time1 solutions Answer 23688 by fractalier(2101)   on 2006-05-17 11:07:43 (Show Source): You can put this solution on YOUR website!Okay, from x = 1 + 6sqrt(x-9), move the one over first and get x - 1 = 6sqrt(x-9) Now square both sides x^2 - 2x + 1 = 36(x - 9) Now expand, combine, factor, solve and check... x^2 - 2x + 1 = 36x - 324 x^2 - 38x + 325 = 0 (x - 13)(x - 25) = 0 x = 13 or x = 25 Both check out, so we have two solutions...
 Circles/38210: two parallel chords, 16 cm and 30 cm are 23 cm apart. find the radius of the circle that contains them.1 solutions Answer 23687 by fractalier(2101)   on 2006-05-17 11:05:23 (Show Source): You can put this solution on YOUR website!Oooh, good problem. Here's how you do it... Make yourself the diagram with the parallel chords, one on either side of the center. Be sure that the 23 cm line that joins the two chords bisects them both. That line goes thru the center. Now draw two radii to the ends of the chords so that two right triangles are formed. Label the distance from the center to the 30 cm chord, x. Thus the distance from the center to the 16 cm is 23 - x. Now you have two Pythagorean Theorems to write: 8^2 + (23 - x)^2 = r^2 and 15^2 + x^2 = r^2 Two equations, two unknowns...we can solve this...here goes... 8^2 + (23 - x)^2 = 15^2 + x^2 64 + 529 - 46x + x^2 = 225 + x^2 -46x + 593 = 225 -46x = -368 x = 8 Thus r^2 = 15^2 + 8^2 and voila, r = 17
 Systems-of-equations/38085: Solve the system of equations by graphing. y-2x=0 y=4x-1 What is the solution of the system of equations? 1 solutions Answer 23686 by fractalier(2101)   on 2006-05-17 10:55:38 (Show Source): You can put this solution on YOUR website!From y - 2x = 0 y = 4x - 1 I can show you the solution but graphing it here is impossible... Normally you can set up an x-and-y chart and plug in values to get the points you plot...or you can put each line in slope-intercept form and graph... In either case, the place where the lines intersect is your solution... In this case, this is x = 1/2 and y = 1 or (1/2, 1)