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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextPolynomials-and-rational-expressions/229231: I'm stuck on a problem. directions tell me to factor the polynomial.
x^3 + 1
I would be very grateful for any help that you may give me.
Thank you, Mike
1 solutions
Answer 169980 by ankor@dixie-net.com(15656)   on 2009-10-20 15:42:46 (Show Source):
You can put this solution on YOUR website!factor the polynomial.
x^3 + 1
:
You should recognize this as "the sum of cubes", which factors as
(a^3 + b^3) = (a + b) (a^2 - ab + b^2)
:
In this problem a = x, and b = 1 (1^3 = 1)
x^3 + 1 = (x + 1) (x^2 - x + 1)
:
:
You can prove this to yourself: let x = 2
2^3 + 1 =
8 + 1 = 9
and
(2 + 1) (2^2 - 2 + 1)
3 * (4 - 2 + 1)
3 * 3 = 9 also
|
Polynomials-and-rational-expressions/229227: If a rock is thrown upward at a speed of 64 ft/sec and over the edge of a cliff 80 feet above a river, its heights h after t seconds is given by the equation  . After how many seconds will it hit the water (h=0)? Solve by factoring the polynomial, using the Zero Factor Property, then solving the linear equations.
1 solutions
Answer 169979 by ankor@dixie-net.com(15656) on 2009-10-20 15:33:31 (Show Source):
You can put this solution on YOUR website!
After how many seconds will it hit the water (h=0)?
:
 = 0
normal form
 = 0
Factor out -16, simplifies and changes the signs
-16(t^2 - 4t - 5) = 0
Factors to
-16(t - 5)(t + 1) = 0
The positive solution
t - 5 = 0
t = +5 sec to hit the water
;
:
prove this to yourself
h = 80 + 320 - 16(25)
h = 400 - 400
h = 0
|
Angles/229211: Please explain the steps this confuses me. I understand what supplementary means and complementary whats confusing me is how to get an equation out of this:
angle AFB is 2 times its supplement.
Find angle A's complement.
1 solutions
Answer 169977 by ankor@dixie-net.com(15656) on 2009-10-20 14:58:14 (Show Source):
You can put this solution on YOUR website!When two angles are complimentary, they add up to 90
For example, an angle of 35 degrees, it's complement is: 90-35 = 55 degrees
just like
When two angles are supplementary, they add up to 180
The supplement of 35 degrees, 180 - 35 = 145 degrees
:
Angle AFB is 2 times its supplement.
:
Let angle AFB = x
x = 2(180 - x)
x = 360 - 2x
x + 2x = 360
3x = 360
x = 360/3
x = 120 degrees is angle AFB
:
Find angle A's complement. I am not sure what they mean by "angle A" here!
Anyway: 90 - A = Angle A's complement
|
Miscellaneous_Word_Problems/228828: Anyone have any idea of how to solve this:
The volume of a cube with the side length x is V(x)=x^3. Find the rate of change of volume with respect to the side length if the surface area is 54cm^2.
1 solutions
Answer 169974 by ankor@dixie-net.com(15656) on 2009-10-20 14:43:59 (Show Source):
You can put this solution on YOUR website!The volume of a cube with the side length x is V(x)=x^3.
Find the rate of change of volume with respect to the side length if the surface area is 54cm^2.
:
We know the surface area of a cube = 6x^2 (total area of the six sides)
6x^2 = 54
x^2 = 
x^2 = 9
x = 3
:
Vol = x^2
V = 3^3
V = 27 cu/cm
:
We can say the relationship  =  =  (where x = 1 side)
:
:
See if this is true
Let v = 125 cu/cm
x^3 = 125
x = 
x = 5 cm
:
Find the surface area
SA = 6(5^2)
SA = 6(25)
SA = 150
:
 = 
|
Geometry_Word_Problems/229192: Given the volume of a box equals 72 cubic inches, the height of the box equals the width of the box, and the length is five more than the width, find the height of the box.
1 solutions
Answer 169968 by ankor@dixie-net.com(15656) on 2009-10-20 13:26:23 (Show Source):
You can put this solution on YOUR website!Given the volume of a box equals 72 cubic inches, the height of the box equals the width of the box, and the length is five more than the width,
find the height of the box.
:
Let x = the width and the height
and
5x = the length
:
Volume = L * W * H = 72 cu/in
:
5x * x * x = 72
5x^3 = 72
x^3 = 
x^3 = 14,4
x = 
x ~ 2.4329 inches is the height
;
:
Check solution on a calc: enter 2.4329 * 2.4329 * 5(2.4329) = 72.00
|
Unit_Conversion_Word_Problems/229149: The average distance between the earth and the sun is 93 million miles. Using the velocity of light, find an approximate value for the amount of time it takes a light ray to travel from the sun to the earth. Please help and thank you.
1 solutions
Answer 169965 by ankor@dixie-net.com(15656) on 2009-10-20 12:58:02 (Show Source):
You can put this solution on YOUR website!The average distance between the earth and the sun is 93 million miles.
Using the velocity of light, find an approximate value for the amount of time it
takes a light ray to travel from the sun to the earth.
:
Using accepted value for the speed of light, 186,000 mi/sec
:
 = 500 sec which is 8 min 20 sec
|
test/228995: this is long division;
(-30+6y^3-28y+y^2)divided by (2y-5)
1 solutions
Answer 169878 by ankor@dixie-net.com(15656) on 2009-10-19 21:57:54 (Show Source):
You can put this solution on YOUR website!Do it a lot like ordinary long division;
(-30+6y^3-28y+y^2) divided by (2y-5)
Put it the degrees in descending order (use.... to keep things lined up
:
..........................3y^2 + 8y + 6
.............---------------------
(2y-5)|6y^3 + y^2 - 28y - 30; choose a value, that, when mult by the divisor = the 1st term
..............6y^3 - 15y^2
...........---------------
...........................16y^2 - 28y
...........................16y^2 - 40y
...........................------------
.........................................12y - 30
.........................................12y - 30
........------------------------------------------
................................................0 remainder
:
Study this carefully and it will make sense to you.
|
Unit_Conversion_Word_Problems/228962: Hi all I have been doing pretty good lately Until Now!!
I need help with writing the problem in a simplified radical form.
Assume that all variables represent positive real numbers. And I have no idea how to write the v------- type thing.
Except it is a solid line and not quite a v at the begining. Does anyone no what I am talking about? Square root symbol maybe?
These are under the line of the 'square root symbol" there is nothing on the left side of the symbol. And the 11 and the 2 are 'to the power numbers.'
12t11 u2
I have no idea if anyone will even understand this but if you do please help me.
Thank you very much!!
1 solutions
Answer 169869 by ankor@dixie-net.com(15656) on 2009-10-19 21:39:34 (Show Source):
|
Equations/228973: 6x-7= 2x=29 My teach helped me to understand this. I got an answer of x=9. My teacher actually did the work for me and I have a test tomorrow. I don't want to fail! I still don't understand it. Please help my by tomorrow! Thanks!~
1 solutions
Answer 169853 by ankor@dixie-net.com(15656) on 2009-10-19 21:23:13 (Show Source):
You can put this solution on YOUR website!6x - 7 = 2x + 29
:
We want to perform operations on both sides of the equation to get the variable
(x) on one side by itself, usually the left side
;
Add 7 to both sides
6x - 7 + 7 = 2x + 29 + 7
so we have
6x = 2x + 36
:
Subtract 2x from both sides
6x - 2x = 2x - 2x + 36
we have
4x = 36
:
Divide both sides by 4
 = 
we have
x = 9
;
;
Confirm your answer by replacing x with 9 in the original problem
6x - 7 = 2x + 29
6(9) - 7 = 2(9) + 29
54 - 7 = 18 + 29
47 = 47; confirms our solution
|
Mixture_Word_Problems/228894: Dan is 1/6 his father's age. In 4 years, Dan will be 1/4 his fathers age. what is Dan's age?
1 solutions
Answer 169813 by ankor@dixie-net.com(15656) on 2009-10-19 20:00:54 (Show Source):
You can put this solution on YOUR website!Dan is 1/6 his father's age.
d =  f
or
f = 6d
:
In 4 years, Dan will be 1/4 his fathers age.
d + 4 =  (f+4)
:
what is Dan's age?
:
Replace f with 6d in the last equation
d + 4 = (6d + 4)
Multiply both sides by 4
4(d + 4) = 6d + 4
:
4d + 16 = 6d + 4
:
16 - 4 = 6d - 4d
:
12 = 2d
:
d = 6 yrs is Dan's age
;
:
Check solution:
f = 6(6) = 36
"In 4 years, Dan will be 1/4 his fathers age."
6 + 4 = 1/4 * 36 + 4
|
Linear_Algebra/228736: What is 2x-y+z=14
-x+2y-4z=5
x+4y-6z=-1
This is solve the system using the elimination method get the x,y, and z please help this is hard.
1 solutions
Answer 169791 by ankor@dixie-net.com(15656) on 2009-10-19 18:51:16 (Show Source):
You can put this solution on YOUR website!2x - y + z = 14
-x+ 2y -4z = 5
x + 4y -6z =-1
:
You're right this is a pain!
:
Add the 2nd and 3rd equations, to eliminate x
-x+ 2y -4z = 5
x + 4y -6z =-1
-----------------adding eliminates x
0 + 6y - 10z = 4
Simplify, divide by 2
3y - 5z = 2
:
Multiply the 2nd equation by 2 and add to the 1st equation
2x - y + z = 14
-2x+ 4y -8z = 10
-----------------addition eliminates x again
0 + 3y - 7z = 24
:
Two 2 unknown equation to deal with now
:
Subtract 3y - 5z = 2 from the above equation
3y - 7z = 24
3y - 5z = 2
---------------subtraction eliminates y, find z
0 - 2z = 22
-2z = 22
z = 
z = -11
:
find y using the equation 3y - 5z = 2
3y - 5(-11) = 2
3y + 55 = 2
3y = 2 - 55
3y = -53
y = 
y = -17.667
:
Find x using the 1st equation 2x - y + z = 14
2x - (-17  ) - 11 = 14
2x + 17 - 11 = 14
2x + 6 = 14
2x = 14 - 6.667; go to decimals here
2x = 7.333
x = 3.667
;
:
It's kind of disgusting they give you a problem that doesn't have integer solutions.
I checked this using the matrix feature on my TI83, so I think it's right
|
Linear-systems/228772: Hello, Im in Gr.10.
Solving Problems dealing with linear systems: (I need to make an equation then solve)
1) A school athletic council sold 835 tickets to the championship football game for a total of $5792. Students pay $4 and nonstudents pay $8. How many nonstudents attended the game?
1 solutions
Answer 169751 by ankor@dixie-net.com(15656) on 2009-10-19 16:18:01 (Show Source):
You can put this solution on YOUR website!1) A school athletic council sold 835 tickets to the championship football game for a total of $5792.
Students pay $4 and nonstudents pay $8.
How many nonstudents attended the game?
:
Let x = no. of non-students
Total ticket were given as 835, therefore
(835-x) = no. of students
:
The total$ equation
8x + 4(835-x) = 5792
8x + 3340 - 4x = 5972; multiply what's inside the brackets
8x - 4x = 5972 - 3340
4x = 2632
x =  ; divide both sides by 4
x = 658 non-students
;
;
Check our solution
835 - 658 = 177 students
8(658) + 4(177) =
5264 + 708 = 5972; confirms our solution
:
:
Did this make sense to you?
|
Rate-of-work-word-problems/228633: In testing the rate at which a polluted stream flows, a boat that travels 5.5mi/hr in still water took 5 hrs to go down stream and 8 hrs to go upstream, between 2 points. what is the rate of flow of the stream
1 solutions
Answer 169750 by ankor@dixie-net.com(15656) on 2009-10-19 16:07:03 (Show Source):
You can put this solution on YOUR website!a boat that travels 5.5mi/hr in still water took 5 hrs to go down stream
and 8 hrs to go upstream, between 2 points.
what is the rate of flow of the stream
:
Let r = rate of flow of the stream
then
(5.5 + r) = boat speed down stream
and
(5.5 - r) = boat speed up stream
:
Write a distance equation, distance is the same for both trips
Dist = speed * time
:
dist down = dist up
5(5.5 + r) = 8(5.5 - r)
:
27.5 + 5r = 44 - 8r
:
5r + 8r = 44 - 27.5
:
13r = 16.5
r = 
r ~ 1.27 mi/hr (flow of the stream)
;
;
See if this is true; find the dist of each (should be equal)
5(5.5 + 1.27) = 33.8 mi
8(5.5 - 1.27) = 33.8 mi
|
Numbers_Word_Problems/228746: I am thibking of a three digit number. It is an odd multiple of three, and the product of its digits is 24. It is larger than 15 squared. What are the five numbers I could be thinking of?
1 solutions
Answer 169745 by ankor@dixie-net.com(15656) on 2009-10-19 15:46:55 (Show Source):
You can put this solution on YOUR website!I am thinking of a three digit number.
It is an odd multiple of three, and the product of its digits is 24.
It is larger than 15 squared.
What are the five numbers I could be thinking of?
;
The three digits whose product is 24
2 * 2 * 6 = 24; all even
2 * 3 * 4 = 24
1 * 3 * 8 = 24
:
Odd multiple of three, last digit has to be odd
Greater than 225 (15^2)
:
243, 423, 381, 831, 813 would be the 5 numbers
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Numbers_Word_Problems/228547: What is the consecutive number of which 4 over 7 of the sum of first and second equals the third numbers decrease by 1?
1 solutions
Answer 169738 by ankor@dixie-net.com(15656) on 2009-10-19 15:01:52 (Show Source):
You can put this solution on YOUR website!What is the consecutive number of which 4 over 7 of the sum of first and second
equals the third numbers decrease by 1?
:
Three consecutive numbers: x, (x+1), (x+2)
:
 (x + (x+1)) = (x+2) - 1
(2x+1) = (x + 1)
Multiply both sides by 7
4(2x + 1) = 7(x + 1)
:
8x + 4 = 7x + 7
8x - 7x = 7 - 4
x = 3
;
Numbers are: 3, 4, 5
;
:
See if that works in the statement:
"4/7 of the sum of first and second equals the third numbers decrease by 1"
(3+4) = (5) - 1
(7) = 4
4 = 4
|
Rectangles/228677: The length of a rectangle is three less than twice its width. If the length is increased by 3 and the width is decreased by 1, a new rectangle is formed whose area is 5 more than the original rectangle. Find:
a) The dimensions of the original rectangle.
b) The area of the new rectangle.
1 solutions
Answer 169730 by ankor@dixie-net.com(15656) on 2009-10-19 14:46:57 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is three less than twice its width. If the length is increased by 3 and the width is decreased by 1, a new rectangle is formed whose area is 5 more than the original rectangle.
Find:
a) The dimensions of the original rectangle.
Let x = the width
then
(2x-3) = the length
and
A = x(2x-3)
A = 2x^2 - 3x; area of original
;
b) The area of the new rectangle.
(x-1) = the width of the new rectangle
and
(2x-3) + 3 = 2x; length of the new rectangle
and
A = 2x(x-1)
A = 2x^2 - 2x; area of new
:
"new rectangle is formed whose area is 5 more than the original rectangle.
New area - old area = 5
2x^2 - 2x - (2x^2 - 3x) = 5
2x^2 - 2x - 2x^2 + 3x = 5
2x^2 - 2x^2 - 2x + 3x = 5
x = 5 units, original width
then
2(5) - 3 = 7 units, original length
and
5 - 1 = 4 units, new width
then
2(5) = 10 units, new length
;
;
Check solution using the area statement
new area - original area
10*4 - 7*5 = 5
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Numbers_Word_Problems/228697: Find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 7 times the third.
1 solutions
Answer 169706 by ankor@dixie-net.com(15656) on 2009-10-19 13:41:31 (Show Source):
You can put this solution on YOUR website!Three positive consecutive integers: x, (x+1), (x+2)
:
Find three consecutive positive integers such that the product of the first
and third, minus the second, is 1 more than 7 times the third.
:
x(x+2) - (x+1) = 7(x+2) + 1
:
x^2 + 2x - x - 1 = 7x + 14 + 1
:
x^2 + x - 1 = 7x + 15
:
Combine like terms on the left:
x^2 + x - 7x - 1 - 15 = 0
:
x^2 - 6x - 16 = 0; our old friend, the quadratic equation!
Factors to
(x - 8)(x + 2) = 0
We only want the positive solution in this problem
x = 8, is the 1st integer, then 9, 10; obviously.
;
:
Check our solution in the statement:
"the product of the first and third, minus the second, is 1 more than 7 times the third.
"
8*10 - 9 = 7*10 + 1
80 - 9 = 70 + 1; confirms our solution
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Mixture_Word_Problems/228403: A mixture of 10% acid and 90% water is added to 5 liters of pure acid. the final mixture is 40% water . How many liters of water are in the final mixture?
thanks
1 solutions
Answer 169703 by ankor@dixie-net.com(15656) on 2009-10-19 13:30:08 (Show Source):
You can put this solution on YOUR website!A mixture of 10% acid and 90% water is added to 5 liters of pure acid.
The final mixture is 40% water.
How many liters of water are in the final mixture?
:
Let x = amt of acid/water mixture added
;
Write an amt of water equation
.90x = .40(x + 5)
.90x = .40x + 2
.9x - .4x = 2
.5x = 2
x = 
x = 4 liters of 90% water mixture added to the 5 liters of pure acid
:
Find the amt of water in the final mixture
w = .4(4+5)
w = .4(9)
w = 3.6 liters is water in the final mixture
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Square-cubic-other-roots/228591: Can someone please please help me with these questions. I am preparing for a quiz on Monday.
1) z sqrt 80zu^2 - u sqrt 5z^3
2) sqrt z +16 = sqrt 7z+12
3) sqrt -6w+16=w
4) sqrt 10+8 / -5 sqrt 10+1
Thank you in advance
1 solutions
Answer 169700 by ankor@dixie-net.com(15656) on 2009-10-19 12:44:38 (Show Source):
You can put this solution on YOUR website!1) 
Factor to reveal the perfect squares
extract the squares and combine like terms
 = 
;
;
2) 
Square both sides:
z + 16 = 7z + 12
16 - 12 = 7z - z
4 = 6z
z =  =
;
;
3) 
square both sides
-6w + 16 = w^2
0 = w^2 + 6w - 16
Factors to:
(w+8)(w-2) = 0
Two solutions
w = -8
w = +2;
Check both solutions in the original equation (only one is valid)
:
:
4)  =  =  = 
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Numbers_Word_Problems/228598: The sum of the digits of a three-digit number is 18. The ten's digit is 2 more than the unit's digit. If the digits are reversed, the resulting number is 396 less than the original number. Find the original number.
1 solutions
Answer 169668 by ankor@dixie-net.com(15656) on 2009-10-19 09:50:15 (Show Source):
You can put this solution on YOUR website!The sum of the digits of a three-digit number is 18.
The ten's digit is 2 more than the unit's digit.
If the digits are reversed, the resulting number is 396 less than the original number.
Find the original number.
:
Three digits, x & y & z
the number: 100x + 10y + z
:
"The sum of the digits of a three-digit number is 18."
x + Y + z = 18
:
" The ten's digit is 2 more than the unit's digit.
y = z + 2
:
"If the digits are reversed, the resulting number is 396 less than the original number."
original number - 396 = reversed number
100x + 10y + z - 396 = 100z + 10y + x
Group like terms and combine
100x - x + 10y - 10y = 100z - z + 396
99x = 99z + 396
Simplify, divide equation by 99
x = z + 4
:
Find the original number.
:
Using the equation x + y + z = 18, replace y and x
(z+4) + (z + 2) + z = 18
3z + 6 = 18
3z = 18 - 6
3z = 12
z = 4
:
I'll let you find x and y using the equations derived from the statements
Construct the number using 100x + 10y + z, check in last statement
Any questions, ankor@att.net
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Geometry_Word_Problems/228492: a clock with a diameter of 23 feet. minute hand is 14ft., hour hand is 9 ft. how much farther does minute hand travel than hr. hand in 24 hours.
1 solutions
Answer 169662 by ankor@dixie-net.com(15656) on 2009-10-19 08:31:04 (Show Source):
You can put this solution on YOUR website!a clock with a diameter of 23 feet. minute hand is 14ft., hour hand is 9 ft.
how much farther does minute hand travel than hr. hand in 24 hours.
:
Assuming this is a 12 hr clock, I guess they mean how far the tip of each hand travels.
:
24 times the circumference of the large hand - 2 times the circumference of the small hand
:
radius of small hand, 9; long hand 15
:
24(  ) - 2(  )
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Triangles/228364: What is the area of the largest triangle that can be inscribed in the semicircle shown? One side of the triangle is the 10 unit diameter of the semicircle. Be sure to justify your answer as being the largest area possible.
1 solutions
Answer 169565 by ankor@dixie-net.com(15656) on 2009-10-18 20:33:26 (Show Source):
You can put this solution on YOUR website!What is the area of the largest triangle that can be inscribed in the semicircle shown?
One side of the triangle is the 10 unit diameter of the semicircle.
Be sure to justify your answer as being the largest area possible.
:
This would be an isocoles triangle, the base is the diameter (10)
and the height is the radius (5)
A = .5*10*5
A = 25 sq units
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Inequalities/228342: 1/4(8y+4)-17=-1/2(4y-8) Solve
It has been determined that at the age of 10, a girl has reached 84.4%of her final adult height. Dana is 4ft 8in. at the age of 10. What will her final adult height be????
A store keeper goes to the bank to get $10.00 worth of change. She requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickels as dimes, and no pennies or dollars. How many of each coin did the storekeeper get?
Please help me ! Also show your work! So I can ! Thank You
Heather
1 solutions
Answer 169558 by ankor@dixie-net.com(15656) on 2009-10-18 20:20:00 (Show Source):
You can put this solution on YOUR website!1/4(8y+4)-17=-1/2(4y-8) Solve
Multiply equation by 4 to get rid of the denominators, results
8y + 4 - 4(17) = -2(4y - 8)
:
8y + 4 - 68 = -8y + 16
:
8y - 64 = 8y + 16
:
8y + 8y = 16 + 64
:
16y = 80
y = 
y = 5
Check solution in original equation
:
;
It has been determined that at the age of 10, a girl has reached 84.4%of her
final adult height. Dana is 4ft 8in. at the age of 10.
What will her final adult height be????
:
Convert 4' 8" to 56 inches
:
Let x = her final adult age
:
.844x = 56
x = 
x = 66.35 inches which is 5 ft 6.35 inches
:
:
A store keeper goes to the bank to get $10.00 worth of change.
She requests twice as many quarters as half dollars, twice as many dimes as quarters,
three times as many nickels as dimes, and no pennies or dollars.
How many of each coin did the storekeeper get?
:
Write an equation for each statement, get all coins in terms of q
:
"twice as many quarters as half dollars,"
q = 2h
h = .5q
:
"twice as many dimes as quarters, "
d = 2q
:
"three times as many nickels as dimes,"
n = 3d
Replace d with 2q
n = 3(2q)
n = 6q
:
"$10.00 worth of change."
.05(6q) + .10(2q) + .25q + .50(.5q) = 10.00
.30q + .20q + .25q + .25q = 10.00
1.0q = 10
q = 10 quarters,
:
You should be able to find the no. of the other coins
Check the solutions in the total$ equation
|
Travel_Word_Problems/228326: A car is driven off a cliff at a speed of 50km an hour. It lands .350 km away from the cliff. How tall is the cliff?
*I usually solve these problems knowing the height of the cliff and asked to find the speed of the car, now I'm confused.
thanks!
1 solutions
Answer 169528 by ankor@dixie-net.com(15656) on 2009-10-18 17:47:11 (Show Source):
You can put this solution on YOUR website!A car is driven off a cliff at a speed of 50km an hour.
It lands .350 km away from the cliff.
How tall is the cliff?
:
Find out how long for a car to travel .350 km at a speed of 50km/hr (seconds)
t = .350/50 * 3600 = 25.2 sec
:
How far will an object fall in 25.2 sec (h = height of the cliff)
h = 4.9(25.2^2)
h = 4.9 * 635
h = 3111.7 meters
:
:
Seem awful high, but I think that is right!
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Mixture_Word_Problems/227994: A chemist needs 130 milliliters of a 28% solution but has only 19% and 58% solutions available. Find how many milliters of each that should be mixed to get the desired solution.
1 solutions
Answer 169502 by ankor@dixie-net.com(15656) on 2009-10-18 16:09:21 (Show Source):
You can put this solution on YOUR website!A chemist needs 130 milliliters of a 28% solution but has only 19% and 58% solutions available.
Find how many milliliters of each that should be mixed to get the desired solution.
:
Let x = amt of 58% solution
It say's the amt of the resulting mixture is to be 130 ml, therefore
(130-x) = amt of 19% solution
:
A typical mixture equation
:
.58x + .19(130-x) = .28(130)
:
.58x + 24.7 - .19x = 36.4
:
.58x - .19x = 36.4 - 24.7
:
.39x = 11.7
x = 
x = 30 ml of 58% solution required
and
130 - 30 = 100 ml of 19% solution
;
:
Check solution in original mixture equation
.58(30) + .19(100) = .28(130)
17.4 + 19 = 36.4
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Rate-of-work-word-problems/228093: Brenda and her husband Randy bicycled cross-country together. One morning, Brenda rode 30 miles. By traveling only 5 miles per hour faster and putting in one more hour, Randy covered twice the distance Brenda covered. What was the speed of each cyclist?
1 solutions
Answer 169488 by ankor@dixie-net.com(15656) on 2009-10-18 15:31:46 (Show Source):
You can put this solution on YOUR website!Brenda and her husband Randy bicycled cross-country together.
One morning, Brenda rode 30 miles.
By traveling only 5 miles per hour faster and putting in one more hour,
Randy covered twice the distance Brenda covered.
What was the speed of each cyclist?
:
Let s = B's speed
then
(s+5) = R's speed
:
Write a time equation Time = dist/speed
B's time + 1 hr = R's time
 + 1 = 
Multiply equation by s(s+5), results
30(s+5) + s(s+5) = 60s
:
30s + 150 + s^2 + 5s = 60s
:
Group like terms on the left
s^2 + 30s + 5s - 60s + 150 = 0
:
A quadratic equation
s^2 - 25s + 150 = 0
:
Factors to
(s - 15)(s - 10) = 0
:
Two solutions
s = 10 mph
s = 15 mph
;
:
Check both these solutions in the original equation, both will work
|
Travel_Word_Problems/228224: I am trying to solve the following question:
a bird flies back and forth between two approaching trains. The bird flies 150mph. The trains are initially 510 miles apart, and are traveling tward each other at 40 and 80 mph, respectively. Hw far does hte bird fly before being crushed between the 2 trains? I have solved each for the equation d=rt and I am stumped. Any suggestions with set up. Thank you.
1 solutions
Answer 169461 by ankor@dixie-net.com(15656) on 2009-10-18 14:03:12 (Show Source):
You can put this solution on YOUR website!a bird flies back and forth between two approaching trains.
The bird flies 150mph.
The trains are initially 510 miles apart, and are traveling tward each other at 40 and 80 mph, respectively.
How far does the bird fly before being crushed between the 2 trains?
:
All we have to do is find out how long before the trains collide, then multiply
that times the bird's speed, to find out how far it flies.
:
The relative speed of the trains to each other: 40 + 80 = 120 mph
:
time of collision * speed of bird = birds distance
 * 150 = 637.5 miles
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