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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextSquare-cubic-other-roots/167014: At a height of h meters you can see V kilometere to the hozizon These number are related by the equation V = 3.5 sqrt(h) A person can see 392 km to the horizon from an airplane window. How high is the airplane?
1 solutions
Answer 123027 by ankor@dixie-net.com(15660)   on 2008-11-11 15:38:52 (Show Source):
You can put this solution on YOUR website!At a height of h meters you can see V kilometers to the horizon. These numbers are related by the equation V = 3.5 sqrt(h) A person can see 392 km to the horizon from an airplane window. How high is the airplane?
:
Substitute 392 for V in the given equation and find h
3.5*  = 392
:
Divide both sides by 3.5:
= 
:
= 112
:
Square both sides:
h = 112^2
:
h = 12,544 meters
:
:
Check solution on a calc: enter 3.5*  = 392
|
Numbers_Word_Problems/167005: The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more that five the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number,
1 solutions
Answer 123026 by ankor@dixie-net.com(15660) on 2008-11-11 15:21:34 (Show Source):
You can put this solution on YOUR website!I am going to re-write the problem to what I think you meant:
:
The sum of the digits of a three-digit number is 11. If the digits are reversed,
the new number is 46 more than five times the old number. If the hundreds digit
plus twice the tens digit is equal to the units digit, then what is the number,
:
Let the number be: 100x + 10y + z
:
Let's try solving this using only the 1st and last statements:
"The sum of the digits of a three-digit number is 11."
x + y + z = 11
:
"the hundreds digit plus twice the tens digit is equal to the units digit,"
x + 2y = z
x + 2y - z = 0
:
Add to the 1st equation to eliminate z
x + y + z = 11
x +2y - z = 0
--------------
2x + 3y = 11
:
2x = 11 - 3y
x = 
Only two values for y will give a positive integer value for x, namely 1 and 3:
From the 2nd statement we know that x is a low value, therefore 3 seems likely:
x = 
x = 
x = 
x = 1 when y = 3
Find z
1 + 3 + z = 11
z = 11-4
z = 7
;
Our number is 137
:
See if that makes the 2nd statement true.
"If the digits are reversed, the new number is 46 more than five times the old number"
731 = 5(137) + 46
731 = 685 + 46
|
Age_Word_Problems/167013: The sum of the ages of four daughters, Abigail, Bonnie, Cena, and Daphne, is 40. The difference between the ages of the youngest, Daphne, and the oldest, Abigail, is 6. The second born, Bonnie, is 2 years younger than the oldest, Abigail, and the third born, Cena, is the average of the ages of the youngest, Daphne, and the second born, Bonnie. How old is the father, who is 30 years older than the youngest daughter?
1 solutions
Answer 123024 by ankor@dixie-net.com(15660) on 2008-11-11 13:52:29 (Show Source):
You can put this solution on YOUR website!Write an equation for each statement, we will try to get everything in terms of a
:
The sum of the ages of four daughters, Abigail, Bonnie, Cena, and Daphne, is 40.
a + b + c + d = 40
:
The difference between the ages of the youngest, Daphne, and the oldest, Abigail, is 6.
a - d = 6
-d = 6 - a
d = a - 6; multiplied equation by -1
:
The second born, Bonnie, is 2 years younger than the oldest, Abigail,
a - b = 2
-b = 2 - a
b = a - 2
:
third born, Cena, is the average of the ages of the youngest, Daphne, and the second born, Bonnie.
c = 
Substitute (a-2) for b and (a-6) for d
c =  = 
Cancel out the denominator and we have:
c = a - 4
:
Substitute for b, c, d in the first equation, find a:
a + (a-2) + (a-4) + (a-6) = 40
4a - 12 = 40
4a = 40 + 12
4a = 52
a = 
a = 13 yrs is Abigail's age
Then
b = 13 - 2
b = 11 yrs is Bonnie
and
c = 13 - 4
c = 9 yrs is Cena
and
d = 13 - 6
d = 7 yrs is Daphne
:
How old is the father, who is 30 years older than the youngest daughter?
Father = 7 + 30 = 37 yrs old
:
:
Check solution, find the total
13 + 11 + 9 + 7 = 40
:
A lot of steps but not that hard, right?
|
Graphs/166915: This question is from textbook Algebra 1
After visiting relatives who live 200 miles away, your family drives home at an average speed of 50 miles per hour. Your distance d (in miles) from home is given by d = 200 - 50t where t is the time (in hours) spent driving. Graph the function and identify its domain and range. What is your distance from home after driving for 1.5 hours?
1 solutions
Answer 123021 by ankor@dixie-net.com(15660) on 2008-11-11 12:36:16 (Show Source):
You can put this solution on YOUR website!After visiting relatives who live 200 miles away, your family drives home at an average speed of 50 miles per hour. Your distance d (in miles) from home is given by d = 200 - 50t where t is the time (in hours) spent driving. Graph the function and identify its domain and range. What is your distance from home after driving for 1.5 hours?
:
A graph of this:
:
You can see from the graph:
Domain; 0 to +4
Range: 0 to +200
:
What is your distance from home after driving for 1.5 hours?
:
You can estimate this from the graph, however find the exact solution:
Substitute 1.5 for t in the equation:
d = 200 - 50(1.5)
d = 200 - 75
d = 125 mi in 1.5 hrs
:
|
Rate-of-work-word-problems/166983: this in rational equations in word problems.
Jay can clean the house in 6 hours. After Jay and Jim have both been cleaning for an hour, they are joined by Jen and they completed the cleaning in 2 more hours. If it takes Jim 10 hours to clean the house alone, how long would it take Jen to do the job alone?
1 solutions
Answer 123013 by ankor@dixie-net.com(15660) on 2008-11-11 09:45:22 (Show Source):
You can put this solution on YOUR website!Jay can clean the house in 6 hours. After Jay and Jim have both been cleaning for an hour, they are joined by Jen and they completed the cleaning in 2 more hours. If it takes Jim 10 hours to clean the house alone, how long would it take Jen to do the job alone?
:
From above information we know:
Jay & Jim have been working a total of 3 hrs,
Jen worked 2 hrs
:
Let t = time required by Jen working alone
:
Let the completed job = 1
:
 +  +  = 1
:
Multiply equation by 30t to get rid of the denominators;
30t* + 30t* + 30t* = 30t(1)
:
Cancel out the denominators and you have;
5t(3) + 3t(3) + 30(2) = 30t
:
15t + 9t + 60 = 30t
:
24t + 60 = 30t
:
60 = 30t - 24t
:
60t = 6t
t = 
t = 10 hrs Jen working alone
:
:
Check solution in original equation
+ +  = 1
|
Surface-area/166932: This problem is from a problem solving worksheet known as "Math Olympiads"
It is labeled "Problems-Division E Olympiads" The title at the top of the page is "Set 3 Olympiad 1"
A circle and a triangle overlap as shown. The area of the circle is three times the area of the triangle. If the common region is removed, then the area of the rest of the circle would be 14 square centimeters more that the area of the reast of the triangle. What is the area of the complete triangle, in sq cm?
Please help us! This is our 5th grade son's homework. We are both college educated and my husband even has a math minor. This is not our finest moment.
Thank You!!
1 solutions
Answer 122971 by ankor@dixie-net.com(15660) on 2008-11-10 21:40:18 (Show Source):
You can put this solution on YOUR website!A circle and a triangle overlap as shown. The area of the circle is three times the area of the triangle. If the common region is removed, then the area of the rest of the circle would be 14 square centimeters more that the area of the rest of the triangle. What is the area of the complete triangle, in sq cm?
:
Let A = triangle area
then
3A = circle area
and
let x = the common area that is removed
:
from the statement we can write an equation:
3A - x = A - x + 14
Add x to both sides and find A
3A - A = 14
2A = 14
A = 7 sq/cm is the area of the triangle
|
Miscellaneous_Word_Problems/166738: a pedestrian is three eights of the way across the a train bridge when he hears a train coming! If he runs as fast as possible back toward the train, he will get off just in in time to aviod a collision. Also, if he runs as fast as possible away from the train, he will get off the bridge (on the other side) just in time to aviod a collision.
If the train is traveling at 60 miles per hour. How fast does the person run?
1 solutions
Answer 122969 by ankor@dixie-net.com(15660) on 2008-11-10 20:00:30 (Show Source):
You can put this solution on YOUR website!a pedestrian is three eights of the way across the a train bridge when he hears a train coming! If he runs as fast as possible back toward the train, he will get off just in in time to avoid a collision. Also, if he runs as fast as possible away from the train, he will get off the bridge (on the other side) just in time to avoid a collision.
If the train is traveling at 60 miles per hour. How fast does the person run?
:
:
Train----------d------------Br.....3x......P..........5x.........Br
:
Let d = dist train is from the bridge
Let 8x = length of the bridge
Pedestrian is 3x from one end and 5x from the other end of the bridge
:
Let s = running speed of p (mph)
:
Toward the train time equation (arrive at end of the bridge at the same time)
 = 
:
Away from the train time equation (arrive at other end at the same time)
 = 
:
After much manipulation of these equations (too much, to record here) I came up with:
d = 7.2
8x = 4.8 mi
P = 1.8 mi from one end and 3 mi from the other end
:
s = 15 mph running speed
:
:
Check this using the "away from the train" situation:
 = 
 = = .2 hrs
:
Check using the "toward the train" situation
 =  = .12 hrs
|
Radicals/166804: Can someone help
the hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.3 units longer then the shorter leg. Find the lengths of the sides of the triangle.
1 solutions
Answer 122934 by ankor@dixie-net.com(15660) on 2008-11-10 15:35:10 (Show Source):
You can put this solution on YOUR website!the hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.3 units longer then the shorter leg. Find the lengths of the sides.
:
Remember our old friend; a^2 + b^2 = c^2
:
Let x = the shorter leg
then
(x+1.3) = the longer leg:
:
Replace a & b with these expressions, replace c with 2.5
:
x^2 + (x+1.3)^2 = 2.5^2
:
x^2 + (x^2 + 2.6x + 1.69) = 6.25
:
x^2 + x^2 + 3.6x + 1.69 - 6.25 = 0; arrange to form a quadratic equation
:
2x^2 + 3.6x - 4.56 = 0
:
Using the quadratic equation, a=2; b=3.6; c=-4.56
x ~ .9938 ~ 1; the shorter leg
and
1 + 1.3 = 2.3; the longer leg
:
Check solution with calc; enter  = 2.508 ~ 2.5
|
Systems-of-equations/166691: Please help with the following equation:
A medical supply company has 1150 worker-hours for production, maintenance, and inspection. Using this and other factors, the number of hours used for each operation, P, M, and I, respectively, is found by solving the following system of equations. Find P, M and I.
P + M + I = 1150
P = 4I - 100
P = 6M + 50
1 solutions
Answer 122845 by ankor@dixie-net.com(15660) on 2008-11-09 16:57:19 (Show Source):
You can put this solution on YOUR website!A medical supply company has 1150 worker-hours for production, maintenance, and inspection. Using this and other factors, the number of hours used for each operation, P, M, and I, respectively, is found by solving the following system of equations. Find P, M and I.
P + M + I = 1150
P = 4I - 100
P = 6M + 50
:
Using the 1st two equations, rearrange the 2nd to have:
P + M + I = 1150
P + 0 -4I = -100
-------------------subtraction eliminates P
M + 5I = 1250
:
Using the 1st and 3rd equation, rearrange the 3rd to have:
P + M + I = 1150
P -6M + 0 = 50
-------------------Subtraction eliminate P
+7M + I = 1100
:
Multiply the above equation by 5, subtract M + 5I = 1250 from it:
35M + 5I = 5500
M + 5I = 1250
---------------------Subtraction eliminates I, find M
34M = 4250
M = 
M = 125 hrs of maint
:
Using M + 5I = 1250, Find I
125 + 5I = 1250
5I = 1250 - 125
I = 
:
I = 225 hrs of inspection
:
Use P = 6M + 50 to find P
P = 6(125) + 50
P = 750 + 50
P = 800 hrs production
:
Confirm solutions in the 1st equation
800 + 125 + 225 = 1150
|
expressions/166657: eleven is subtracted form a number and then the difference is multiplied by 5 the result is 30
1 solutions
Answer 122844 by ankor@dixie-net.com(15660) on 2008-11-09 16:19:31 (Show Source):
You can put this solution on YOUR website!Just write an equation for what it says: x = "a number"
:
eleven is subtracted form a number and then the difference is multiplied by 5 the result is 30
5(x - 11) = 30
5x - 55 = 30
5x = 30 + 55
5x = 85
x = 
x = 17
:
You can check it in the original equation
|
Miscellaneous_Word_Problems/166678: When the digits of a two-digit number are reversed, the new nwmber is 9 more than the original number, and the sum of the digits of the original number is 11.What is the original number?
1 solutions
Answer 122843 by ankor@dixie-net.com(15660) on 2008-11-09 16:13:48 (Show Source):
You can put this solution on YOUR website!When the digits of a two-digit number are reversed, the new number is 9 more
than the original number, and the sum of the digits of the original number
is 11. What is the original number?
:
Write the two digit number as: (10x + y); where x=10's digit and y=units digit
:
"When the digits of a two-digit number are reversed, the new number is 9 more than the original number,"
(10y+x) = (10x+y) + 9
10y - y = 10x - x + 9
9y = 9x + 9
Simplify, divide equation by 9
y = x + 1
:
and the sum of the digits of the original number is 11.
x + y = 11
:
What is the original number?
:
Substitute (x+1) for y in the above equation
x + (x+1) = 11
2x = 11 - 1
2x = 10
x = 5, then obviously y = 6
;
The number is: 56
:
:
Check solution in the statement:
"When the digits of a two-digit number are reversed, the new number is 9 more than the original number,"
65 = 56 + 9
|
Sequences-and-series/166647: you are building an addition on to your house. you only have enough money to buy 70 feet or exterior building materials. one side will be against the original house, so you only have to have materials for 3 sides. what would be the dimensions of the additon needed to give the maximim area? the is the maximum area?
thank you i really need help
1 solutions
Answer 122842 by ankor@dixie-net.com(15660) on 2008-11-09 16:03:10 (Show Source):
You can put this solution on YOUR website!You are building an addition on to your house. you only have enough money to
buy 70 feet or exterior building materials. one side will be against the
original house, so you only have to have materials for 3 sides. what would
be the dimensions of the addition needed to give the maximum area? the is the maximum area?
:
Treat this as the 70' perimeter of three sides:
The length of one side is against the the house, therefore:
L + 2W = 70
L = (70 - 2W)
:
Find the area:
A = L * W =
Substitute (70-2W) for L
A = (70-2W)*W
A = -2W^2 + 70W
:
This is a quadratic equation, max area will be on the axis of symmetry
Find that using x =  ; in this equation a=-2; b=70
W = 
W = 
W = +17.5 ft it the width for max area
:
L = 2(17.5)
L = 35 ft is the length
:
What is the maximum area?
;
35 * 17.5 = 612.5 sq/ft
:
:
You can confirm this by substituting 17.5 for W and finding the vertex:
A = -2(17.5^2) + 70(17.5)
A = -612.5 + 1225
A = + 612.5 sq ft is the vertex (max)
|
Polynomials-and-rational-expressions/166548: Can someone help me with this question please?
Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x).
P(x)= x^4+2x^3-2x+4
d(x)= x-2
Thanks
1 solutions
Answer 122823 by ankor@dixie-net.com(15660) on 2008-11-09 14:29:24 (Show Source):
You can put this solution on YOUR website!Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x).
P(x)= x^4+2x^3-2x+4
d(x)= x-2
:
You need to set it up like this, note the 0x^2:
:......____________________________
(x-2) | x^4 + 2x^3 + 0x^2 - 2x + 4
:
Follow the rules of long division and you will have:
:
..........................x^3 + 4x^2 + 8x + 14; remainder 32/(x-2)
:...........-----------------------------
(x-2) | x^4 + 2x^3 + 0x^2 - 2x + 4
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Quadratic_Equations/166632: An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and the f(x) is the vertical distance the football travels. The bottom of the uprights is 3.5 yards above the ground.
1. Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not?
2. Would the kicker have made a 42-yard field goal with the same kick? Why or Why not?
1 solutions
Answer 122812 by ankor@dixie-net.com(15660) on 2008-11-09 13:29:29 (Show Source):
You can put this solution on YOUR website!An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and f(x) is the vertical distance the football travels. The bottom of the upright is 3.5 yards above the ground.
Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not?
:
Find value of (x) (dist) when f(x) = 3.5 (height)
-.0625x² + 2.7x = 3.5
:
-.0625x² + 2.7x - 3.5 = 0
:
Use the quadratic formula:
In this problem a=-.0625; b=+2.7; c=-3.5
:
:
:
x = 1.33; not the solution we want here
and
x = 41.86 yds; clears the upright nicely
:
The ball had traveled almost 42 yds when it had descended to 3.5 meters
:
:
2. Would the kicker have made a 42-yard field goal with the same kick? Why or Why not?.
Find the height at 42 yds
h = -.0625x² + 2.7x
Substitute 42 for x
h = -.0625(42^2) + 2.7(42)
h = -.0625(1764) + 113.4
h = -110.25 + 113.4
h = 3.15 yds, So No; just under the bar at 3.5 yds high
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Linear_Algebra/166513: For x²(a-b)+a²(b-x)+b²(x-a) show that (x-a) is a linear factor.
PLEASE HELP ME!!!!!!
1 solutions
Answer 122803 by ankor@dixie-net.com(15660) on 2008-11-09 12:20:56 (Show Source):
You can put this solution on YOUR website!For x²(a-b)+ a²(b-x)+ b²(x-a) show that (x-a) is a linear factor.
:
Multiply to eliminate the brackets, we can leave the last term alone
x^2a - x^2b + a^2b - xa^2 + b^2(x-a)
:
Regroup:
x^2a - xa^2 + a^2b - x^2b + b^2(x-a)
:
Factor out xa and b
xa(x-a) + b(a^2 - x^2) + b^2(x-a)
:
Change the sign of b to -, to change signs inside the brackets
xa(x-a) - b(x^2 - b^2) + b^2(x-a)
:
Note that x^2 - b^2 is the "difference of squares and can be factored
xa(x-a) - b(x-a)(x+a) + b^2(x-a)
:
Note that each term contains the factor (x-a) now
|
Travel_Word_Problems/166415: Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?
1 solutions
Answer 122766 by ankor@dixie-net.com(15660) on 2008-11-08 21:44:28 (Show Source):
You can put this solution on YOUR website!Two cyclists start biking from a trail's start 3 hours apart. The second cyclist
travels at 10 miles per hour and starts 3 hours after the first cyclist who is
traveling at 6 miles per hour. How much time will pass before the second cyclist
catches up with the first from the time the second cyclist started biking?
:
Let t = travel time of the 2nd cyclist (10 mph)
then
(t+3) = travel time of the 1st cyclist (6 mph)
:
When the 2nd cyclist catches up with the 1st they will have traveled the same distance
:
Write a distance equation using this fact: (Dist = speed * time)
:
10s = 6(s+3)
:
10s = 6s + 18
:
10s - 6s = 18
:
4s = 18
s = 
s = 4.5 hrs travel time of the 2nd cyclist
:
;
Check solution by confirming they traveled the same distance
7.5 * 6 = 45 mi
4.5 * 10 = 45 mi
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Systems-of-equations/166466: A local electronics store will sell 7 AC adaptors and 3 rechargeable flashlights for $84. what is the price of a single AC adaptor and a single reachargeable flashlight?
1 solutions
Answer 122762 by ankor@dixie-net.com(15660) on 2008-11-08 20:58:49 (Show Source):
You can put this solution on YOUR website! A local electronics store will sell 7 AC adapters and 3 rechargeable flashlights for $84. what is the price of a single AC adapter and a single rechargeable flashlight?
:
We know that the cost of 7 Adapters is a multiple of 7
and the cost of 3 flashlights is a multiple of 3, and together they add up to 84
Multiples of 7: 21, 28, 35, 42, 49, 56, 63
Multiples of 3: 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54
:
Find the the multiple of each which add up to 84
:
A little research reveals $21 for 3 flashlights, and $63 for 7 Chargers
:
$9 for a charger and $7 for flashlight
|
test/166509: a picture is 1 inch longer than it is wide. it is put into a frame one half inch wider on every side. find the area of the picture if the frame area is eight inches squared.
1 solutions
Answer 122717 by ankor@dixie-net.com(15660) on 2008-11-08 13:55:00 (Show Source):
You can put this solution on YOUR website!a picture is 1 inch longer than it is wide. it is put into a frame one half inch wider on every side. find the area of the picture if the frame area is eight inches squared.
:
Let x = width of the picture
then
(x+1) = length of the picture
:
Frame 1/2 inch wider all around, therefore
x + 2(.5)=
(x+1) = width of the frame
and
(x+1) + 2(.5) =
x + 1 + 1 =
(x+2) = length of the the frame
:
Frame area given as 8 sq/in, therefore
(x+1)*(x+2) = 8
FOIL
x^2 + 3x + 2 = 8
x^2 + 3x + 2 - 8 = 0
:
a quadratic equation
x^2 + 3x - 6 = 0
Use the quadratic formula to find x: a=1; b=3; c=-6
:
You should get a positive solution about x = 1.37 inches is the width of the pic
then, 2.37 = length
:
A = 1.37 * 2.37
A = 3.25 sq/in is the picture
:
:
Check solution: Frame dimensions 2.37 by 3.37
Frame area = 2.37 * 3.37 = 7.77 ~ 8 sq/in as given
|
Equations/166459: 7x-2 divided by 10 = 9x divided by 4 + 6
I understand that I must get rid of the fractions first but cannot determine how to do this with the fractions on both sides. If I multipy by 10 on the right side and left side do I then multipy by 4 on both sides.
1 solutions
Answer 122710 by ankor@dixie-net.com(15660) on 2008-11-08 12:39:50 (Show Source):
You can put this solution on YOUR website!7x-2 divided by 10 = 9x divided by 4 + 6
:
 =  + 6
:
Multiply equation by common denominator, a value which is a multiple of 10 and 4
20 would do this for us
20* = 20* + 20(6)
:
Cancel out the denominators and you have:
2(7x - 2) = 5(9x) + 120
:
14x - 4 = 45x + 120
:
14x - 45x = 120 + 4
:
-31x = 124
x 
x = -4
:
:
Check solution in original equation:
 =  + 6
 =  + 6
 = + 6
-3 = -9 + 6; confirms our solution
|
Travel_Word_Problems/166236: Lerry drove 329 miles in 2 hours more then it took Terrell to drive 260 miles. Terrell drove at and average reate of 5 miles per hour faster then Larry. How fast did Larry travel?
1 solutions
Answer 122559 by ankor@dixie-net.com(15660) on 2008-11-06 21:18:36 (Show Source):
You can put this solution on YOUR website!Lerry drove 329 miles in 2 hours more then it took Terrell to drive 260 miles.
Terrell drove at an average rate of 5 miles per hour faster then Larry.
How fast did Larry travel?
:
Let s = Larry's speed
then
(s+5) = Terry's speed
:
Write a time equation: Time = dist/speed
:
L's time - 2 hr = T's time
 - 2 = 
:
Multiply equation by s(s+5)
s(s+5)* - 2s(s+5) = s(s+5)*
:
This eliminates the denominators and you have:
329(s+5) -2s^2 - 10s = 260s
:
329s + 1645 - 2s^2 - 10s - 260s = 0; arrange as a quadratic on the left
:
-2s^2 + 329s - 260s - 10s + 1645 = 0
:
-2s^2 + 59s + 1645 = 0
:
Easier to factor if change the signs, mult by -1
2s^2 - 59s - 1654
Factors to:
(2s + 35)(s - 47) = 0; use the quadratic formula if you need to:
Positive solution
s = 47 mph is L's speed
then
47 + 5 = 52 mph is T's speed
:
:
Check solution by finding the travel time of each
329/47 = 7 hr
260/52 = 5 hr
-------------
differ = 2 hrs as given
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Human-and-algebraic-language/166271: Three lighthouses on three nearby islands flash their lights every evening beginning at 8:35pm. On one island, the ligh flashes every 45 seconds. The lighthouse on the second island has a light that flashes every 2 minutes. The third lighthouse flashes a light every 1 1/4 minutes. At what time will all three lights flash together again?
This is a problem of the week just given to my child on a single piece of paper.
1 solutions
Answer 122552 by ankor@dixie-net.com(15660) on 2008-11-06 20:46:58 (Show Source):
You can put this solution on YOUR website!Three lighthouses on three nearby islands flash their lights every evening
beginning at 8:35pm. On one island, the ligh flashes every 45 seconds.
The lighthouse on the second island has a light that flashes every 2 minutes.
The third lighthouse flashes a light every 1 1/4 minutes.
At what time will all three lights flash together again?
:
Convert 2 min to seconds and 1.25 min to seconds.
:
So we have:
:
Lt1 = 45; Lt2 = 120; Lt3 = 75
:
Prime factor each:
45: 3,3,5,
120: 2,2,2,3,5
75: 3,5,5
:
Lcm of all three: 2,2,2,3,3,5,5 Multiply this: 1800 secs they will all Flash
:
1800/60 = 30 min: At 9:05Pm this should occur
|
Inverses/166215: Hi there please help I am parent trying to help my eldest on Equation in year 9, this the question, This is where I am stuck because I don't if my equation is correct or not?
thanks Nick.
1 solutions
Answer 122489 by ankor@dixie-net.com(15660) on 2008-11-06 14:27:47 (Show Source):
You can put this solution on YOUR website!In two years time Geoff will be three times as old as he was ten years ago.
a)Using y for his present age, write down an equation connecting his present
age with his age ten years ago?
:
Two things to note in this:
:
Age in two years: (y+2)
Age 10 yrs ago: (y-10)
:
In two yrs = 3 times age 10 yrs ago
y + 2 = 3(y - 10)
:
b)Solve the equation.
:
y + 2 = 3y - 30; multiplied what's inside the bracket
:
y + 2 + 30 = 3y; add 30 to both sides
:
32 = 3y - y; subtract y from both sides
:
y = 
:
y = 16 yrs; his age now
:
:
Try this in the original statement, see if works
"In two years time Geoff will be three times as old as he was ten years ago."
16 + 2 = 3(16 - 10)
18 = 3(6)
:
You don't need brackets around the problem
|
Travel_Word_Problems/165965: an airplane made a flight of 1600 miles in 5 hours. during the first 3 hours of the trip it had good weather. it then ran into bad weather, which decreased its rate by 75 mph for the rest of the flight. find the rate on each part of the flight.
1 solutions
Answer 122487 by ankor@dixie-net.com(15660) on 2008-11-06 14:17:36 (Show Source):
You can put this solution on YOUR website!an airplane made a flight of 1600 miles in 5 hours. during the first 3 hours of the trip it had good weather. it then ran into bad weather, which decreased its rate by 75 mph for the rest of the flight. find the rate on each part of the flight.
:
Let s = speed the 1st 3 hrs (good weather)
Then
(s-75) = speed the last two hours
:
Write a distance equation: Dist = time * speed
:
3s + 2(s-75) = 1600
:
3s + 2s - 150 = 1600
:
5s = 1600 + 150
:
5s = 1750
s = 
s = 350 mph in good weather
and
350 - 75 = 275 mph in bad weather
:
:
Check solution find the distance
3(350) = 1050 mi
2(275) = 550 mi
----------------
total = 1600 mi, confirms our sollutions
;
:
That wasn't so hard, was it?
|
Complex_Numbers/166032: can someone help me with this problem:
Solve the problem.
If the average cost per unit C(x) to produce x units of plywood is given by:
C(x) = 900 / x+30
What do 600 units cost? Round your answer to the nearest cent.
a. $857.14
b. $899.95
c. $180.00
d. $18,000.00
1 solutions
Answer 122477 by ankor@dixie-net.com(15660) on 2008-11-06 12:52:39 (Show Source):
You can put this solution on YOUR website!If the average cost per unit C(x) to produce x units of plywood is given by:
C(x) = 
:
What do 600 units cost? Round your answer to the nearest cent.
;
You are looking for the total cost which is
no. of units sold (x) times cost/unit, which is the given equation
:
C(x) = x*
:
Substitute 600 for x in the given equation:
C(x) = 600* 
:
C(x) = 600* 
:
C(x) = 600 * 1.42857
:
C(x) = $857.14
|
test/166179: 36.) If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. Find the weekly revenue if the price is $8 for each football.
This is the answer that it is showing r(q)= -150q^2 + 3000q, 14,400
Can you show me how they got this answer please.
1 solutions
Answer 122473 by ankor@dixie-net.com(15660) on 2008-11-06 12:34:32 (Show Source):
You can put this solution on YOUR website!This football problem has been kicking around for few days.
:
If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week.
:
Revenue = price times number sold (q=price), (number sold = 3000-150q)
R(q) = q(3000-150q)
;
Multiply what's inside the brackets
R(q) = 3000q - 150q^2
or
R(q) = -150q^2 + 3000q
:
:
Find the weekly revenue if the price is $8 for each football.
:
Take the above equation, substitute 8 for q and find R(q)
R(q) = -150(8^2) + 3000(8)
:
R(q) = -150(64) + 24000
:
R(q) = -9600 + 24000
:
R(q) = $14,400
:
:
Did this explain it to you?
|
test/166033: 36.) If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. Find the weekly revenue if the price is $8 for each football.
This is the answer that it is showing r(q)= -150q^2 + 3000q, 14,400
Can you show me how they got this answer please.
1 solutions
Answer 122472 by ankor@dixie-net.com(15660) on 2008-11-06 12:31:38 (Show Source):
You can put this solution on YOUR website!This football problem has been kicking around for few days.
:
If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week.
:
Revenue = price times number sold (q=price), (number sold = 3000-150q)
R(q) = q(3000-150q)
;
Multiply what's inside the brackets
R(q) = 3000q - 150q^2
or
R(q) = -150q^2 + 3000q
:
:
Find the weekly revenue if the price is $8 for each football.
:
Take the above equation, substitute 8 for q and find R(q)
R(q) = -150(8^2) + 3000(8)
:
R(q) = -150(64) + 24000
:
R(q) = -9600 + 24000
:
R(q) = $14,400
:
:
Did this explain it to you?
|
Polynomials-and-rational-expressions/166017: This question is from textbook
Physics: The mass of an electron is 9.109x10(-31power)kg. The mass of a proton is 1.673x10(-27power)kg. Hwo many times heavier is a proton than a electron.
1 solutions
Answer 122466 by ankor@dixie-net.com(15660) on 2008-11-06 11:28:59 (Show Source):
You can put this solution on YOUR website!The mass of an electron is 9.109x10(-31power)kg. The mass of a proton is 1.673x10(-27power)kg. How many times heavier is a proton than a electron.
:
 =  =  = 
:
We can say that the proton is 1837 times heavier than the electron
|
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