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1 solutions
Answer 223529 by mananth(12270)   on 2010-06-08 21:58:43 (Show Source):
You can put this solution on YOUR website!diagonal of square = 10 in.
let the side be x in.
The diagonal and the sides of square form a right angle.
Apply pythagoras theorem
x^2 +x^2 = 10^2
2x^2 =100
x^2=50
x= 7.07 in
Area = 50 sq. in
perimeter = 4*7.07
=28.28 inches
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Miscellaneous_Word_Problems/312658: the length of a rose garden is 6 feet more than the width. the garden is surrounded by a uniform pathway which is three feet wide. the area of the pathway alone is 216 square feet. what is the perimeter of the rose garden?
1 solutions
Answer 223527 by mananth(12270) on 2010-06-08 21:53:07 (Show Source):
You can put this solution on YOUR website!let the width of the rose garden be x feet
The length will be x+6 feet
..
Pathway is 3 feet wide.
So width and length will increas by 6 feet
..
x+6 will be the width of whole plot
x+6+6 will be the length of the whole plot
..
Area of whole plot - area of pathway = area of rose garden.
(x+6)(x+12)-216 = x(x+6)
x^2+18x+144-216=x^2+6x
12x=72
x= 6 the width
Length will be x+6 = 12
..
The perimeter of rose garden will be 2*6+2*12
=36 feet
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Polynomials-and-rational-expressions/312666: the product of the page numbers of 2 facing pages of a book is 110. Find the page numbers.
1 solutions
Answer 223525 by mananth(12270) on 2010-06-08 21:45:52 (Show Source):
You can put this solution on YOUR website!if the pages are facing each other they have to be cosequtive pages.
let one page number be x
the other will be x+1
..
x(x+1)=110
x^2+x-110=0
x^2+11x-10x-110=0
x(x+11)-10(x+11)=0
(x+11)(x-10)=0
x=10 since page number cannot be negative
10 & 11 are the page numbers
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Polynomials-and-rational-expressions/312663: a rectangular table is 4 feet longer as long as it is wide. If the area is 144 ft to the 2nd power find the length and width.
1 solutions
Answer 223523 by mananth(12270) on 2010-06-08 21:42:32 (Show Source):
You can put this solution on YOUR website!let the width be x feet
length = x+4 feet
Area = L*W
..
x(x+4)=144
x^2+4x-144=0
..
Find X1, X2 the roots
X1= -4 +sqrt(16+576) / 2
= 10.165
X2 =-4 -sqrt(16+576) / 2
= -14.165
..
X= 10.165 feet the width
Length = 14.165 feet
.
CHECK
14.165*10.165== 143.98
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Expressions-with-variables/312659: I am confused on the following problem:
During a 3000 mi flight, a plance encountered a strong tail wind that increased its speed by 100 mi/h. This increase in speed shortened the flying time by one hour. Find the speed of the plane relative to the ground.
1 solutions
Answer 223519 by mananth(12270) on 2010-06-08 21:32:24 (Show Source):
You can put this solution on YOUR website!distance traveled = 3000 miles.
let speed of plane in still air be x mph
speed with tail wind = x+100 mph
..
if it had traveled without any wind it would take 3000 / x hours
with tail wind the time = 3000/x+100.
..
It took 1 hour less.
3000/x - 3000/ x+100 =1
LCM = x(x+100)
3000(x+100) - 3000x = x(x+100)
3000x +300 000 - 3000x = x^2 +100x
x^2+100x-300000=0
x^2 +600x-500x-300000=0
x(x+600)-500(x+600)=0
(x+600)(x-500)=0
x=500 mph in still air
speed with tail wind = 600 mph
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Mixture_Word_Problems/312625: How many milliliters of water must be added to 10 milliliters of a 30%-sulfuric acid solution to make a 15%-sulfuric acid solution?
1 solutions
Answer 223510 by mananth(12270) on 2010-06-08 20:08:33 (Show Source):
You can put this solution on YOUR website!30% sulphuric acid = 70% water
15% sulphuric acid = 85% water
Let quantity of water be x ml
concentration equation
x+0.7*10 = 0.85(x+10)
x+7=0.85x+8.5
0.15x=1.5
x= 1.5/0.15
x=10 ml
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Average/312593: Please help me solve this finance: Ben, Jim, Alice, Erin, and Rick are friends. Ben is 20 years old, Jim is 17 years old, Alice is 21 years old, and Erin is 19 years old. The average age of the 5 friends is 20. How old is Rick?
1 solutions
Answer 223488 by mananth(12270) on 2010-06-08 18:50:18 (Show Source):
You can put this solution on YOUR website!The average age of 5 = 20. The total of their ages =100
..
The total age of Ben, Jim, Alice, Erin,= 20+17+21+19=77
The difference = 33
So Ricks age = 33 years
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Unit_Conversion_Word_Problems/312407: A school club is planning a bus trip to the wildlife park. A bus which will hold up to 45 people will cost 600 dollars and admission tickets cost 30 dollars each.
If you intend to charge each person 50 dollars, including bus and admission ticket, what is the minimum number of people who must participate to ensure that these costs are covered?
1 solutions
Answer 223310 by mananth(12270) on 2010-06-08 09:03:13 (Show Source):
You can put this solution on YOUR website!let the number of persons be x
cost will be 30x +600
50x will be the amount collected.
if the costs have to be met the revenue must be equal to the collection
30x+600=50x
20x =600
x= 30
To break even they have to have a minimum of 30 persons.
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Travel_Word_Problems/312281: How much work is done when a 40.0kg mass is lifted vertically against gravity to a height of 5.0 meters?
1 solutions
Answer 223270 by mananth(12270) on 2010-06-07 20:28:59 (Show Source):
You can put this solution on YOUR website!W= F* S
F= force
g= 9.8 m/sec^2
m= 40 kg
..
F= mg
= 40*9.8 N
=39.2 N
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Distance moved = 5 meters
work done = F * displacement
work done =39.2 * 5 J
=195 J
Work done = 195 J
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Travel_Word_Problems/312273: a train leves at 9 am going 60 mph and another train leaves at 12 noon going 75 mph. how long until the second train catches the first
1 solutions
Answer 223267 by mananth(12270) on 2010-06-07 20:07:33 (Show Source):
You can put this solution on YOUR website!train A leaves 9.00am at 60 mph.
Train B leaves at 12 noon at 75 mph
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Before train B leaves train A has traveled 60*3 = 180 miles.
From this point let train A travel x miles before they meet.
..
So train B travels x+180 miles to catch up.
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time taken by train A = x/60
time taken by train B = x+180 / 75
..
x/60 = x+180 / 75
75x = 60(x+180)
75x=60x +10800
15x=10800
x= 720 miles.
Train B has to travel 720 miles to catch up.
its speed is 75 mph
time taken = 720/75
=9.6 hours
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Geometry_Word_Problems/312263: two buildings are 60 feet apart acrooss a street. a person on top of the building finds the angle of elevation of the roof of the taller building to be 20 degrees and the angke of depression of its base to be 35 degrees. how tall is the taller building to the nearest foot?
1 solutions
Answer 223264 by mananth(12270) on 2010-06-07 19:51:12 (Show Source):
You can put this solution on YOUR website!Angle of elevation = 20
angle of depression to the foot = 35
.
let h1 be the difference in heights of the building
Let h2 be the height of the smaller building
h1+h2 = H the height of the taller building.
.
tan 20 + tan 35 = h1/D+h2/D
tan 20 + tan 35= h1+h2 /D
d*(tan 20 + tan 35)= H
60*(tan 20 + tan 35)=H
163 feet
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Triangles/312226: find area of equilateral triangle of side 4a using heron’s formula. using this formula find area of an equilateral triangle whose perimeter is 540cm.
1 solutions
Answer 223251 by mananth(12270) on 2010-06-07 19:21:28 (Show Source):
You can put this solution on YOUR website!heron's formula
area of triangle = sqrt(s(s-a)(s-b)(s-c))
s= half perimeter = 4a+4a+4a /2 = 6a
Area = sqrt(6a(2a)(2a)(2a))
area = sqrt48a^4.
.
perimeter = 540
side = 180
s=270
area =sqrt(270(90)(90)(90))
=14029.26 sq cm
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Money_Word_Problems/312241: how many years will it take for an amount of money to double when it is compounded annually by a 4.3% interest rate?
1 solutions
Answer 223241 by mananth(12270) on 2010-06-07 19:02:43 (Show Source):
You can put this solution on YOUR website!let us assume the invested amount = 100
The money at the end of 1 year = 200
rate of interest = 4.3 %
compounded annually.
.
Formula
A= p(1+r/t)^nt
200=100(1+.043)^n
2=1.043^n
log2/log1.043= n
number of years = 16.46 for the money to double
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Travel_Word_Problems/311941: Horizons have a manufacturing plant located 300 mi from company headquarters. Their corporate pilot must fly from headquarters to the plant and back in 4 hrs. If there is a 20-mph headwind going and a 20-mph headwind tailwind returning, how fast must the plane be able to travel in still air?
1 solutions
Answer 223071 by mananth(12270) on 2010-06-07 04:25:28 (Show Source):
You can put this solution on YOUR website!300/x+20 + 300 / x-20 = 4
LCM (x+20)(x-20)
..
300(x-20)+300(x+20)= 4x^2-1600
300x-6000 +300x+6000= 4x^2-1600
4x^2-600x-1600=0
x^2-150x-400=0
Find X1 , X2 the roots of the equation
X1= 150+sqrt((-150)^2+1600) / 2
x= 152.6 mph
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Travel_Word_Problems/311966: An airplane travels 6030km against the wind in 30 hours and 6750 with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
1 solutions
Answer 223069 by mananth(12270) on 2010-06-07 04:03:56 (Show Source):
You can put this solution on YOUR website!let the speed of plane in still air be xmph
speed of wind = y
..
against wind speed will be x-y.
Time traveled = 30 hour
distance = 6030 miles
so 30(x-y) = 6030
..
with wind speed will be x+y
time taken = 30 hours
distance = 6750 miles
30(x+y)=6750
..
30x-30y=6030
30x+30y=6750
ADD
..
60x = 12780
x= 12780/60
x= 213 mph the speed of plane in still air
plug the value of x in any equation
x+y= 225
213+y=225
y=12 mph the speed of wind
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