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1 solutions
Answer 355325 by mananth(12270)   on 2011-12-10 04:13:24 (Show Source):
You can put this solution on YOUR website!speed of wind in still air = x kmph
speed against wind = y kmph
with wind speed = 158 kmph
x+y=158
x-y=112
Add the two equations
2x=270
/2
x= 135 kmph speed of plane.
plug x in x+y=158
135+y=158
y=23 kmph
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Trigonometry-basics/544873: Find the length of the sides of a 45 degree right triangle if the hypotenuse is 7?
1 solutions
Answer 355322 by mananth(12270) on 2011-12-10 04:00:00 (Show Source):
You can put this solution on YOUR website!If one angle is 45 deg the other will also be 45deg in a right triangle.
sum of all angles of triangle = 180 deg.
The legs will be x each.
hypotenuse = 7
x^2+x^2=7^2 by pythagoras theorem
2x^2=49
x^2=49/2
x= 7/sqrt(2)
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Equations/544891: The ratio between the present ages of Prakash and Vikas is 5 : 7 respectively. If the difference between Vikas’s present age and Prakash’s age after 6 years is 2, what is the total of their present ages ?
1 solutions
Answer 355320 by mananth(12270) on 2011-12-10 03:55:11 (Show Source):
You can put this solution on YOUR website!prakash to Vikas ratio = 5/7
multiply by common factor x
Prakash = 5x & Vikas = 7x
prakash after 6 years = 5x+6
7x-(5x+6)=2
7x-5x-6=2
2x=8
x=4
Prakash = 5*4 = 20
Vokas = 7*4 = 28
Sum = 20+28=48 years
m.ananth@hotmail.ca
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Travel_Word_Problems/544480: On a journey of 300km, the train driver calculates that if he reduces his average speed by 10km/h he would take 25 mins longer. Find his average speed
1 solutions
Answer 355120 by mananth(12270) on 2011-12-09 01:29:18 (Show Source):
You can put this solution on YOUR website!Original speed x
Changed speed x - 10
Distance = same 300 miles
original time – time with decreased speed =0.42
t=d/t
300/(x-10)-300/x= 5/12
300x-300(x-10)= 5*x(x-10)/12
300x-300x+3000=(5x^2-50x)/12
multiply by 12
36000=5x^2-50x
5x^2-50x-36000=0
/5
x*2-10x-7200=0
x^2-90x+80x-7200=0
x(x-90)+80(x-90)=0
(x-90)(x+80=0
x= 90 mph the average speed.
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Graphs/544491: For the equation y = 3x + 5 write the equation of the lines in slope intercept form that pass through point (-4,1) and are parallel and perpendicular to the given line.
1 solutions
Answer 355118 by mananth(12270) on 2011-12-09 01:06:59 (Show Source):
You can put this solution on YOUR website!1 y = 3 x + 5
Divide by 1
y = 3 x + 5
Compare this equation with y=mx+b
slope m = 3
The slope of a line parallel to the above line will be the same
The slope of the required line will be 3
m= 3 ,point ( -4 , 1 )
Find b by plugging the values of m & the point in
y=mx+b
1 = -12 + b
b= 13
m= 3
Plug value of the slope and b in y = mx +b
The required equation isy = 3 x + 13
For perpendicular line the slope will be negative reciprocal.
which is -1/3
the line passes through (-4,1)
y= mx +b
1=-1/3(-4)+b
1=4/3+b
b=-1/3
The equation will be y= -(1/3) x -1/3
m.ananth@hotmail.ca
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Mixture_Word_Problems/544528: Two solutions of salt water contain 0.04% and 0.19% salt respectively. A lab technician wants to make 1 liter of solution which contains 0.13% salt. How much of each solution should she use?
1 solutions
Answer 355117 by mananth(12270) on 2011-12-09 01:04:05 (Show Source):
You can put this solution on YOUR website!percent ---------------- quantity
Salt solution I 0.04 ---------------- x L
Salt solution II 0.19 ------ 1 - x L
Mixture 0.13% ---------------- 1
0.04x+0.19(1-x) =0.13* 1
0.04x+0.19-0.19 x=0.13
0.04x- 0.19x =0.13- 0.19
-0.15 x=-0.06
/ -0.15
x= 0.4 L 0.04% Salt solution I
0.6 L 0.19% Salt solution II
m.ananth@hotmail.ca
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Travel_Word_Problems/544511: A motorboat can travel 20 mph in still water. If the boat can travel 3 miles downstream in the same time it takes to travel 2 miles upstream, what is the rate of the current?
1 solutions
Answer 355115 by mananth(12270) on 2011-12-09 00:58:21 (Show Source):
You can put this solution on YOUR website!Boat speed = 20 mph
current speed = x mph
speed against current 20 - x
speed with current 20 + x
Distance against current 2 miles
Distance with current 3 miles
t=d/r time against = time with current
2/(20-x )=3/(20 +x)
2(20+x )= 3( 20-x )
40+2x = 60-3x
3x +2x=20
5x=20
/5
x = 4 mph current speed
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Mixture_Word_Problems/544527: how much of a 20% solution of nitric acid should be added to 3 L of 12% solution to produce a 15% solution?
1 solutions
Answer 355113 by mananth(12270) on 2011-12-09 00:51:38 (Show Source):
You can put this solution on YOUR website! --------percent ---------------- quantity
Nitric acid I 12 ---------------- 3 L
Nitric Acid II 20 ---------------- x L
Mixture 15 ---------------- 3 + x L
12 * 3 + 20 x = 15 ( 3 + x )
36 + 20 x = 45 + 15 x
20 x + -15 x = 45 - -36
5 x = 9
/ 5
x = 1.8
1.8 L of Nitric Acid II
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Linear-equations/544516: Please help me solve this equation: 
I can figure it out when I have to solve for an x when the y is given but don't understand when there is two y's. Please help and thanks!
1 solutions
Answer 355112 by mananth(12270) on 2011-12-09 00:49:05 (Show Source):
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Money_Word_Problems/544381: Linda invested her savings in two investment funds. The amount she invested in Fund A was twice as much as the amount she invested in Fund B. Fund A returned a 7% profit and Fund B returned a 3% profit. How much did she invest in Fund A, if the total profit from the two funds together was $1700?
1 solutions
Answer 355107 by mananth(12270) on 2011-12-09 00:43:15 (Show Source):
You can put this solution on YOUR website!Fund A 3.00% per annum ------------- x
Fund B 7.00% per annum ------------ y= 2x
Interest----- $1,700.00
3.00% x + 7.00% * 2 x = $1,700.00
0.03 x + 0.07 * 2 x = $1,700.00
0.03 x + 0.14 x = $1,700.00
0.17 x = $1,700.00
/ 0.17
x= $10,000.00 --- Fund A
2 x = $20,000.00 Fund B
CHECK
$300.00 + $1,400.00 = $1,700.00
m.ananth@hotmail.ca
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Linear-equations/544379: WRITE THE EQUATION in slope intercept form of the line that is perpendicular to y=-5x+2 and passes through 10, 8
1 solutions
Answer 355062 by mananth(12270) on 2011-12-08 20:06:25 (Show Source):
You can put this solution on YOUR website!1 y = -5 x + 2
Divide by 1
y = -5 x + 2
Compare this equation with y=mx+b, m= slope & b= y intercept
slope m = -5
The slope of a line perpendicular to the above line will be the negative reciprocal 1/5
m1*m2=-1
The slope of the required line will be 1/5
m= 1/5 ,point ( 10 , 8 )
Find b by plugging the values of m & the point in
y=mx+b
8 = 2 + b
b= 6
m= 1/5
The required equation isy = 1/ 5 x + 6
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/544372: Here is the problem I am trying to solve:
The sum of the digits of a two-digit number is 6. If the digits are reversed, the new number is 9 less than four times the original number. Find the original number.
Thanks!
1 solutions
Answer 355061 by mananth(12270) on 2011-12-08 20:03:30 (Show Source):
You can put this solution on YOUR website!let the number be xy. x in the tens place.
x+y=6------------(1)
10y+x=4(10x+y)-9
10y+x=40x+4y-9
6y-39x=-9------------(2)
Add equation (1) & (2)
1.00 x + 1 y = 6 .............1
-39 x + 6 y = -9 .............2
Eliminate y
multiply (1)by -6
Multiply (2) by 1
-6 x -6 y = -36
-39 x + 6 y = -9
Add the two equations
-45 x = -45.000
/ -45
x = 1
plug value of x in (1)
x + y = 6
+ y = 6
y = 6 -1
y = 5
y = 5
The number is 15
m.ananth@hotmail.ca
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Linear-equations/544363: Find A and B so that the graph of Ax+By=-26 contains the points (4,-5) and (1,-11)
1 solutions
Answer 355060 by mananth(12270) on 2011-12-08 19:56:15 (Show Source):
You can put this solution on YOUR website!Plug the values of the points in the equation Ax+by=-26
we get
4.00 a -5 b = -26 .............1
1 a -11 b = -26 .............2
Eliminate b
multiply (1)by -11
Multiply (2) by 5
-44 a 55 b = 286
5 a + -55 b = -130
Add the two equations
-39 a = 156.000
/ -39
a = -4
plug value of a in (1)
4 a + -5 b = -26
-16 + -5 b = -26
-5 b = -26 + 16
-5 b = -10
b = 2
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test/543200: Can you please help me to Solve this equation containing a rational exponent on the variable.
4x^3/4-31=77
1 solutions
Answer 354785 by mananth(12270) on 2011-12-07 07:11:05 (Show Source):
You can put this solution on YOUR website!4x^3/4 -31=77
4x^3/4=77+31
4x^3/4 =108
take the 4th power of the equation
(4x^(3/4))^4= 108)^4
256x^3=108^4
x^3=108^4/256
x^3=531441
x= cuberoot(531441)
x=81
m.ananth@hotmail.ca
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Mixture_Word_Problems/543131: How many ounces of a 35% alcohol solution and a 38% alcohol solution must be combined to obtain 63 ounces of a 36% solution?
1 solutions
Answer 354774 by mananth(12270) on 2011-12-07 01:24:40 (Show Source):
You can put this solution on YOUR website!percent ---------------- quantity
Alcohol I 35 ---------------- x Oz
Alcohol II 38 ------ 63 - x Oz
Mixture 36.00% ---------------- 63
35 x + 38 ( 63 - x ) = 36 * 63
35 x + 2394 - 38 x = 2268
35 x - 38 x = 2268 - 2394
-3 x = -126
/ -3
x= 42Oz 35.00% Alcohol I
21Oz 38.00% Alcohol II
m.ananth@hotmail.ca
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Travel_Word_Problems/543154: With a north wind blowing at 20 mi/hr a helicopter flies due north for 30 miles and then returns. If the total traveling time was 48 mins find the helicopters speed in still air.
1 solutions
Answer 354773 by mananth(12270) on 2011-12-07 01:17:58 (Show Source):
You can put this solution on YOUR website!Helicopter speed x mph
wind speed 20 mph
against wind x- 20 mph
with wind x+ 20 mph
Distance= 30 miles
Time against + time with = 0.8 hours
t=d/r
30 /( x + 20 ) + 30 /(x - 20 ) = 0.8
LCD = (x - 20 ) ( x + 20 )
30 *( x - 20 ) + 30 (x + 20 ) = 0.8
30 x - 600 + 30 x + 600 = 0.8 ( x ^2 - 400 )
60 x = 0.8 x ^2 - 320
0.8 x ^2 - -60 x - 320
Find the roots of the equation by quadratic formula
a= 0.8 , b= -60 , c= -320
b^2-4ac= 3600 + 1024
b^2-4ac= 4624 
x1=( 60 + 68 )/ 1.6
x1= 80
x2=( 60 -68 ) / 1.6
x2= -5
Ignore negative value = 80 mph speed
m.ananth@hotmail.ca
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Travel_Word_Problems/542512: A plane traveled 300 miles to Lagos and back. The trip there was with the wind. It took 3 hours. The trip back was into the wind. The trip back took 6 hours. What is the speed of the plane in still air? What is the speed of the wind? Please help!
1 solutions
Answer 354605 by mananth(12270) on 2011-12-06 10:05:17 (Show Source):
You can put this solution on YOUR website!plane speed speed =x mph
wind speed =y mph
against wind , x-y 6 hours
with wind , x+y 3 hours
Distance = same= 300 miles
t=d/r against wind
300 / ( x - y )= 6.00
6 ( x - y ) = 300.00
With wind
6 x -6 y = 300 ....................1
300 / ( x + y )= 3.00
3.00 ( x + y ) = 300
3.00 x + 3.00 y = 300 ...............2
Multiply (1) by 1.00
Multiply (2) by 2.00
we get
6 x + -6 y = 300
6 x + 6 y = 600
12 x = 900
/ 12
x = 75 mph
plug value of x in (1)
6 x -6 y = 300
450 -6 y = 300
-6 y = 300 -450
-6 y = -150
y = 25 mph
plane speed 75 mph
wind 25 mph
m.ananth@hotmail.ca
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Rectangles/542498: How far up a wall will an 11 meter ladder reach, if the foot of the ladder must be 4 meters from the base of the wall? Enter the numerical answer only rounded to the nearest hundredth.
1 solutions
Answer 354599 by mananth(12270) on 2011-12-06 09:55:34 (Show Source):
You can put this solution on YOUR website!The ladder,the floor & the wall form a right triangle.
The base is one leg The height is the other leg
The ladder acts as the hypotenuse
Pythagoras theorem
(Hyp)^2= (leg1)^2+ Leg2^2
Hypotenuse = 11 ft
leg1= 4 ft
Leg2= ?
leg2^2=hyp^2-leg1^2
Leg2^2= 11 ^2 - 4 ^2
Leg2^2= 121 - 16
Leg2^2= 105
Leg2= 
Leg2= 10.25 ft
The ladder touches the wall at a height of 10.25 ft
m.ananth@hotmail.ca
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