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# Recent problems solved by 'mananth'

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 Trigonometry-basics/334035: A 12 foot ladder leans against a wall at a 70% angle with the ground. What is the distance between the ground and the top of the ladder? 1 solutions Answer 239324 by mananth(12270)   on 2010-08-23 00:03:55 (Show Source): You can put this solution on YOUR website!A 12 foot ladder leans against a wall at a 70 deg angle with the ground. What is the distance between the ground and the top of the ladder? .. the ground ladder and the wall form a right triangle .. hypotenuse = 12 angle = 70 deg. vertical height = ? perpendicular height = = sin(70)* 12 = 11.2 feet
 Average/334038: The temp was 17 degrees below zero; today the temp is 53 Degrees what is the change in Temp?1 solutions Answer 239322 by mananth(12270)   on 2010-08-22 23:56:34 (Show Source): You can put this solution on YOUR website!it was -17 deg now it is 53 deg .. Change in temperature = -17 - 53 = 70 deg.
 Reduction-of-unit-multipliers/334040: 6 Ft 18In Convert the Ratio to an Equivalent Fraction 1 solutions Answer 239321 by mananth(12270)   on 2010-08-22 23:54:13 (Show Source): You can put this solution on YOUR website!6 Ft 18In Convert the Ratio to an Equivalent Fraction .. 6 feet. 18 = 1.5 feet = 3/2 feet ratio = = = 4
 Rate-of-work-word-problems/334039: It takes one painter 12 days to paint a house, it takes another painter 8 days to paint a house the Identical size. How many days will it take to paint a house together? 1 solutions Answer 239320 by mananth(12270)   on 2010-08-22 23:51:02 (Show Source): You can put this solution on YOUR website!It takes one painter 12 days to paint a house, he paints 1/2 of the house in 1 day. .. it takes another painter 8 days to paint a house he paints 1/8 of the house in 1 day. .. together they paint 1/8 + 1/12 of the house in 1 day = LCM =24 3+2 / 24 = 5/24 of the job they do in 1 day so they will take 24/5 days together = 4.8 days to complete the job together.
 Geometry_Word_Problems/334030: A fortress has been built on top of a cliff. You measure the angle of elevation of the top of the cliff from a point 200 ft horizontally away from the base of the cliff to be 30' and the angle of elevation of the top of the fortress wall from the same point to be 45'. What is the height of the fortress wall?1 solutions Answer 239319 by mananth(12270)   on 2010-08-22 23:47:42 (Show Source): You can put this solution on YOUR website!Angle of elevation of cliff base = 30/60 deg ( 60 ' = 1 deg) distance on ground = 200 feet so height of cliff = 200*Tan(1/2) .. Angle of elevation of wall top = 45/60 deg distance on ground = 200 feet so height of cliff+ wall = 200*Tan(3/4) 200*tan(3/4)-200*tan(1/2) = height of wall = 77.05 feet
 Linear-equations/334032: (0,2); 2x+9y=7 write the equation of the line containing the given points and perpendicular to the given line. y=mx+b format1 solutions Answer 239318 by mananth(12270)   on 2010-08-22 23:33:50 (Show Source): You can put this solution on YOUR website!(0,2); 2x+9y=7 add-2x to both sides 2x-2x+9y=-2x-7 9y=-2x-7 divide by 9 y= -2/9x -7/9 .. slope = -2/9 .. the slope of a lin perpendicular to this line will be 9/2 .. y = mx +b (0,2) plug the value of x,y to get b 2= 0+b b=2 y= 9/2 *x +2 is the line ..
 Polynomials-and-rational-expressions/334031: I am having a real problem with long division. This is the problem I have: (2u^3-13u^2-8u+7) divided by (u-7)1 solutions Answer 239317 by mananth(12270)   on 2010-08-22 23:26:30 (Show Source): You can put this solution on YOUR website!........2u^2 +u -1 ----------------------- (u-7) |(2u^3-13u^2-8u+7) .......(-)2u^3 -14u^2 ----------- ........u^2-8u .....(-)u^2-7u --------- .........-u+7 ......(-)-u+7 ----------------
 Surface-area/333743: what is the circumference of a circle that has a 9cm diameter and how do you work it out1 solutions Answer 239174 by mananth(12270)   on 2010-08-22 09:53:00 (Show Source): You can put this solution on YOUR website!circumference of a circle = pi*D D=9 circumference = =28.27 cm
 Geometric_formulas/333747: solve for x: 10^3X=1000 1 solutions Answer 239173 by mananth(12270)   on 2010-08-22 09:50:34 (Show Source): You can put this solution on YOUR website!10^3X=1000 .. 10^3 =1000 1000x = 1000 divide by 1000 1000x/1000 = 1000/1000 x=1
 Geometric_formulas/333748: solve 10X=51 solutions Answer 239172 by mananth(12270)   on 2010-08-22 09:46:18 (Show Source): You can put this solution on YOUR website!10x=5 divide by 10 on both sides 10x/10 = 5/10 x= 1/2
 Quadratic_Equations/333752: Given the equation p = q2 + 5q +2. Find the values of q corresponding to p = -2. 1 solutions Answer 239171 by mananth(12270)   on 2010-08-22 09:43:30 (Show Source): You can put this solution on YOUR website!p = q2 + 5q +2. Find the values of q corresponding to p = -2. .. -2=q^2+5q+2 add +2 to both sides q^2+5q+4 =0 q^2+4q+q+4=0 q(q+4)+1(q+4)=0 (q+1)(q+4)=0 q=-1 OR q=-4
 Functions/333753: x^3-5=3 could you help me solve this i have to school my work1 solutions Answer 239168 by mananth(12270)   on 2010-08-22 09:35:37 (Show Source): You can put this solution on YOUR website!x^3-5=3 add -3 to both sides x^3-5-3= 3-3 x^3-8=0 This is similar to a^3-b^3 = (a-b)(a^2+ab+b^2) =(x-2)(x^2+2x+4)
 Linear_Equations_And_Systems_Word_Problems/333754: A total of \$20,000 is to be invested in bonds and some in certificates of deposit. If the amount invested in bonds is to exceed that of certificates of deposit by \$2,000, how much will be invested in each type?1 solutions Answer 239167 by mananth(12270)   on 2010-08-22 09:32:06 (Show Source): You can put this solution on YOUR website!let amount invested in certificates be \$x the amount invested in bonds will be (20,000-x) .. (20,000-x)= x+2000 20,000-x= x +2000 2x= 18,000 x = 9000 amount invested in certificates \$ 11,000 will be invested in bonds
 Quadratic_Equations/333758: how do I factor 180m^2n - 5n^3?1 solutions Answer 239166 by mananth(12270)   on 2010-08-22 09:25:40 (Show Source): You can put this solution on YOUR website!180m^2n - 5n^3
 Surface-area/333744: a circle with a 9cm diameter, has a piece cut out with a degree of 44. how do you work out the lenghtof the piece? and what is the circumference of the whole circle and how do you work that out?1 solutions Answer 239161 by mananth(12270)   on 2010-08-22 06:32:00 (Show Source): You can put this solution on YOUR website!You need the length of the arc of the circle. angle = 44 deg arc length = 44*(pi/180) * 4.5 = 3.46 cm .. circumference = pi*9= 28.27 cm
 Numbers_Word_Problems/333671: Four times the larger number was 11 greater than 7 times the smaller number. If the smaller number was 8 less than the larger number, what was the smaller number?1 solutions Answer 239160 by mananth(12270)   on 2010-08-22 06:23:15 (Show Source): You can put this solution on YOUR website!let larger number be x smaller number be y .. 4x =7y+11 4x-7y=11...................1 x-y=8......................2 .. multiply equation 2 by -4 and add to equation 1 -4x+4y+4x-7y=-32+11 -3y=-21 y=7 .. x-y =8 x=8+y x=15
 Miscellaneous_Word_Problems/333742: Solve the quetion according to "Volume and Surface Area" formula A rectangular tank measures 4m long,2m wide and 4.8m high.Intially it is half filled with water .Find the depth of water in the tank after 4000 liters more of water added to it . 1 solutions Answer 239159 by mananth(12270)   on 2010-08-22 06:17:56 (Show Source): You can put this solution on YOUR website!A rectangular tank measures 4m long,2m wide and 4.8m high.Intially it is half filled with water .Find the depth of water in the tank after 4000 liters more of water added to it . .. Volume of full tank = 4*2*4.8 =38.4 cu.m 1/2 volume = 38.4 /2 = 19.2 cu.m 19.2 cu. m = 19.2 *1000 liters = 19200 liters .. 19200 liters = 2.4 m height ( half tank) 4000 liters = ? = 2.4*4000/19200 =0.5 meters height for 4000 l Total depth will be 2.4 + 0.5= 2.9 m
 Travel_Word_Problems/333635: Karen left her house heading east, and her sister left two hours later heading west at a rate 5 mph faster than Karen. Six hours after Karen left, she and her sister were 600 miles apart. How fast was Karen moving?1 solutions Answer 239158 by mananth(12270)   on 2010-08-22 06:03:40 (Show Source): You can put this solution on YOUR website!Karen left her house heading east, her sister left two hours later heading west at a rate 5 mph faster than Karen. Six hours after Karen left, she and her sister were 600 miles apart. How fast was Karen moving? Karen speed be x mph Karen has traveled 6x miles (in 6 hours) .. sister x+5 mph . Sister has traveled 4(x+5) miles. left 2 hours later. .. 4(x+5)+6x =600 4x+20+6x=600 10x+20=600 10x=600-20 10x=580 x= 58 mph speed of Karen
 absolute-value/333739: Find, to the nearest degree, the angle made with the positive direction of the x-axis if y+x=3. Give your answers as obtuse angles1 solutions Answer 239157 by mananth(12270)   on 2010-08-22 05:51:12 (Show Source): You can put this solution on YOUR website!y=3-x .. (1,2)... x=1, y=2 (2,1) (3,0) (-1,4) (-2,5) (0,3) From the various points obtained by plugging the values of x in the equation The line intercepts the x & yaxis at x=3 & y=3. The line forms an isoscles triangle with the axes. So the angle will be 45 deg
 Surface-area/333738: What is the area of a circle that has a 6cm diameter, and how do you work it out 1 solutions Answer 239156 by mananth(12270)   on 2010-08-22 05:41:34 (Show Source): You can put this solution on YOUR website!Area of circle = pi*r^2 where r is the radius. .. diameter = 6 so r= 3 .. Area = pi*3^2 = 28.27 sq.cm
 Numbers_Word_Problems/333669: Could you write this is an algebraic expression.... The product of 4 less than a number and 2?1 solutions Answer 239155 by mananth(12270)   on 2010-08-22 05:38:57 (Show Source): You can put this solution on YOUR website!let number be x 4 less than a number = x-4 (x-4)*2
 Linear-equations/333699: Find the ordered pair solution to the following system of equations (Use any method): 3x – y = 5 2x + 5y = -8 1 solutions Answer 239154 by mananth(12270)   on 2010-08-22 05:35:32 (Show Source): You can put this solution on YOUR website!3x – y = 5 2x + 5y = -8 .. multiply equation 1 by 5 and add it to equation 2 15x-5y=25 2x+5y=-8 .. 17x=17 x=1 .. plug value of x in equation 1 3-y=5 y=-2
 Numbers_Word_Problems/333675: 3 consecutive odd numbers add to give 405. Find the smallest of the numbers.1 solutions Answer 239153 by mananth(12270)   on 2010-08-22 05:24:25 (Show Source): You can put this solution on YOUR website!Let the numbers be x, x+2, x+4 their sum =405 .. x+x+2+x+4=405 3x+6=405 add -6 3x+6-6=405-6 3x=399 divide by 3 x= 133 the numbers are 133, 135,137.
 Linear-equations/333700: Solve the following word problem (Hint: setup and solve a system of equations): One number plus twice another number gives a sum of 42. The difference of these same two numbers equals –3. Find the two numbers 1 solutions Answer 239152 by mananth(12270)   on 2010-08-22 03:16:24 (Show Source): You can put this solution on YOUR website!let one number be x & the other be y x+2y= 42 x-y= -3 .. (x+2y)-(x-y)=42-(-3) x+2y-x+y=45 3y=45 y=9 x=6
 absolute-value/333733: Hello, I'm not not entirely sure if the answer is 32 or but can someome please verify/ =) |a^2 - b^2| A = 6 & B = -2 1 solutions Answer 239151 by mananth(12270)   on 2010-08-22 03:13:05 (Show Source): You can put this solution on YOUR website!32 is right
 Square-cubic-other-roots/333717: if we want to convert 7083m3 in cubic foot want formula we can use1 solutions Answer 239150 by mananth(12270)   on 2010-08-22 03:11:56 (Show Source): You can put this solution on YOUR website!1 cu.m = 35.3 cu.ft multiply 7083 *35.3 =250,030 cu.ft (rounded off)
 Length-and-distance/333722: Any assistance is greatly appreciated: A runner is training for a marathon on a track whose straightaways are 500 ft and semicircles have a diameter of 40 ft. What is the total distance he will run if he runs the track 13 times? What is his average speed in MPH if it takes him 40 minutes and 35 seconds after 13 times? Thank you for your time.1 solutions Answer 239149 by mananth(12270)   on 2010-08-22 03:02:18 (Show Source): You can put this solution on YOUR website!length of 1 round = 500+500+ pi*40 ( 2 semicircles on either end) =1000+40*pi =1125.66 feet is the length of 1 lap. 13 laps will be 13 * 1125.66 =14633.62 feet .. 5280 feet = 1 mile 14633.62 feet = 146322.62/5280 = 2.77 miles .. 40 minutes 35 seconds is the time taken for 13 laps. =2400+35 = 2435 seconds .. 2435/3600 = 0.676 hours speed = distance / time =2.77 miles/0.676 = 6.9 mph
 Word_Problems_With_Coins/333724: A coin purse has 20 coins consisting of dimes and nickles. It totals \$1.40. How many nickles are there?1 solutions Answer 239148 by mananth(12270)   on 2010-08-22 02:26:20 (Show Source): You can put this solution on YOUR website!let dimes be x the nickels will be 20-x .. total value = 140 cents .. VALUE 10x+5(20-x)=140 10x+100-5x=140 5x=140-100 5x=40 x= 40/5 x= 8 dimes nickels = 20-8=12
 Money_Word_Problems/333726: if mrp of product is 2250 and i deduct 30% on it then it comes to 1575 but if i add 30% to it that will not come to 22501 solutions Answer 239147 by mananth(12270)   on 2010-08-22 02:23:28 (Show Source): You can put this solution on YOUR website!while calculating discount you are taking it on mrp 2250*30/100=675 2250-675=1575. .. but while doing the reverse you may be taking 30% 0f 1575 which is incorrect. take 30% of 2250 = 675 .. add it back to 1575 = 2250.. .. OR when sale price is 70 the mrp will be 100 when it is 1575 the mrp will be 1575*100/70 = 2250
 absolute-value/333727: Hello, I'm not not entirely sure if the answer is 32 or but can someome please verify/ =) |a^2 - b^2| A = 6 & B = -21 solutions Answer 239146 by mananth(12270)   on 2010-08-22 02:15:50 (Show Source): You can put this solution on YOUR website!(a+b)(a-b) (6-2)(6+20) 4*8=32
 Linear-equations/333725: Let C = Celsius degree and F= Fahrenheit degree scales for temperature. Assuming that relation between C and F is linear and drawing F on vertical axis. Two data points on the line relating C and F are (5, 41), (25, 77) Find the equation relating C and F. Can it be applied for practical purposes?1 solutions Answer 239145 by mananth(12270)   on 2010-08-22 02:14:02 (Show Source): You can put this solution on YOUR website!(5, 41), (25, 77) the slope of the line passing through the above points = 77-41 / 25-5 =36/20 =9/5 = m the slope .. general equation of line = y = mx +b plug value of any point and the slope m in the equation (5,41) 41=9/5 *5 +b 41=9+b 41-9=b b=32 .. so the general equation will be y = 9/5 x + 32 f is drawn on they axis and c on the x axis f= 9/5 c + 32 .. Plot the points and join the points to get a graph as given below.