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# Recent problems solved by 'mananth'

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 Geometry_Word_Problems/331525: The surface area of two cups are in the ratio 9:64 .if the smaller cup has a height of 25 cm and a volume of 2400 cm^3 calculate a)the height of larger cup. b)the volume of larger cup.1 solutions Answer 237588 by mananth(12270)   on 2010-08-13 02:32:05 (Show Source): You can put this solution on YOUR website!volume of cylinder = pir^2h smaller cup volume = 2400= pi*r^2*25 r^2=2400/(pi*25) r=sqrt(2400/(pi*25) r=5.3 cm .. surface area of smaller cup = 2*pi*r*h S=2*pi*5.3*25 S= 832.5 sq. cm .. Ratio of surface area = 9/64 9/64= 832.5/x x=64*832.5/9 = 5920 sq. cm is the surface area of larger cup
 Equations/331504: Find all set of three consecutive even integers whose sum is between 20 and 30.? show your work.1 solutions Answer 237587 by mananth(12270)   on 2010-08-13 02:19:14 (Show Source): You can put this solution on YOUR website!20<3x+6<30 add -6 20-6<3x+6-6<30-6 14<3x<24 divide by3 .. 14/3 = 4.6 even integer between 4.6 & 8 = 6 so the numbers are 6 ,8,10
 Numeric_Fractions/331515: WHAT IS THE PRODUCT OF 8 AND T1 solutions Answer 237586 by mananth(12270)   on 2010-08-13 01:56:07 (Show Source): You can put this solution on YOUR website!8T
 Numbers_Word_Problems/331514: Perimeter of a triangle. The perimeter of a triangle is 195 mm. If the lengths of the sides are consecutive odd integers, find the length of each side.1 solutions Answer 237585 by mananth(12270)   on 2010-08-13 01:55:24 (Show Source): You can put this solution on YOUR website!let the sides be x, x+2,x+4 x+x+2+x+4= 195 3x+6=195 add -6 3x+6-6=195-6 3x=189 divide by 3 x=189/3 x=63 .. The sides are 63 , 65,67 mm
 logarithm/331517: log8+log21 solutions Answer 237584 by mananth(12270)   on 2010-08-13 01:51:54 (Show Source): You can put this solution on YOUR website!log8+log2 log a + log b = log (a*b) log 8 +log 2 =log(8*2) =log 16
 Linear-equations/331519: Please show me how to find the slope and the y-intercept of the line. 9y+6x+4=17+6x I'm coming up with a slope of 13/9 and y-intercept is (0,0) I know that's incorrect. Please help1 solutions Answer 237583 by mananth(12270)   on 2010-08-13 01:46:10 (Show Source): You can put this solution on YOUR website!9y+6x+4=17+6x add -6x 9y+6x-6x+4=17+6x-6x 9y=17-4 y=13/9 It is a line parallel to x axis. The line intersects the y axis at 13/9 ..
 Miscellaneous_Word_Problems/331520: A road is inclined at an angle of 5°. After driving 5000 feet along this road, find the driver's increase in altitude.1 solutions Answer 237582 by mananth(12270)   on 2010-08-13 01:38:19 (Show Source): You can put this solution on YOUR website!inclination = 5 deg slant travel length = 5000 altitude = ? .. In a right angled traingle sine5*5000= altitude 0.0872*5000= 436 feet
 Geometry_Word_Problems/331493: An American flag has a perimeter of 28ft. Find the dimensions of the flag if the length is 4 ft less than twice its width.1 solutions Answer 237570 by mananth(12270)   on 2010-08-12 23:05:36 (Show Source): You can put this solution on YOUR website!let width be x length = 2x-4 .. Perimeter = 2*(L+W) 28=2(x+2x-4) 28=6x-8 add 8 28+8=6x+8-8 36=6x divide by 6 36/6= 6x/6 6=x width = 6 feet length = 2x-4 =2*6-4 =12-4 =8 feet
 Angles/331495: factor out a factor with a negative coefficient. -7s-28. (factor completely)1 solutions Answer 237568 by mananth(12270)   on 2010-08-12 22:58:48 (Show Source): You can put this solution on YOUR website!-7s-28 -7(s+4)
 Angles/331500: factor completely 27s^4-64s1 solutions Answer 237567 by mananth(12270)   on 2010-08-12 22:55:11 (Show Source): You can put this solution on YOUR website!27s^4-64s s{(3s)^3-(4)^3} s{(3s-4)(9s^2+12s+16)}
 Polynomials-and-rational-expressions/331468: In a study of worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled by the formula N(t)=-3t^3+23t^2+8t a) Rewrite the formula by factoring the right-hand side completely. b) Use the factored version of the formula to find N(3). 1 solutions Answer 237559 by mananth(12270)   on 2010-08-12 21:47:43 (Show Source): You can put this solution on YOUR website!N(t)=-3t^3+23t^2+8t N(t)=-t(3t^2-23t-8) N(t)=-t((3t^2-24t+t-8)) N(t)=-t(3t(t-8)+1(t-8)) N(t)=-t(3t+1)(t-8) .. N(3)=-3(9+1)(3-8) N(3)=150
 Expressions-with-variables/331471: How do you write b + c + twice a?1 solutions Answer 237556 by mananth(12270)   on 2010-08-12 21:33:37 (Show Source): You can put this solution on YOUR website!b+c+2a
 Permutations/331470: how do you figure out 3=x^2-4x1 solutions Answer 237555 by mananth(12270)   on 2010-08-12 21:33:02 (Show Source): You can put this solution on YOUR website!x^2-4x-3=0 use the quadratic formula to get the roots of the equation a=1,b=-4,c=-3 .. x1=-(-4)+sqrt((-4)^2-4*1*(-3)))/2*1 x1=4+sqrt(16+12)/2 x1=4+sqrt28 /2 x1=(4+2sqrt7)/2 x1=2+sqrt7 x2=2-sqrt7
 Quadratic_Equations/331210: 16d^2/2d^2-16d+32 multiplied by 2d-8/4d I'm totaly lost on this one.1 solutions Answer 237414 by mananth(12270)   on 2010-08-12 09:31:24 (Show Source): You can put this solution on YOUR website!16d^2/2d^2-16d+32 multiplied by 2d-8/4d .. .. .. 4d/(d-4)
 Linear-equations/331201: could you please simplify (-2a^6 c^5)^3 over (8a^8 c^17)asap please thanks1 solutions Answer 237413 by mananth(12270)   on 2010-08-12 09:25:18 (Show Source): You can put this solution on YOUR website! .. ..
 Travel_Word_Problems/331202: barbara drove 330 miles from home to tuscan on her round trip she was able to increase her speed by 11miles per hour.If the return trip took 1 hour less than find her original speed to tuscan1 solutions Answer 237411 by mananth(12270)   on 2010-08-12 09:09:58 (Show Source): You can put this solution on YOUR website!let the original speed be x mph on her return it was x+11 mph .. distance is constant = 330 miles. .. return was 1 hour less. time taken while going - time returning = 1 hour .. time while going = 330/x time while returning = 330/x+11 .. 330/x-330/(x+11)=1 LCD = x(x+11) 330(x+11)-330x/ x (x+11)=1 330x+3630-330x=x(x+11) 3630= x^2 +11x x^2+11x-3630=0 x^2+66x-55x-3630=0 x(x+66)-55(x+66)=0 (x-55)(x+66)=0 x=55 ignore negative value original speed = 55 mph
 Linear_Equations_And_Systems_Word_Problems/331159: Charles and Paul enter the Center Poin-Comfort Hill Country Run. Charles runs at 8 mi/h and Paul at 6 mi/h. If they start together, how long before charles is 1/4 mi head of Paul?1 solutions Answer 237400 by mananth(12270)   on 2010-08-12 06:44:30 (Show Source): You can put this solution on YOUR website!let x be the distance 1/4 mi ahead of paul. charles speed = 8mph paul's speed = 6mph time taken by both is the same. time taken by charles = x/8 time taken by paul = x-1/4 / 6 .. x/8= (x-(1/4) /6 x/8=(4x-1)/4*6 x/8= 4x-1/24 24x=8(4x-1) 24x=32x-8 8x =8 x=1 the distance at which charle's is 1/4 mi ahead of paul. speed of charles = 8 mph time = distance / speed time = 1/8 hour =7.5 minutes. after 7.5 minutes charles will be 1/4 mi ahead of paul
 Linear_Equations_And_Systems_Word_Problems/331155: the petty-cash drawer of a small office containing \$16.25. If there were twice as many nickels as quarters and as many dimes as nickels and quarters combined, how many coins of each type were there? 1 solutions Answer 237390 by mananth(12270)   on 2010-08-12 04:45:57 (Show Source): You can put this solution on YOUR website!let quarters be x nickels =2x dimes = (2x+x) .. Total money = 16.25 25x +5*2x+10*(2x+x)=1625 25x+10x+20x+10x=1625 65x=1625 x= 1625/65 x= 25 the number of quarters nickels = 2x = 2*25=50 dimes = 3x=3*25=75
 Numbers_Word_Problems/331144: i have a number add 8 to my number and the sum is less than twice my number subtract 6 from number and the difference is 1 less than half of my number whats my number1 solutions Answer 237387 by mananth(12270)   on 2010-08-12 03:27:00 (Show Source): You can put this solution on YOUR website!x+8<2x 8<2x-x 8 ; x-6 x-x/2<6-1 x/2<5 x<10 .. x is greater than 8 & less than 10. so 9 is the number
 Miscellaneous_Word_Problems/331149: a mountain resort that featured skiing in the winter was partially staffed by college students in the summer. One summer there were 3 times as many students employed as there were year-round employees. When September came, 40 of the students were back to school and 30 nonstudents were hired for the winter. if there were then twice as many non students as students, how many people staffed the resort in winter?1 solutions Answer 237385 by mananth(12270)   on 2010-08-12 03:21:53 (Show Source): You can put this solution on YOUR website!let employed be x students be y y=3x..........................1 .. (y-40)=2(x+30) y-40 =2x+60 y-2x=60+40 y-2x=100......................2 plug value of y in equation 2 3x-2x=100 x= 100 employed students = 300
 Systems-of-equations/331127: The difference of two numbers is 10. Two times the larger number is 20 more that the smaller. What are the two numbers?1 solutions Answer 237384 by mananth(12270)   on 2010-08-12 02:27:17 (Show Source): You can put this solution on YOUR website!let the bigger number be a smaller number be b a-b=10.................1 .. 2a=b+20 2a-b=20................2 multiply equation 1 by -1 and add equation 2 to it -1(a-b)+(2a-b)=-10+20 -a+b+2a-b=10 a=10 plug value of a in equation1 10-b=10 b=0
 Age_Word_Problems/331147: Fred is 3 years older than his sister mary. In 7 years she will be six-sevenths of his age. how old are they?1 solutions Answer 237383 by mananth(12270)   on 2010-08-12 02:20:20 (Show Source): You can put this solution on YOUR website!mary's age =x fred's age will be x+3 .. after 7 years mary's age = x+7 Fred's age = x+3+7 = x+10 .. x+7= 6/7 * (x+10) multiply by 7 7(x+7)=(6/7)*7(x+10) 7x+49=6x+60 7x-6x= 60-49 x= 11 years - Mary's age Fred's age = x+3 = 11+3=14
 Linear_Algebra/331145: im a little stuck heres my question: during one calendar year a state trooper issued a total of 375 citations for warnings and speeding tickets. of these, there were 37 more warnings than speeding tickets. how many warnings and how many speeding tickets were issued?1 solutions Answer 237382 by mananth(12270)   on 2010-08-12 02:14:59 (Show Source): You can put this solution on YOUR website!speeding tickets be x warning will be x+37 .. x+x+37 = 375 2x+37=375 add-37 2x+37-37=375-37 2x=338 x= 169 speeding tickets warning= 169+37= 206
 Polynomials-and-rational-expressions/331136: Factor the following polynomial 7y + 60 + y^2 1 solutions Answer 237381 by mananth(12270)   on 2010-08-12 02:10:34 (Show Source): You can put this solution on YOUR website!y^2+7y+60 .. find roots using quadratic formula .. x= .. x1= a=1,b=7,c=60 x1= x1= x2=
 test/331143: Can you please help me solve this story problem. Soybean meal is 16% protein. Cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320 pounds mixture that is 12% protein? How many pounds of cornmeal should be in the mixture? How many pounds of the soybean meal should be in the mixture? Thanks for your help :O)1 solutions Answer 237380 by mananth(12270)   on 2010-08-12 02:01:55 (Show Source): You can put this solution on YOUR website!Soybean meal is 16% protein. let this be x Cornmeal is 8% protein. this will be 320-x 320 pounds mixture that is 12% protein? .. 0.16x+0.08(320-x)=320*.12 0.16x+25.6-0.08x=38.4 0.08x=38.4-25.6 0.08x=12.8 x=12.8/0.08 x=160 pounds soyabean corn will be 160 pounds
 test/331134: #1---The length of one leg of a right triangle is 12 meters. the length of the hypotenuse is 8 meters longer than the other leg. find the length of the hypotenuse and the other leg of the triangle. #2---Two angles are supplementary if the sum of their angles is 180 degrees. One of two supplementary angles is 8 degrees less than three times the other. find the measure of each angle.1 solutions Answer 237379 by mananth(12270)   on 2010-08-12 01:53:43 (Show Source): You can put this solution on YOUR website!#1---The length of one leg of a right triangle is 12 meters. the length of the hypotenuse is 8 meters longer than the other leg. find the length of the hypotenuse and the other leg of the triangle. let the other leg be x one leg = 12 hyp = x+8 (x+8)^2=x^2+12^2 x^2+16x+64=x^2+144 16x+64=144 add -64 16x+64-64=144-64 16x=80 x= 5 the other leg. Hypotenuse = x+8 = 5+8=13 #2---Two angles are supplementary if the sum of their angles is 180 degrees. One of two supplementary angles is 8 degrees less than three times the other. find the measure of each angle. let one angle be x the other angle = 3x-8 .. 3x-8+x=180 4x-8=180 add 8 4x-8+8=180+8 4x=188 divide by 4 4x/4=188/4 x=47 one angle second angle = 180 -47=133
 Polynomials-and-rational-expressions/331137: Factor the following polynomial 8y - 20 + y^21 solutions Answer 237378 by mananth(12270)   on 2010-08-12 01:46:03 (Show Source): You can put this solution on YOUR website!8y - 20 + y^2 ..
 Polynomials-and-rational-expressions/331138: Factor the following polynomial y^3 - 27x^31 solutions Answer 237377 by mananth(12270)   on 2010-08-12 01:42:29 (Show Source):
 Geometry_Word_Problems/331139: the measure of the supplement of an angle is 12 degrees greater than three times the measure of a complement. Find the measure of the angle. 180-12 = 3(x) but this does not work. the answer is 51 degrees. I don't know how to get it.1 solutions Answer 237376 by mananth(12270)   on 2010-08-12 01:39:49 (Show Source): You can put this solution on YOUR website!the measure of the supplement of an angle is 12 degrees greater than three times the measure of a complement. Find the measure of the angle. .. let angle be x complement = 90-x supplement = 180-x .. 180-x=3(90-x)+12 180-x =270-3x+12 add +x 180-x+x=270-3x+x+12 180=-2x+12 +270 add-12 180-12=-2x+12-12 -102=-2x x=-102/-2 x=51
 Miscellaneous_Word_Problems/331142: a store sells 8 more pencils than pens one day. The cost of the pencil is \$0.05 and the cost of the pen is \$0.20. If the day's sales of pens and pencils equals \$8.90, how many pencils were sold. I know there is something with x + x+8, but I can't figure out what to do with the different prices. Thanks.1 solutions Answer 237375 by mananth(12270)   on 2010-08-12 01:31:52 (Show Source): You can put this solution on YOUR website!let pens sold be x pencils sold will be x+8 .. cost of pen = 20 cents cost of pencils= 5 cents .. total sales = 890 cents .. 20x+5(x+8)=890 20x+5x+40=890 25x=890-40 25x=850 x=34 pens sold pencils sold = x+8 = 34+8=42 .. CHECK 34*20+42*5=890
 Linear-equations/331121: Simplify please (5y^8z^3)^2(6y^5)1 solutions Answer 237367 by mananth(12270)   on 2010-08-11 23:31:29 (Show Source):