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# Recent problems solved by 'mananth'

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 test/437276: Write an equation in point slope form of the line that passes through the given points ( -3, 1/2) ; (-7,5/2)1 solutions Answer 302448 by mananth(12270)   on 2011-04-18 09:02:45 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -3 0.5 -7 2.5 slope m = (y2-y1)/(x2-x1) -0.5 m= -0.5 Plug value of the slope and point ( -3 , 0.5 ) in Y = m x + b 0.50 = 1.5 + b b= 0.5 1.5 b= -1 So the equation will be Y = -0.5 x + -1
 Volume/437243: how many litres of water can a 5(length) by 2(width) by 2(height) feet tank hold?1 solutions Answer 302411 by mananth(12270)   on 2011-04-18 05:13:37 (Show Source): You can put this solution on YOUR website!Volume of Tank = 5*2*2= 20 cu.ft 1 cu.ft = 28.3 liters 20 cu.ft = 566 liters
 Volume/437171: An ice cube that measures 2.7 centimeters on each side contains how many cubic centimeters of ice? Include correct units with your solution. 1 solutions Answer 302410 by mananth(12270)   on 2011-04-18 04:34:22 (Show Source): You can put this solution on YOUR website!(2.7)^3 19.68 cu.cm
 Numbers_Word_Problems/437186: The sum of fifteen and four times x is the same as the difference of three times x and seven. Find x.1 solutions Answer 302409 by mananth(12270)   on 2011-04-18 04:32:49 (Show Source): You can put this solution on YOUR website!4x+15=3x-7 4x-3x=-15-7 x=-22
 Linear-systems/437190: AFTER SOLVING A SYSTEM OF LINEAR EQUATIONS, HOW CAN YOU CHECK YOUR ANSWER TO DETERMINE WHETHER IT IS CORRECT? please demonstrate the process by checking an answer for a set of equations (that you have created) THANK YOU ! 1 solutions Answer 302408 by mananth(12270)   on 2011-04-18 04:30:15 (Show Source): You can put this solution on YOUR website!3x+2y=4 .............1 5x+2y=8 .............2 Eliminate y multiply (1)by -1 Multiply (2) by 1 -3x-2y= -4 5x+2y=8 Add the two equations 2x=4 /2 x=2 plug value of x in (1) 3x+2y=4 6+2y=4 2y=4-6 2y=-2 y=-1 CHECK plug the value of x & y in any equation from above 3x+2y=4 6-2=4 4=4
 Volume/437227: two sphere just fit into a cylindrical container of radius 4.5 cm . Calculate the volume occupied by both sphere.1 solutions Answer 302407 by mananth(12270)   on 2011-04-18 04:23:53 (Show Source): You can put this solution on YOUR website!Volume of sphere = V= 4/3 * pi* r^3 V= 4/3 * 3.14*(4.5)^3 V= 381.5 cu.cm of i sphere 2*381.5 = 763 cu.cm Volume of two spheres
 Travel_Word_Problems/437231: If i drive 60 mph and i have 75 miles to go how long will it take me to reach my destination?1 solutions Answer 302405 by mananth(12270)   on 2011-04-18 04:20:06 (Show Source): You can put this solution on YOUR website!distance/speed = time 75/60 =5/4 =1.25 hours = 1 hour 15 minutes
 Geometry_Word_Problems/437230: A kite flying 20 ft. above the ground is attached to a string 80 ft. long. The string is being held by a person on the ground.if the kite fell vertically to the ground, how far away from the stake would the kite land?1 solutions Answer 302404 by mananth(12270)   on 2011-04-18 03:15:21 (Show Source): You can put this solution on YOUR website!sin = vertical/hypotenuse Sine = 20/80 Sine= 1/4 =15 deg .. Cos = base/hyptenuse Cos 15* 80 = base 0.9659*80= 77 feet ground distance (approx)
 Rate-of-work-word-problems/437217: A farmer has 200 hectares of land suitable for cultivating crops A, B, and C. The cost of cultivating each crop is • \$40 per hectare for crop A • \$60 per hectare for crop B • \$80 per hectare for crop C The labour hours required for each crop are • 20 labour hours per hectare for crop A • 25 labour hours per hectare for crop B • 40 labour hours per hectare for crop C. The farmer has 200 hectares of land, a budget of \$12600, and a workforce that can work a total of 5950 labour hours. How many hectares of each crop should he plant to use up all his available land, budget, and labour hours? [Hint: land, budget and labour correspond to 3 linear equations]1 solutions Answer 302398 by mananth(12270)   on 2011-04-18 01:40:14 (Show Source): You can put this solution on YOUR website!Crop A - x Crop B -y Crop C-z x+y+z=200.....................1 40x+60y+80z= 12600.............2 20x+25y+40z=5950...............3 consider equation 1 &2 Eliminate y Multiply 1 by -60 Multiply 2 by 1 we get -60x-60y-60z=-12000 40x+60y+80z=12600 Add the two -20x+20z=600 -------------4 consider equation 2 & 3 Eliminate z Multiply 2 by -5 multiply 3 by 12 we get -200x-300y-400 z=-63000 240x+300y+480z= 71400 Add the two 40x+80z=8400 -------------5 5 Consider (4) & (5) Eliminate z Multiply 4 by 2 Multiply (5) by 1 we get -40x+40z=1200 40x+80z=8400 Add the two 120z=9600 /120 z=80 Plug the value of z in 5 40x+6400=8400 40x=2000 x=50 plug value of x & z in 1 50+y+80=200 y=-50-80+200 y=70
 Travel_Word_Problems/437218: If I have the distance and the speed of travel, how can I figure out the length of time it will take to reach my destination?1 solutions Answer 302395 by mananth(12270)   on 2011-04-18 01:01:39 (Show Source): You can put this solution on YOUR website!Time = Distance /speed distance = 500 miles speed = 50 mph time = 500/550 = 10 hours
 Polynomials-and-rational-expressions/437189: Is x = -1 a solution to 4x – 3 = -7? Write yes or no.1 solutions Answer 302386 by mananth(12270)   on 2011-04-17 23:51:07 (Show Source): You can put this solution on YOUR website!yes
 Linear-equations/437184: Determine wheather the lines a parallel, perpendicular, or neither. 2x+5y=8 -5x+3=2y1 solutions Answer 302384 by mananth(12270)   on 2011-04-17 23:43:05 (Show Source): You can put this solution on YOUR website!2x+5y=8 .............1 -5x-2y= -3 .............2 Eliminate y multiply (1)by 2 Multiply (2) by 5 4x-y= 16 -25x+2y=-15 Add the two equations -21x= 1 /-21 x=-0.05 plug value of x in (1) 2x+5y=8 -0.1+5y=8 5y=8+0.1 5y=8.1 y=1.62 They intersect at(0,1.62) .................. CHECK by graphing equation1 when x= 0,y=1.6(0,1.6) when y =0,x=4(4,0) Equation 2 when x= 0,y=1.5(0,1.5) when y =0,x=0.6(0.6,0)
 Systems-of-equations/437188: solve with substitutions: -2 x + 1 y = 10 .............1 1 y = -6 -2 x ---------2 / 1 = y = -6 + -2 x Plug the value of y in (1) -2 x + 1 ( -6 + -2 x ) = 10 -2 x + -6 + -2 x = 10 -2 x + -2 x = 10 6 -4 x = 16 / -4 x= -4 Plug the value of x in (1) -2 x + 1 y = 10 -2 * -4 + 1 y = 10 8 + 1 y = 10 1 y = 2 / 1 y= 2 1 solutions Answer 302382 by mananth(12270)   on 2011-04-17 23:18:10 (Show Source): You can put this solution on YOUR website!-2x+y=10 .............1 y=-6-2x ---------2 Plug the value of y in (1) -2x+(-6-2x)= 10 -2x-6-2 x=10 -2x-2x=10+6 -4x=16 /-4 x=-4 Plug the value of x in (1) -2x+y=10 -2*-4+ y=10 8+y=10 y=2
 Travel_Word_Problems/437119: An airplane leaves Los Angeles for Denver at a speed of 430 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 500 mph. When they meet, how far are they from Denver? 1 solutions Answer 302356 by mananth(12270)   on 2011-04-17 21:27:33 (Show Source): You can put this solution on YOUR website!Plane to Denver 430 km/h Plane from Denver 500 km/h, 0.5 hours late Distance 850 miles ,0.5 hours Plane to Denver has traveled 215 miles before Plane from Denver starts So distance = 635 when second plane starts Let time they take to meet be x hours Time taken to meet is same t=d/r combined speed= 930 mph 930x=635 x= 0.68 hours Plane to Denver 430x +215 m = 508.6 miles Plane from Denver (850-508.6)= 341.4 miles
 Quadratic_Equations/437124: Make a graph of y=6x^2-4x-3 and find the vertex, y-intercept, extra points. I don't understand how I can find the vertex, y-intercept and extra points.1 solutions Answer 302348 by mananth(12270)   on 2011-04-17 21:05:54 (Show Source): You can put this solution on YOUR website!6x^2-4x-3 vertex = x=-b/2a vertex y= c-b^2/4a x= -(-4)/2*6= 0.33 y= -3-(16/24)= -3.6666 Vertex ( 0.33,-3.6666) xintercepts y=0 6x^2-4x-3=0 Find the roots of the equation by quadratic formula a= 6 b= -4 c= -3 b^2-4ac=16-72 b^2-4ac=88 , = 9.38 x1=(4+9.38)/12 x1=1.12 x2=(4-9.38)/12 x2= -0.45 (-0.45,0) (1.12,0) x intercepts ...... y intercepts plug x=0 6x^2-4x-3 -3 is the y intercept
 test/437121: 15. sue can shovel snow from her driveway in 30mins. jim can do the same job in 35mins. how long would i ttake sue and ime to shovel teh driveway if they worked together? 16.simplify by removing factors of 1 (7y-14)/2-y1 solutions Answer 302332 by mananth(12270)   on 2011-04-17 20:29:06 (Show Source): You can put this solution on YOUR website!Showelling the snow is one job Sue 30 minutes she does 1/30 of the job in 1 minute Jim 35 minute he does 1/35 of thejob in 1 minute Together they will do 1/30 + 1/35 + Together they will do 6/97 of the job in one minute So they will take 16 1/7 minutes (7y-14/(2-y) -7(2-y)/(2-y) =-7
 Expressions-with-variables/437118: 3y - x = 4 2x + 2y = 24 how do i solve this with substitution?1 solutions Answer 302331 by mananth(12270)   on 2011-04-17 20:21:49 (Show Source): You can put this solution on YOUR website! Rewrite the equations -1x+3y= 4 .............1 2y=24-2x---------2 /2 y=12-x Plug the value of y in (1) -x+3(12-x)=4 -x+36-3x=4 -x-3x=4-36 -4x=-32 /-4 x=8 Plug the value of x in (1) -x+3y=4 -1*8+3y=4 -8+3y=4 3y=12 /3 y=4
 Word_Problems_With_Coins/437114: In her purse Anita has 16 coins (nickels,dimes,and quarters), worth \$2.05. She has three times as many dimes as nickels. How many of each coin does she have?1 solutions Answer 302329 by mananth(12270)   on 2011-04-17 20:16:48 (Show Source): You can put this solution on YOUR website!--------------value-----------numbers nickels 5 x dimes 10 3x quarters 25 16-4x Value= 205 5x+30x-100x+400 =205 -65x=-195 -65x=-195 /-65 x=3nickels, 9 dimes,4 quarters (15+90+100)= 205 15
 Linear-equations/436791: Write an equation of the given point and perpendicular to the given line. (5,-6);6x+5y=8 The equation of the line is y=?1 solutions Answer 302217 by mananth(12270)   on 2011-04-17 09:52:17 (Show Source): You can put this solution on YOUR website!6x+5y=8 Find the slope of this line 5y=-6x-8 Divide by 5 y=-1 1/5x-1.6 Compare this equation with y=mx+b slope m =-1.20 The slope of a line perpendicular to the above line will be the negative reciprocal 0.83 m1*m2=-1 The slope of the required line will be 0.83 m= 0.83 ,point (5,-6) Find b by plugging the values of m & the point in y=mx+b -6=4.17+b b=-10.17 m=0.83 The required equation is y=0.83x-10.17
 Exponential-and-logarithmic-functions/436863: Find the future value of an initial investment of \$5,000 invested at 7% compounded annually, for 25 years. the formula is: FV=PV(1+i)^n when FVn is the Futer value of the investment after n years Pv is the initial amount of the investment i is the interest rate. n is the length of the investment, in years. I have set the equation up like this FVn= 5,000(1+7%)^25 FVn=5,000(1+0.07)^25 FVn=5,000(1.07)^25 Is this the correct set up? Now I know since I have the 25 exponent, I have to multiply the 1.07 times itself 25 times, can someone help me from that step. I do not have a scientific calculator so I really need assistance with the multiplication of the exponent and the solution to the problem. thank you in advance for your assistance1 solutions Answer 302215 by mananth(12270)   on 2011-04-17 09:44:48 (Show Source): You can put this solution on YOUR website!Principal P = 5000 Amount= A years=n 25 compounded 1 times a year Rate = 7.00 0.07 Amount = P*((n+r)/n)^n Amount =5000*(1+0.07)^25*1 Amount =5000*(1 +0.07)^ 25 5000 *(1.07)^25 Amount = 27137.16
 Graphs/436861: You need 30 tons of rock to cover the area. If each ton costs \$50 and each tree is \$84, what is the maximum number of trees you can buy with a budget of \$2,400? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer. 1 solutions Answer 302212 by mananth(12270)   on 2011-04-17 09:30:53 (Show Source): You can put this solution on YOUR website!each ton rock \$50 required 30 tons Cost = \$1500 cost of each tree = \$84 number of trees = x cost of trees = 84x Budget = \$2400 1500+84x<=2400 84x<= 2400-1500 84x<=900 x<=900/84 x<=10.7 10 trees
 Quadratic_Equations/436832: Write a quadratic equation having the given numbers as solutions -8 and -21 solutions Answer 302179 by mananth(12270)   on 2011-04-17 01:44:34 (Show Source): You can put this solution on YOUR website!(x+2)(x+8) x^2+8x+2x+16 x^2+10x+16
 Graphs/436822: The amount of money that a salesperson makes varies directly as the total amount of sales made. If the salesperson receives \$7,500 for selling a house for \$120,000, how much will he or she make if he or she sells a house for \$150,000? Set up a proportion. I figured out the problem but am not sure how to show a check on it. Please help.1 solutions Answer 302178 by mananth(12270)   on 2011-04-17 01:43:08 (Show Source): You can put this solution on YOUR website!7500/120,000 = x/150,000 7500*150000/120000=x x= \$9375
 Polynomials-and-rational-expressions/436828: Factor s^6 -64 I got (s + 8)(s-8) is that correct?1 solutions Answer 302177 by mananth(12270)   on 2011-04-17 01:38:08 (Show Source): You can put this solution on YOUR website!s^6 -64
 Money_Word_Problems/436823: How long does it take \$875 to double if it is invested at 8% compounded monthly?1 solutions Answer 302176 by mananth(12270)   on 2011-04-17 00:30:25 (Show Source): You can put this solution on YOUR website!Principal P = 875 Amount= 1750 years=n compounded (t) 12 Rate = 8 0.01 Amount =P*((1+r/t))^n*t 1750 =875*(1+0.01)^ n*t 2 = *( 1 + 0.01 )^ n* 12 ln 2 = 12 n *ln 1.01 0.69 = 12* 0.01 *n 8.69 = n
 Surface-area/436795: Hi tutors!, Help me please. :) QUESTION: The surface area of a candle is .If the candle has a diameter of 4inches,What is the height of a candle? (This is a cylinder I found out) What ive tried: = ......=...But..I think thats wrong! Please help!1 solutions Answer 302175 by mananth(12270)   on 2011-04-17 00:13:24 (Show Source): You can put this solution on YOUR website!diameter = 4 inches radius = 2 inches surface area = 2pir^2*h + 2pirh S= 2pir(r+h) S= 2*3.14*2(2+h) 125.6/12.56= 2+h 10=2+h h=8 in.
 Linear-equations/436810: Can you help me figure out how to do this? In 1995, the life expectancy of males in a certain country was 72.7 years. In 2002, it was 75.0 years. Let E represent the life expectancy in year t and let t represent the number of years since 1995. The linear function that fits the data is E(t)=?1 solutions Answer 302173 by mananth(12270)   on 2011-04-16 23:54:38 (Show Source): You can put this solution on YOUR website!In 1995, the life expectancy of males in a certain country was 72.7 years. In 2002, it was 75.0 years. Let E represent the life expectancy in year t and let t represent the number of years since 1995. The linear function that fits the data is E(t)=? 1995 = 72.7 2002= 75 in 7 years it increased by 2.3 years in 1 year it increased by 2.3/7=0.328 E(t) = 72.7 + 0.328t m.ananth@hotmail.ca
 Travel_Word_Problems/436798: A canoeist paddled 6 miles upstream in 6 hours and returned to his starting point downstream in 45 minutes. What was the speed of the current?1 solutions Answer 302158 by mananth(12270)   on 2011-04-16 23:25:04 (Show Source): You can put this solution on YOUR website!A canoeist paddled 6 miles upstream in 6 hours and returned to his starting point downstream in 45 minutes. What was the speed of the current? distance = same both ways let speed of canoe be x mph current speed = y mph .. speed = distance/time against current x-y = 6/6 with current x+y = 6/(3/4)===>6*4/3===>8 x-y =1 x+y=8 Add the two equations 2x=9 x= 4.5 mph speed of boat speed of current = 8-4.5 = 3.5 mph
 Percentage-and-ratio-word-problems/436799: p=14,000, m = 14, r = 6% compounded annually1 solutions Answer 302150 by mananth(12270)   on 2011-04-16 23:12:40 (Show Source): You can put this solution on YOUR website!Principal P = 14000 Amount= A years=n 14 compounded 1 times a year Rate = 6.00 0.06 Amount =P*((n+r)/n)^n Amount =14000*(1+0.06)^14*1 Amount =14000*(1+0.06)^14 14000*(1.06)^14 Amount =31652.66
 Linear-equations/436783: Find an equation in slope-intercept form passing through the points (-6.2, 18.1) and (-3.4,18.1).1 solutions Answer 302140 by mananth(12270)   on 2011-04-16 21:36:58 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -6.2 18.1 -3.4 18.1 slope m = (y2-y1)/(x2-x1) 0 m= 0 Plug value of the slope and point ( -6.2 , 18.1 ) in Y = m x + b 18.10 = 0 + b b= 18.1 0 b= 18.1 So the equation will be Y = 18.1
 Linear-equations/436782: Write an equation of the given line containing the given point and parallel to the given line. express in the form y=mx+b Problem (-5,7);4x=5y+7 the equation of the line is y=1 solutions Answer 302135 by mananth(12270)   on 2011-04-16 21:29:54 (Show Source): You can put this solution on YOUR website!4 x -5 y = 7 Find the slope of this line -5 y = -4 x + 7 0.8 Divide by -5 y = 0.8 x + -1.4 Compare this equation with y=mx+b slope m = 0.8 The slope of a line parallel to the above line will be the same The slope of the required line will be 0.8 m=0.8 ,point(-5,7) Find b by plugging the values of m & the point in y=mx+b 7=-4.00+b b=11 m=0.8 Plug value of the slope and b The required equation isy=0.8x+11