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mananth answered: 12270 problems
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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?
Thanks
1 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
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Word_Problems_With_Coins/736003: Hey my name is savannah and I do not even know how to begin this problem: Paul E. Bank has $2.25 in quarters and dimes. He has 15 coins. Find the number of quarters and dimes he has.
1 solutions
Answer 449622 by mananth(12270) on 2013-04-10 08:28:43 (Show Source):
You can put this solution on YOUR website!quarter is 25 cents
dime = 10 cents
I am sure you know this (Ha,Ha)
total coins = 15
if I have x dime then the balance will be 15-x
dimes = x
quarters = 15-x
Value of dimes = 10x
Value of quarters = 25(15-x)
total amount is $ 2.25 = 225 cents
10x+25(15-x)=225
10x+375-25x=225
-15x+375=225
-375
-15x=225-375
-15x=-150
/-15
x=10 the number of dimes
balance 5 will be quarters
CHECK to make sure
10*10 + 25 *5 = 225
There you are
cheers!
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Linear-systems/735949: I have tried many times i need serious help!this equation isn't working out right i don't know why, help!
Solve the linear system by using substitution:
2x+2y=6 and
-3x+5y=(-33)
1 solutions
Answer 449617 by mananth(12270) on 2013-04-10 06:12:03 (Show Source):
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Trigonometry-basics/735965: cos 4θ + 4 cos 2θ ≡ 8 cos4 θ − 3.
1 solutions
Answer 449616 by mananth(12270) on 2013-04-10 06:05:53 (Show Source):
You can put this solution on YOUR website! cos(4θ) =
cos(2*(2θ)) =
2cos^2(2θ) - 1 =
2[ 2cos^2(θ) - 1 ]^2 - 1
2 [ 4cos^4(θ) - 4cos^2(θ) + 1 ] - 1
8cos^4(θ) - 8cos^2(θ) + 1.....................(1)
.............
4 cos 2theta
4(2 cos^2  -1)
8 cos^2  -4................................(2)
(1)+(2)= RHS
8cos^4(θ) - 8cos^2(θ) + 1 + 8 cos^2 -4= RHS
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Trigonometry-basics/735545: Angles of Depression/Elevation: From the top of a tower 83 feet high, a man observes that the angle of elevation of the top of a certain tree is 13 degrees and the angle of depression of its base is 72 degrees. Find the height of the tree.''.
1 solutions
Answer 449463 by mananth(12270) on 2013-04-09 08:16:51 (Show Source):
You can put this solution on YOUR website!tower = 83 ft
let the tree be x ft taller than the tower
Tree height = (83+x) ft
Let y be the distance between tree and tower
Tan 13 = x/y
y=x/ Tan 13.........................(1)
Tan 72 = 83/y
y= 83/tan 72.........................(2)
x/ tan 13 = 83/ tan 72
x= 83 * tan 13 / tan 72
x= 6,23 ft
Height of tree = 83+6.23= 89.23 feet
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Trigonometry-basics/735516: a) prove that (1+tan A + sec A)(1+cot A-cosecA)=2
b) Prove that Sin 20degree.sin40degree.sin 60degree.Sin80degree = 3/16
c) sin 5A+2sin7A+sin9A/Cos3A+2cos5A+Cos7A = Sin2A+Cos2A.Tan5A
d) Show that Sin112+Cos12 / Cos12-Sin12 = Cot35
e) Prove that Sin 7x+Sinx / Cos5x-Cos3x = Sin2x-Cos2x.cotx
1 solutions
Answer 449461 by mananth(12270) on 2013-04-09 08:02:22 (Show Source):
You can put this solution on YOUR website!a) prove that (1+tan A + sec A)(1+cot A-cosecA)=2
LHS => 
= 2
LHS = RHS
b) Prove that Sin 20degree.sin40degree.sin 60degree.Sin80degree = 3/16
sin(A+B) = sin A cos B + cos A sin B
sin(40) as sin(60-20)
sin(80) as sin(60+20)
sin(20)•sin(60-20)•[√(3)/2]•sin(60+20)
- Simplify sin(60-20)•sin(60+20)
sin(60-20) = sin60•cos20 - sin20•cos60
sin(60+20)= sin60•cos20 + sin20•cos60
multiply
= sin²60•cos²20 - sin²20•cos²60
cos²A = 1 - sin²A
sin²60•cos²20 - sin²20•cos²60
= sin²60•(1-sin²20) - sin²20•(1-sin²60)
= sin²60- sin²20•sin²60 - sin²20 + sin²20•sin²60
= sin²60 - sin²20
= 3/4 - sin²20
We get
= sin20•[√(3)/2]•(3/4 - sin²20)
= [√(3)/8]•(3sin20 - 4sin³20)
we know that
sin(3A) = 3sin(A) - 4sin³(A)
(3sin20 - 4sin³20) = sin60
we have
= [√(3)/8]•sin60
= [√(3)/8]•[√(3)/2)
= 3/16
LHS = RHS
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Sequences-and-series/735082: The sum of 3 numbers in an A.P is 21 and their product is 280. find the numbers
1 solutions
Answer 449281 by mananth(12270) on 2013-04-08 09:21:55 (Show Source):
You can put this solution on YOUR website!let the numbers be
a-d, a , a+d
sum = 21
a-d+a+a+d=21
3a=21
a=7
(a-d)(a)(a+d)=280
(a^2-d^2)*a=280
(49-d^2)*7=280
49-d^2= 280/7
49-d^2= 40
d^2=49-40
d^2=9
d= +/-3
(a-d),a,(a+d)
if d=3
4,7,10
if a=-3
10,7,4
(Academic)
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Circles/735112: the extremities of the diameter of a circle have coordinates(-4,3)and (6,-2). then the length of the intercept which the circle makes on the y-axis is
1 solutions
Answer 449279 by mananth(12270) on 2013-04-08 09:11:09 (Show Source):
You can put this solution on YOUR website!Step 1: Find the Midpoint (h,k) of AB:
h = A1 + B1
2
h = -4 + 6
2
h = 2
2
h = 1
k = A2 + B2
2
k = 3 + -2
2
k = 1
2
k = 0.5
From above, the center of our circle is (h, k) = (1, 0.5)
Calculate radius:
r = Square Root((y1 - x1)2 + (y2 - x2)2)
r = Square Root((6 - -4)2 + (-2 - 3)2)
r = ½Square Root((102 + -52))
r = ½√(100 + 25)
r = ½√125
r = ½√125
r = ½(11.1803398875)
r = 5.5902
Now calculate our circle equation using (h, k), and r
Find the equation of the circle with center (h,k) = (1,0.5) and radius r = 5.5902
The standard equation for a circle is (x - h)2 + (y - k)2 = r2
Plugging in our numbers, we get:
(x - 1)2 + (y - 0.5)2 = 5.5902^2
(x - 1)2 + (y - 0.5)2 = 31.25033604
plug x= 0
you will get two values of y
add up the two intercepts to get the length of the chord
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Money_Word_Problems/735075: Okay, so I am a very slow learner, and I find it hard to learn things myself if I do not have a fully worked example infront of me.
We have just moved onto exam prep and I am revising simple interest
The question is
At what rate must $24 000 be invested to earn $180 per month?
My working so far consists of
180 = 24000 x R x T
The text book has given us T (time)... being 1/2 I know how to solve, I am just very confused at to why the time is 1/2?
Thank you so much
Kate
1 solutions
Answer 449271 by mananth(12270) on 2013-04-08 06:50:03 (Show Source):
You can put this solution on YOUR website!P= Principal
r= rate percent per year
t= time in years
I= interest earned
you need 180 per month
180*12= 2160 per year
The formula is
I = P * R * T
2160 = 24000 *R *1 ( 1 year)
=0.09
0.09*100 = 9%
You have to invest at 9%
CHECK
If I invest $24000 @9% for 1 year
24000 * 0.09
=2160
2160/12= 180 per month
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Trigonometry-basics/735049: The angles of elevation of the top of a tower from the points P and Q at distances of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary.What is the height of the tower?
1 solutions
Answer 449263 by mananth(12270) on 2013-04-08 01:29:15 (Show Source):
You can put this solution on YOUR website!And let Q be at a distance of b from the tower making an angle 
Let P be at distance a from the tower. This will make an angle 
Let height of tower be h
Tan =h/a
Cot =h/a
Tan =a/h
Tan  = h/b
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Money_Word_Problems/734653: A water trough is constructed by bending a
4- by 6-foot rectangular sheet of metal down the middle and
attaching triangular ends (see the figure). If the volume of
the trough is 9 cubic feet, find the width correct to two decimal
places.
1 solutions
Answer 449076 by mananth(12270) on 2013-04-07 01:48:34 (Show Source):
You can put this solution on YOUR website!bend in the middle . you will get an isosceles triangle .
The height of triangle will be 
= 
Area of triangle = (1/2) * base * height
A= sqrt(3)/2 * base
Length = 6 feet
Volume of tank = 6*sqrt(3)/2 * base
9=sqrt(3)/2 * base
Base = width of tank = 6sqrt(3)
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Linear-equations/734630: I am really having trouble understanding how to solve a system of equations by graphing. Can someone please help me understand how to set up and work through these types of problems?
I do not want to give the problems I have because they are homework, and I want to work my own homework. If you could just provide examples of how to set up, work, and graph I would be grateful.
1 solutions
Answer 449073 by mananth(12270) on 2013-04-07 01:38:23 (Show Source):
You can put this solution on YOUR website!-3x-2y = 6 .............1
3x-y = 12 .............2
equation1
when x= 0, y=-3(0,-3)
when y = 0,x=-2(-2,0)
Equation 2
when x= 0,y=-12 (0,-12)
when y =0,x=4(4,0)
Plot these points and draw the lines.
The point of intersection is the solution of the system.
The solution is (2,-6)
m.ananth@hotmail.ca
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Volume/734646: a cylindrical water tank near the town library is 15 meters high and has a circumference of 85 meters. what is the APPROXIMATE volume, to the nearest whole number, of the water tank?
A) 1,275m^3
B) 2,875m^3
C) 8,627m^3
D) 34,497m^3
1 solutions
Answer 449070 by mananth(12270) on 2013-04-07 01:23:22 (Show Source):
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Equations/734608: I have a algebra question that I have been struggling to figure out for a while. It is simplifing a radical equation. The equation is(2√5+3√7)^2. If you can please add the steps so I can work through it to understand it better. Thank you very much!
1 solutions
Answer 449053 by mananth(12270) on 2013-04-06 21:58:36 (Show Source):
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Linear-systems/734261: Use a specified method to solve the system of equations.
(graphically)
y=4-x
y=x-6
I understand that the first ordered pair is (-1,4) and the second is (1,-6)
I just have no clue how to graph these.
1 solutions
Answer 448871 by mananth(12270) on 2013-04-05 22:23:28 (Show Source):
You can put this solution on YOUR website!y=4-x
y=x-6
Find the x & y intercept points by plugging x=0,y=0 in both equations.
equation I
when x= 0 y= 4 ,( 0 , 4 )
when y = 0 x= 4 ,( 4 , 0 )
Equation 2
when x= 0 y= -6 ( 0 , -6 )
when y = 0 x= 6 ( 6 , 0 )
You will observe that the point of intersection is 5,-1)
The solution of the system is ( 5 ,-1 )
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Volume/734275: suppose that a box has a base with a width of x, a length of x+1, and a height of 2. It is cut from a rectangular sheet of material with an area of 182 inches2
find the dimension of the box.
1 solutions
Answer 448868 by mananth(12270) on 2013-04-05 22:11:36 (Show Source):
You can put this solution on YOUR website!width of x, a length of x+1, and a height of 2. It is cut from a rectangular sheet of material with an area of 182
since the height is 2 , 2 inches is cut off from the sides
width will be x+4
length will e x+5
area of sheet = (x+4)(x+5)= 182
x^2+9x+20=182
x^2+9x-162=0
x^2+18x-9x-162=0
x(x+18)-9(x+18)=0
(x+18)(x-9)=0
x= 9 which is positive
Box dimension 9 by 10 by 2"
width = 13" and length = 14" of sheet
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Travel_Word_Problems/734319: a motorist travels 60 miles while driving in the rain. In sunny weather, he drives 21 mph faster and covers 96 miles in the same amount of time. what is the speed in the rain and the speed in sunny weather? Please help me solve this problem.
1 solutions
Answer 448864 by mananth(12270) on 2013-04-05 22:00:53 (Show Source):
You can put this solution on YOUR website!Time 60 miles in rain = time 96 miles in sun
speed in rain = x
speed in sun = x+21
time in rain = 60/x
Time in sun = 96/(x+21)
60/x= 96/(x+21)
60(x+21) = 96x
60x+1260=96x
36x=1260
x=35 km/h
you can continue
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Numbers_Word_Problems/734133: Please walk me through the steps to the following problem. I don't even know how to start.
A Ford Explorer can hold a driver and four passengers. A Dodge Caravan can hold a driver and six passengers. The biology dept. is taking a total of 95 people on a field trip. The college wants to use twice as many Caravans as Explorers because the Caravans get better gas mileage. How many of each kind of vehicle are needed?
1 solutions
Answer 448740 by mananth(12270) on 2013-04-05 10:13:26 (Show Source):
You can put this solution on YOUR website!A Ford Explorer can hold a driver and four passengers. A Dodge Caravan can hold a driver and six passengers. The biology dept. is taking a total of 95 people on a field trip. The college wants to use twice as many Caravans as Explorers because the Caravans get better gas mileage. How many of each kind of vehicle are needed?
let explorers be x
and caravans be y
y=2x
5x+7y=95
substitute y=2x
5x+7(2x)=95
5x+14x=95
19x=95
x=5
5 explorers and 10 caravans
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Travel_Word_Problems/734136: A boat travels 7 km upstream and 7km back. The time for the round trip is 10 hours. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?
1 solutions
Answer 448739 by mananth(12270) on 2013-04-05 10:09:15 (Show Source):
You can put this solution on YOUR website!A boat travels 7 km upstream and 7km back. The time for the round trip is 10 hours. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?
let speed in still water = x km/h
with current x+4 km/h
against current speed = x-4 km/h
time up + time return = 10
7/(x+4)+7/(x-4)=10
multiply equation by (x+4)(x-4)
7(x-4)+7(x+4)= 10(x^2-16)
7x-28+7x+28 = 10x^2-160
14x=10x^2-160
10x^2-14x-160=0
/2
5x^2-7x-80=0
Find the roots of the equation by quadratic formula
a= 5 , b= -7 , c= -80
b^2-4ac= 49 + 1600
b^2-4ac= 1649
x1=( 7 + 40.61 )/ 10
x1= 4.76
x2=( 7 -40.61 ) / 10
x2= -3.36
Ignore negative value
boat speed 4.761 kph
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test/734125: A new still unsharpened, wooden pencil has the form of a cylinder. It is 19cm long and has a diameter of 0.8cm.The cylinder hole for the core in the middle of the pencil has a diameter of 0.2cm
1) calculate how much cm3 of wood is needed for such a pencil
1 solutions
Answer 448729 by mananth(12270) on 2013-04-05 09:14:46 (Show Source):
You can put this solution on YOUR website!outer volume - inner volume = volume of wood for the pencil
outer radius =0.8/2 = 0.4 cm
length = 9 cm
inner radius = 0.2/2 = 0.1
length = 9 cmm
V cylinder = pir^2h
V(whole pencil) = pi * 0.4^2*9
V (core) = pi*0.1^2*9
V ( wood) = pi*0.4*2*9-pi*0.1^2*9
= 9*pi(0.4^2-0.1^2)
=4.24 cm^3
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Travel_Word_Problems/734095: A train leaves a station at 9.00 p.m. Another train leaves same station at 10.00 p.m. first train runs at 35 kmph and Second train crosses the first train in 4 hours. Find the speed of the second train.
1 solutions
Answer 448728 by mananth(12270) on 2013-04-05 09:05:20 (Show Source):
You can put this solution on YOUR website!difference of time between Train I and Train II 1 hour
speed of train I = 35 kmph
speed of train II = x kmph
catch up speed = x-35
catch up time = 4 hours
catch up distance = 35 km ( distance traveled in 1 hour by Train I)
t= d/s
4 = 35/(x-35)
4(x-35)=35
4x-140=35
4x=140+35
4x=175
x= 43.75 kmph
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Linear_Equations_And_Systems_Word_Problems/734074: An investor invested a total of $2200 in two mutual funds. One earned 5% profit while the other earned a 3% profit. If the investor's total profit was $86, how much was invested in each mutual fund?
1 solutions
Answer 448705 by mananth(12270) on 2013-04-05 02:07:17 (Show Source):
You can put this solution on YOUR website! Part I 3.00% per annum ------------- Amount invested =x
Part II 5.00% per annum ------------ Amount invested = y
2200
Interest----- 86.00
Part I 3.00% per annum ---x
Part II 5.00% per annum ---y
Total investment
x + 1 y= 2200 -------------1
Interest on both investments
3.00% x + 5.00% y= 86
Multiply by 100
3 x + 5 y= 8600.00 --------2
Multiply (1) by -3
we get
-3 x -3 y= -6600.00
Add this to (2)
0 x 2 y= 2000
divide by 2
y = 1000
Part I 3.00% $ 1200
Part II 5.00% $ 1000
CHECK
1200 --------- 3.00% ------- 36.00
1000 ------------- 5.00% ------- 50.00
Total -------------------- 86.00
m.ananth@hotmail.ca
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