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# Recent problems solved by 'mananth'

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 Geometry_proofs/737699: Can somebody please help me with this proof that I am stuck on? I need to solve it by manipulating only the left side... (secx-tanx)/(secx+tanx) = ((1-sinx)/cosx)^2 Thanks in advance!1 solutions Answer 450501 by mananth(12270)   on 2013-04-15 00:59:10 (Show Source): You can put this solution on YOUR website! LHS
 Trigonometry-basics/737656: Find the exact values of cos theta and sin theta for the angle measure. 5 pi/6 radians 1 solutions Answer 450485 by mananth(12270)   on 2013-04-14 21:39:33 (Show Source): You can put this solution on YOUR website! Angle=
 Radicals/737647: Solve the radical equation. sqrt(3x+4)=2+ sqrt(x) This will usually involve squaring each side twice. I don't know how to resolve this, can you please give an explanation as to how to perform this?1 solutions Answer 450480 by mananth(12270)   on 2013-04-14 21:32:22 (Show Source): You can put this solution on YOUR website!sqrt(3x+4)=2+ sqrt(x) square rearrange square /4x x=4
 Geometry_proofs/737632: 1/(1-cosx)-1/(1+secx) = csc^2x+cot^2x Can somebody help me do the following proof (solving from the left)? Thanks in advance!1 solutions Answer 450474 by mananth(12270)   on 2013-04-14 21:23:15 (Show Source): You can put this solution on YOUR website! LHS = Take LCD LHS = RHS
 Equations/737638: for which of the following equations are x=5and x=-5........................... A x2-x^2-5x-25=0.....B..x^2+25=0......C.. x^2+10x-25=0....D.. x^2-25=01 solutions Answer 450469 by mananth(12270)   on 2013-04-14 20:53:35 (Show Source): You can put this solution on YOUR website!D.x^2-25 (x+5)(x-5)=0 so x=5 or x=-5
 Linear-equations/737079: What is the equation of the line in slope point and general form? Same slope as 2x-5y+6=0 and through the origin. Thanks1 solutions Answer 450186 by mananth(12270)   on 2013-04-13 05:38:02 (Show Source): You can put this solution on YOUR website!slope of the given line = 2/5 passes through (0,0) y-0=2/5(x-0) y=(2/5)x -(2/5)x+y=0
 Sequences-and-series/737093: if x, y, and z are the first three terms of a geometric sequence, show that x^2, y^2 and z^2 form another geometric sequence1 solutions Answer 450185 by mananth(12270)   on 2013-04-13 05:30:55 (Show Source): You can put this solution on YOUR website!x y z are in geometric x/y = y/z OR y^2=xz x^2, y^2, z^2 x^2, xz, z^2 If they are in geometric sequence then xz/x^2 = z^2/xz z/x = z/x The ratios are common so x^2,y^2 & z^2 is a GP
 Mixture_Word_Problems/737125: Determine the slope and the angle of inclination of the line joining the point ( -2,5 ) and ( 3,-6 )1 solutions Answer 450184 by mananth(12270)   on 2013-04-13 05:24:31 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -2 5 3 -6 slope m = (y2-y1)/(x2-x1) ( -6 - 5 )/( 3 - -2 ) ( -11 / 5 ) m= -2 1/5 slope = -11/5 Tan = -11/5 Theta = tan ^-1(11/5) = -65.55 deg
 Trigonometry-basics/737089: Use the given information to find cos 2x, sin 2x, and tan 2x. cosx=sqrt3/7 and 3π/2 < x < 2π since I have cos, I created a triangle using sqrt3 as the opposite side. and 7 as the adjacent side. Then I used the Pythagorean theorem to find the hypotenuse. hypotenuse^2=(sqrt3)^2+(7)^2 hypotenuse^2=3+49 hypotenuse^2=52 hypotenuse=sqrt52 Then to find sin2x, I used sin2x=2sin(xcos(x), so... sin2x=2sin(xcos(x) = 2(sqrt3/sqrt52)(sqrt3/7) = 2 (sqrt9/7sqrt52) = 3/7sqrt13 but that was incorrect and I can't go any further in the problem with an incorrect sin2x. Please assist me with where I went wrong or how to go about finding this answer. thanks! 1 solutions Answer 450182 by mananth(12270)   on 2013-04-13 05:12:09 (Show Source): You can put this solution on YOUR website!cos x = square both sides cos^2 x=3/49 1-cos^2 x=1-3/49 sin^2 x = 46/49 cos 2x = 2 cos^2 x -1 =2*3/49-1 =6/49-1 =-43/49 Cos 2x= -43/49 Sin 2x = 2sin x . cos x = = Tan (2x) = sin (2x)/cos (2x)
 �t�e�s�t/737102: A line passes through the point (-2,4), and its y-intercept is (0,-6). What is the equation of the line that is perpendicular to the first line and passes through the point (5, -4)? A. y = 1/5x - 3 B. y = 5x - 3 C. y= 1/5x - 5 D. y = 5/3x - 2 1 solutions Answer 450177 by mananth(12270)   on 2013-04-13 04:22:20 (Show Source): You can put this solution on YOUR website!option C
 �t�e�s�t/737104: What is the equation of the line that passes through the points (4/5, 1/5) and (1/2, 3/2)? A. y = -x - 1 B. y = -x + 1 C. y = -13/3x + 11/3 D. y = 7/3x + 1/31 solutions Answer 450176 by mananth(12270)   on 2013-04-13 04:15:21 (Show Source): You can put this solution on YOUR website!option (c)
 logarithm/736847: Log base 3 1/27=x 1 solutions Answer 450016 by mananth(12270)   on 2013-04-12 00:06:41 (Show Source): You can put this solution on YOUR website!log(3) 1/27=x 3= (1/27)^x 1=-3x -1/3 =x
 Graphs/736837: find the equation in slope intercept form: slope: -1 ordered pair (2,4)1 solutions Answer 450014 by mananth(12270)   on 2013-04-11 23:55:25 (Show Source): You can put this solution on YOUR website!The equation in point slope form is y-y1=m(x-x1) m=-1 (x1,y1)=> (2,4) y-4 = -1(x-2) y-4=-x+2 y=-x+2+4 y=-x+6
 Travel_Word_Problems/736793: two planes having the same airspeed depart at the same time, flying in opposite directions. one plane flies into 35mph wind, and the other flies in the same direction as the wind. After a period of time, on plane has traveled 460 m an the other has traveled 404 m. let x = airspeed of each plane ( airspeed is the same for each plane) a) write an expression for the speed of the plane traveling into the wind. b) Traveling with the wind c) write an expression for the time the same plane has been in the air when it has traveled 460 m d) what is the relationship for the times the planes have been in the air c) write an equation modeling this relationship.1 solutions Answer 450007 by mananth(12270)   on 2013-04-11 22:13:03 (Show Source): You can put this solution on YOUR website!two planes having the same airspeed depart at the same time, flying in opposite directions. one plane flies into 35mph wind, and the other flies in the same direction as the wind. After a period of time, on plane has traveled 460 m an the other has traveled 404 m. let x = airspeed of each plane ( airspeed is the same for each plane) a) write an expression for the speed of the plane traveling into the wind. x-35 mph b) Traveling with the wind x+35 mph c) write an expression for the time the same plane has been in the air when it has traveled 460 m 460/(x+35) d) what is the relationship for the times the planes have been in the air Times are equal second plane time = 404/(x-35) c) write an equation modeling this relationship. 460/(x+35)=404/(x-35) 460(x-35)=404(x+35) 460x-16100=404x+14140 56x=30240 x=540 mph
 Trigonometry-basics/736790: I need a walkthrough of how i would do this problem "Philly can reach his second floor window with an 18 foot ladder at a 75 degree angle to the ground. His friend willy claims that Philly could reach the window with a 16 foot ladder. Justify or disprove Willys claim. "1 solutions Answer 450002 by mananth(12270)   on 2013-04-11 22:02:22 (Show Source): You can put this solution on YOUR website!18 feet ladder 75 deg angle Height of window Sin 75 = height / ladder length height = sin 75 * 18 =>0.965*18 =>17.37 feet height of window =17.37 if ladder length is 16 feet even when kept vertically it will not reach the window.
 Miscellaneous_Word_Problems/736767: Laura received an e-mail from Billy. After 10 minutes Laura forwarded it to 3 of her friends. After 10 minutes each of those 3 friends forwarded the message to 3 more friends. If the message was forwarded like this every 10 minutes, how many people had received Billy's e-mail after 50 minutes? 1 solutions Answer 449996 by mananth(12270)   on 2013-04-11 21:44:25 (Show Source): You can put this solution on YOUR website!Laura received an e-mail from Billy. After 10 minutes Laura forwarded it to 3 of her friends. After 10 minutes each of those 3 friends forwarded the message to 3 more friends. If the message was forwarded like this every 10 minutes, how many people had received Billy's e-mail after 50 minutes? the email was sent every 10 minutes Total emails 5 first email 3, 9,27 81, 243..... it is a GP Sn = 3*242/2 =363 emails will be sent in 50 minutes
 Rational-functions/736770: Find the x- and y-intercepts. If no x-intercepts exist, state so. f(x) = 3x2 + 6x + 1 1 solutions Answer 449990 by mananth(12270)   on 2013-04-11 21:17:38 (Show Source): You can put this solution on YOUR website!f(x) = 3x2 + 6x + 1 On X axis y=0 3x^2+6x+1=0 Find the roots of the equation by quadratic formula a= 3 b= 6 c= 1 b^2-4ac= 36 - 12 b^2-4ac= 24 = 4.9 x1=( -6 + 4.9 )/ 6 x1= -0.18 x2=( -6 -4.9 ) / 6 x2= -1.82 Intersection at -0.18 and -1.82
 Travel_Word_Problems/736756: Pensacola is 792 miles away from key west . Bus A leaves at 6am and travels at 42 mph . Bus B leaves at 7am and travels at 33 mph . What time and distance from key west, will the two buses meet ?1 solutions Answer 449989 by mananth(12270)   on 2013-04-11 21:11:44 (Show Source): You can put this solution on YOUR website!If they are moving in same direction they will not meet. if opposite then it can be worked out
 Mixture_Word_Problems/736421: The equation of the gas line is 2x+y=2 . a factory located at the point ( 6,7) will connect with the gas line perpendicularly . find the equation of the connecting line and the length of the pipe required if the units are miles .1 solutions Answer 449833 by mananth(12270)   on 2013-04-11 08:59:04 (Show Source): You can put this solution on YOUR website!2 x + 1 y = 2 Find the slope of this line 1 y = -2 x + 2 Divide by 1 y = -2 x + 2 Compare this equation with y=mx+b, m= slope & b= y intercept slope m = -2 The slope of a line perpendicular to the above line will be the negative reciprocal 1/2 Because m1*m2 =-1 The slope of the required line will be 1/2 m= 1/2 ,point ( 4 , 7 ) Find b by plugging the values of m & the point in y=mx+b 7 = 2 + b b= 5 m= 1/2 The required equation is y = 1/ 2 x + 5 where do they intersect 2.00 x + 1.00 y = 2.00 .............1 Total value -0.50 x + 1.00 y = 5.00 .............2 Eliminate y multiply (1)by -1.00 Multiply (2) by 1.00 -2.00 x -1.00 y = -2.00 -0.50 x + 1.00 y = 5.00 Add the two equations -2.50 x = 3.00 / -2.50 x = -1.20 plug value of x in (1) 2.00 x + 1.00 y = 2.00 -2.40 + y = 2.00 y = 2.00 + 2.40 y = 4.40 y = 4.40 (-1.20,4.40) (6,7) Find the distance between the points. that's the length of the pipe line Distance between two points x1 y1 x2 y2 -1.2 4.4 6 7 d= d= d= d= d= 7.66 m.ananth@hotmail.ca m.ananth@hotmail.ca
 Travel_Word_Problems/736420: A BOAT TRAVELED 336 MILES DOWNSTREAM AND BACK. THE TRIP DOWNSTREAM TOOK 12HOURS. THE TRIP BACK TOOK 14 HOURS. WHAT IS THE SPEED OF THE BOAT IN STILL WATER? WHAT IS THE SPEED OF THE CURRENT? SOLVE USING A SYSTEM OF TWO EQUATIONS1 solutions Answer 449832 by mananth(12270)   on 2013-04-11 08:51:09 (Show Source): You can put this solution on YOUR website!Boat speed speed =x mph current speed =y mph against current 14 hours with current 12 hours Distance against 336 miles distance with 336 miles t=d/r against current - 336 / ( x - y )= 14 14 ( x - y ) = 336 14 x - 14 y = 336 ....................1 336 / ( x + y )= 12 12 ( x + y ) = 336 12 x + 12 y = 336 ...............2 Multiply (1) by 6 Multiply (2) by 7 we get 84 x + -84 y = 2016 84 x + 84 y = 2352 168 x = 4368 / 168 x = 26.00 mph plug value of x in (1) y 14 x -14 y = 336 364 -14 -364 = 336 -14 y = 336 -14 y = -28 mph y = 2.00 Boat speed speed 26.00 mph current speed 2.00 mph m.ananth@hotmail.ca
 Travel_Word_Problems/736425: A van departs from a rest stop at 9am heading west and travels at an average rate of 40 miles per hour. two hours later a car departs from the same rest stop also heading west and travels at an average rate of 65 miles per hour. at what time will the car catch up to the van and how far will they have traveled at that time? I need to build an equation, and so far all i have is this; Rate x Time = Dist 40 x 40x 40-x 2 2(40-x) this just feels all wrong... 40x + 65(2+x) = 91 solutions Answer 449829 by mananth(12270)   on 2013-04-11 08:45:04 (Show Source): You can put this solution on YOUR website!First car 40 mph Car II 65 mph First car 09:00 Car II 11:00 Difference in time= 02:00 => 2.00 hours First car will have covered 80.00 miles Car II starts catch up distance= 80.00 miles catch up speed = 65 -40 catch up speed = 25 mph Catchup time = catchup distance/catch up speed catch up time= 3.2 catch up time= 3.20 hours They will meet at 12:20 pm Car II speed = 65 hours Time to catch up = 3.2 D=Speed * time D= 65 * 3.2 D= 208 miles Car II will catch up when it has traveled 208 miles
 Volume/736368: A cylinder with a top and bottom has a volume of 30 cubic inches. Find the minimum amount of material needed to create the can. (Surface area=2pir^2 + 2pirh & volume = pir^2h) I tried to create two separate equations, 30 = pir^2h (and then solve for r^2) and 2pir^2 and then I was going to substitute the r value into the other equation. This did not work. Thanks in advance! 1 solutions Answer 449825 by mananth(12270)   on 2013-04-11 06:51:55 (Show Source): You can put this solution on YOUR website!we have two unknown variables, the radius (r) and the height (h). Volume (V) = pir^2h 30 = pir^2h h = 30/pir2 Substitute this into the surface area equation for h, we get A = (2pir( 30 )/pir^2) + 2pir2) A = (60/r) + 2pir2 Take the derivative for r A = 60r-1 + 2pir2 A' = -60r-2 + 4pir when slope is zero 0 = -60r-2 + 4pir 60r-2 = 4pir Multiply both sides by r^2 60 = 4pir3 4.775 = r3 1.68 = r h = 30/pir^2 h=30/pi*(1.68)^2 h = 3.38 A = 2pirh + 2pir^2 A = 2*pi*(1.68)(3.38) + 2pi*(1.68)^2 A = 35.68 + 17.73 A = 53.41 square inches CHECK V= pi*1.68^2*3.38= 29.96 you can check for maxima or minima by taking the second derivate for more detailing
 Mixture_Word_Problems/736373: A merchant buys tea at the rate of Rs.4.10,Rs.3.75 and 4.50 per kg and mixes them in the proportion of 5:4:1.At what price should he sell the mixture to gain 25%?1 solutions Answer 449823 by mananth(12270)   on 2013-04-11 05:49:42 (Show Source): You can put this solution on YOUR website!4.10,Rs.3.75 and 4.50 per kg suppose he mixes 5 kg,4kg & 1 kg of mix to make 10 kg 5*4.10+4*3.75+1*4.5=40 Mixture costs 40/10 = Rs.4.00 /kg 4*1.25 = Rs. 5 /kg
 Sequences-and-series/736406: If (3-x)+(6)+(7-5x) is a geometric series, find two possible values for a) x b) the common ratio c) the sum of the GP.1 solutions Answer 449822 by mananth(12270)   on 2013-04-11 05:22:15 (Show Source): You can put this solution on YOUR website!(3-x)+(6)+(7-5x) is a geometric series, find two possible values for a) x b) the common ratio c) the sum of the GP. (3-x)(7-5x)=6^2 21-15x-7x+5x^2=36 5x^2-22x-15=0 5x^2-25x+3x-15=0 5x(x-5)+3(x-5)=0 (x-5)(5x+3)=0 x=5 OR -3/5 if x=5 -2,6,-28 common ratio = -4 you should be able to continue
 Equations/736367: how do i rewrite 3x^2-30x+77 to look like f(x)=a(x-h)^2+k1 solutions Answer 449807 by mananth(12270)   on 2013-04-11 00:02:57 (Show Source): You can put this solution on YOUR website! put it in the right format
 Polynomials-and-rational-expressions/736374: Solve =1 solutions Answer 449806 by mananth(12270)   on 2013-04-10 23:55:15 (Show Source): You can put this solution on YOUR website!= = = =0 since the index is odd x=1
 Travel_Word_Problems/736351: david canoes upstream a distance of 8 miles and then returns. The round-trip took 5 1/3 hours. The current of the stream was flowing at 2 miles per hour. What was david's canoeing speed?1 solutions Answer 449803 by mananth(12270)   on 2013-04-10 23:14:02 (Show Source): You can put this solution on YOUR website!canoe speed x mph current speed 2 kph against current x- 2 mph with current x+ 2 mph Distance= 8 miles Time against + time with = 5 1/3 hours t=d/r 8 /( x + 2 ) + 8 /(x - 2 ) = 5 1/3 LCD = (x - 2 ) ( x + 2 ) 8 *( x - 2 ) + 8 (x + 2 ) = 5 1/3 (x^2 - 4 ) 8 x - -16 + 8 x + 16 = 5 1/3 ( x ^2 - 4 ) 16 x = 5 1/3 x ^2 -21.33 5 1/3 x ^2 - -16 x - 21.33 Find the roots of the equation by quadratic formula a= 5 1/3 , b= -16 , c= -21.33 b^2-4ac= 256 + 455.04 b^2-4ac= 711.04 0 1.33 x1=( 16 + 26.67 )/ 10.67 x1= 4.00 x2=( 16 -26.67 ) / 10.67 x2= -1.00 Ignore negative value canoe speed 4.000 mph m.ananth@hotmail.ca canoe speed x mph current speed 2 kph against current x- 2 mph with current x+ 2 mph Distance= 8 miles Time against + time with = 5 1/3 hours t=d/r 8 /( x + 2 ) + 8 /(x - 2 ) = 5 1/3 LCD = (x - 2 ) ( x + 2 ) 8 *( x - 2 ) + 8 (x + 2 ) = 5 1/3 (x^2 - 4 ) 8 x - -16 + 8 x + 16 = 5 1/3 ( x ^2 - 4 ) 16 x = 5 1/3 x ^2 -21.33 5 1/3 x ^2 - -16 x - 21.33 Find the roots of the equation by quadratic formula a= 5 1/3 , b= -16 , c= -21.33 b^2-4ac= 256 + 455.04 b^2-4ac= 711.04 0 1.33 x1=( 16 + 26.67 )/ 10.67 x1= 4.00 x2=( 16 -26.67 ) / 10.67 x2= -1.00 Ignore negative value canoe speed 4.000 mph m.ananth@hotmail.ca canoe speed x mph current speed 2 kph against current x- 2 mph with current x+ 2 mph Distance= 8 miles Time against + time with = 5 1/3 hours t=d/r 8 /( x + 2 ) + 8 /(x - 2 ) = 5 1/3 LCD = (x - 2 ) ( x + 2 ) 8 *( x - 2 ) + 8 (x + 2 ) = 5 1/3 (x^2 - 4 ) 8 x - -16 + 8 x + 16 = 5 1/3 ( x ^2 - 4 ) 16 x = 5 1/3 x ^2 -21.33 5 1/3 x ^2 - -16 x - 21.33 Find the roots of the equation by quadratic formula a= 5 1/3 , b= -16 , c= -21.33 b^2-4ac= 256 + 455.04 b^2-4ac= 711.04 0 1.33 x1=( 16 + 26.67 )/ 10.67 x1= 4.00 x2=( 16 -26.67 ) / 10.67 x2= -1.00 Ignore negative value canoe speed 4 mph m.ananth@hotmail.ca
 Linear-equations/736271: Which equation below is perpendicular to th line y=1/3x+7? A. X+3y=4 B. x-3y=4 C. 3x+y=4 D. 3x-y=4 1 solutions Answer 449802 by mananth(12270)   on 2013-04-10 23:03:58 (Show Source): You can put this solution on YOUR website!option (c) the slopes are negative reciprocals slope of given line is 1/3 slope of perpendicular line will be -3
 Trigonometry-basics/736309: John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º. This particular tree grows at an angle of 83º with respect to the ground rather than vertically (90º). How tall is the tree? Thanks, paulaficarella@gmail.com 1 solutions Answer 449800 by mananth(12270)   on 2013-04-10 22:46:10 (Show Source): You can put this solution on YOUR website!here you have to use the law of sines let tree make an angle of 83 deg.with the ground. (YZ)angle ZYX = 83deg he walks 100 feet away from tree to point X (YX)angle YXZ= 33 deg so remaining angle YZX = 64 deg triangle YXZ is formed sin A /a = sin B /b = sin C /c Sin YZX/100 = sin YXZ/ YZ sin 64/100 = sin 33/YZ 100 * sin 33/sin 64 = YZ 100*0.54/0.898= YZ YZ= 60.13 feet the height of the tree You can solve the problem in a similar way if the tilt is to the other side.
 Travel_Word_Problems/736297: Lily's family took a motor boat 24 km down a river for a picnic. It took them 1 hr to get to the picnic spot. The ride back to the dock took an hour and a half. What was the average speed at which the river flowed? What would the boat's average speed be on a lake?1 solutions Answer 449772 by mananth(12270)   on 2013-04-10 21:20:45 (Show Source): You can put this solution on YOUR website!Boat speed =x kph current speed =y kph against current 1.5 hours with current 1 hours Distance against 24 miles distance with 24 miles t=d/r against current - 24.00 / ( x - y )= 1.50 1.50 ( x - y ) = 24.00 1.50 x - 1.50 y = 24.00 ....................1 24.00 / ( x + y )= 1.00 1.00 ( x + y ) = 24.00 1.00 x + 1.00 y = 24.00 ...............2 Multiply (1) by 1.00 Multiply (2) by 1.50 we get 1.50 x + -1.50 y = 24.00 1.50 x + 1.50 y = 36.00 3.00 x = 60.00 / 3.00 x = 20.00 mph plug value of x in (1) y 1.50 x -1.50 y = 24.00 30.00 -1.50 -30.00 = 24.00 -1.50 y = 24.00 -1.50 y = -6.00 kph y = 4.00 Boat speed 20.00 mph current speed 4.00 kph
 Travel_Word_Problems/736018: I am a librarian. A patron needs a solution to this problem: The speed of a boat in still waters is 10 km/h The boat travels 12 km upstream and 28 km downstream in a total of 4 hours. What is the speed of the stream? Thanks1 solutions Answer 449635 by mananth(12270)   on 2013-04-10 09:51:37 (Show Source): You can put this solution on YOUR website!let speed of current be c kph upstream speed = 10-c upstream distance = 12 down stream speed = 10+c down stream distance = 28 km upstream time + downstream time = 4 t=d/r 12/(10-c) + 28/(10+c)= 4 multiply the equation by (10+c)(10-c) 12(10+c)+28(10-c)=4(10+c)(10-c) 120+12c+280-28c=4(100-c^2) 400-16c=400-4c^2 re arrange 4c^2=16c /4c c=4 current speed = 4 kph