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Linear-systems/62026: Two trains left the same city at the same time, traveling in opposite directions. The eastbound train travels for 10 hours, and the westbound train travels for 5 hours. They are now 1300 km apart. The westbound train's rate is 20 km/h faster than the eastbound train. Find the rate speed of each train.
1 solutions
Answer 42760 by funmath(2925)   on 2006-11-18 19:02:27 (Show Source):
You can put this solution on YOUR website!Two trains left the same city at the same time, traveling in opposite directions. The eastbound train travels for 10 hours, and the westbound train travels for 5 hours. They are now 1300 km apart. The westbound train's rate is 20 km/h faster than the eastbound train. Find the rate speed of each train.
:
distance = rate*time --> d=rt
The time east t= 10 hr
the rate east r= x
the time west t= 5
the rate west r= x+20
The total distance between them d= 1300 km
:
Therefore it makes sence that if we add the distance that they travel we get 1300 km.
The distance east r*t=10x
the distance west r*t=5(x+20)
:
Probalem to solve:
10x+5(x+20)=1300
10x+5x+100=1300
15x+100-100=1300-100
15x=1200
15x/15=1200/15
x=80
The rate east is x=80 km/h
the rate west is x+20=80+20=100 km/h
Happy Calculating!!!
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Inequalities/61886: Could someone please help me?
Solve the following inequalities. Write your answer using interval notation.
(x+4)(2x-3)>0
x^2-2x<8
Thank you
1 solutions
Answer 42758 by funmath(2925) on 2006-11-18 18:51:29 (Show Source):
You can put this solution on YOUR website!Solve the following inequalities. Write your answer using interval notation.
(x+4)(2x-3)>0
x+4=0 and 2x-3=0
x+4-4=0-4 and 2x-3+3=0+3
x=-4 and 2x=3
x=-4 and 2x/2=3/2
x=-4 and x=3/2
These are your critical numbers, they tell you the possible intervals, (-infinity,-4),(-4,3/2), (3/2,infinity):
Check the interval (-infinity,-4) by using a test number in that interval like -5
(-5+4)(2(-5)-3)>0 ?
(-1)(-13)>0
13>0 This is true.
This tells us that the interval (-infinity, -4) is in the solution.
:
Now test the interval (-4,3/2) with a test number like 0.
(0+4)(2*0-3)>0 ?
(4)(-3)>0
-12>0 This is not true so the interval (-4,3/2) is not part of the solution.
:
Now test the interval (3/2,infinity) with a test number like 2.
(2+4)(2*2-3)>0 ?
(6)(1)>0
6>0 This is true
This tells us that the interval (3/2,infinity) is part of the solution.
The Solution is: (-infinity,-4)U(3/2,infinity)
:
x^2-2x<8
x^2-2x-8<8-8
x^2-2x-8<0 Factor
(x-4)(x+2)<0
x-4=0 and x+2=0
x-4+4=0+4 and x+2-2=0-2
x=4 and x=-2
These tell you that your possible intervals are:(-infinity,-2),(-2,4), and (4,infinty)
:
Test the interval of (-infinity,-2) with a test number like, -3.
(-3-4)(-3+2)<0 ?
(-7)(-1)<0
7<0 This is not true.
(-infinty,-2) is not part of the solution.
Test the interval (-2,4) with a test number like 0.
(0-4)(0+2)<0 ?
-4(2)<0
-8<0 this is true.
(-2,4) is part of the solution.
Test the interval (4,infinity) with a test number like 5.
(5-4)(5+2)<0 ?
1(7)<0
7<0 this is not part of the soltuion.
The solution therefore is: (-2,4)
Happy Calculating!!!
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Exponential-and-logarithmic-functions/61836: Exponential and Logarithmic Functions
(1) Let f(z) = 3^z
(a) Find what value of z does f(z) = 81?
(b) For what value of z does f(z) = 1?
(2) Graph each of the following. Give coordinates of at least 3 points on each graph.
(a) y = 3^x
(b) y = logsub 3 x
(3) The population of a large U.S. city is growing according to the function P = 1,400,000(1.023)^t, where t is the number of years since 1990.
(a) What was the population in 1990?
(b) What will the population be in 2007 according to this formula?
(c) What does the value of 1.023 mean in the context of the problem?
1 solutions
Answer 42750 by funmath(2925) on 2006-11-18 18:06:36 (Show Source):
You can put this solution on YOUR website!Exponential and Logarithmic Functions
(1) Let f(z) = 3^z
(a) Find what value of z does f(z) = 81?
Method of like bases:
Same thing by taking the log of both sides but it requires a calculator.
 <--anytime you can't figure it out by making like bases you can do this.
:
(b) For what value of z does f(z) = 1?
Or you can take the log of both sides.
:
(2) Graph each of the following. Give coordinates of at least 3 points on each graph.
:
(a) y = 3^x
If x=-1
y=3^(-1) --> y=1/3 Plot (-1,1/3)
If x=0
y=3^0 --> y=1 Plot (0,1)
If x=1
y=3^1 --> y=3 Plot (1,3)
:
(b) y = logsub 3 x
x=3^y
If y=-1
x=3^(-1) --> x=1/3 Plot(1/3,-1)
If y=0
x=3^0 --> x=1 Plot(0,1)
If y=1
x=3^1 --> x=3 Plot (3,1)
:
(3) The population of a large U.S. city is growing according to the function P = 1,400,000(1.023)^t, where t is the number of years since 1990.
(a) What was the population in 1990?
t=0 in 1990
P=1,400,000(1.023)^0
P=1,400,000(1)=1,400,000
:
(b) What will the population be in 2007 according to this formula?
t=2007-1990=17
P=1,400,000(1.023)^(17)=2,060,700
:
(c) What does the value of 1.023 mean in the context of the problem?
:
The reason that I didn't answer this sooner is I'm not sure what vocabulary you need to use. Look it up in your book to be sure. It might be that it represents the population rate of growth.
:
Happy Calculating!!!
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Exponential-and-logarithmic-functions/61834: Exponential and Logarithmic Functions
(1)Let f(x) = 2^x , g(x) = (1/8)^x, and h(x) = log sub 2(x). Find each of the following:
f(3)
f(-2)
f(1/2)
g(2)
g(-1)
g(1/3)
h(2)
h(1/2)
(2) Solve each of the following equations for the given variable
(a) 2^a = 16
(b) 3^z = 1/9
(c) 9^n = 3
(d) (1/5)^x = 25
1 solutions
Answer 42744 by funmath(2925) on 2006-11-18 16:13:09 (Show Source):
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Divisibility_and_Prime_Numbers/61789: This question is from textbook Pre-Algebra
Use the clues to find the missing numbers.(Clue) The greatest common factor (GCF) of two numbers is 6.
1 solutions
Answer 42743 by funmath(2925) on 2006-11-18 16:06:45 (Show Source):
You can put this solution on YOUR website!Use the clues to find the missing numbers.(Clue) The greatest common factor (GCF) of two numbers is 6.
There must be other clues or there is more than one possible answer.
The GCF of 6 and 12 is 6
The GCF of 6 and 18 is 6
The GCF of 6 and 24 is 6
The GCF of 12 and 18 is 6
The possibilities are endless. What else did it say?
Happy Calculating!!!
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Equations/62017: If n= 3p, for what value of p is n = p?
according to the answer provided on the back of the book, the answer is zero. However, i think the book is incorrect and the real answer is 1/3.
How do you solve this question?
1 solutions
Answer 42741 by funmath(2925) on 2006-11-18 16:00:04 (Show Source):
You can put this solution on YOUR website!If n= 3p, for what value of p is n = p?
Let n=3p
3p=p
3p-p=p-p
2p=0
2p/2=0/2
p=0
:
This one was weird, I might not have given this one a try if you hadn't have indicated to answer from the book. Thanks for the brain teaser.
Happy Calculating!!!
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Points-lines-and-rays/61634: a triangle has 3 sides 3x7 and 4x9 and 5x+6 find the expressions that represents this perimiter
1 solutions
Answer 42705 by funmath(2925) on 2006-11-18 07:26:22 (Show Source):
You can put this solution on YOUR website!a triangle has 3 sides 3x^7 and 4x^9 and 5x+6 find the expressions that represents this perimiter (If the 7 and 9 are not exponents, let me know)
Perimeter is found by adding the sides together:
 Since there are no like terms, the best you can do is put the terms in descending order.
Happy Calculating!!!
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logarithm/61958: This question is from textbook
Solve the equation.
cuberoot2^(2-x) = 2^(x^2)
This problem is very confusing for me, please help!
1 solutions
Answer 42700 by funmath(2925) on 2006-11-18 07:00:32 (Show Source):
You can put this solution on YOUR website!Solve the equation.
cuberoot2^(2-x) = 2^(x^2)
 Since the bases are the same, their exponents are equal.
 Factor by what ever method you use, I'm using arch,ac,or grouping.
 Set each parntheses=0.
x+1=0 and 3x-2=0
x+1-1=0-1 and 3x-2+2=0+2
x=-1 and 3x=2
x=-1 and 3x/3=2/3
x=-1 and x=2/3
:
Check:
for x=-1
cubedroot 
cubed root 
cubed root 
 x=-1 is valid
for x=2/3
cubed root 
cubed root 
cubed root 
 x=2/3 is also valid.
There's another method for solving this, but you have to use a calculator if you take the log of both sides, so don't freak out if this is not the method you were taught.
Happy Calculating!!!
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Functions/61900: Some help Please
given f(x)=3x-7, find f^-1(x)
thank you for your time
1 solutions
Answer 42641 by funmath(2925) on 2006-11-17 17:06:51 (Show Source):
You can put this solution on YOUR website!given f(x)=3x-7, find f^-1(x)
Let f(x)=y
y=3x-7
Swap the x and y and solve for y
x=3y-7
x+7=3y-7+7
x+7=3y
(x+7)/3=3y/3
(1/3)x+7/3=y
Let y=f^-1(x)
f^(-1)(x)=(1/3)x+7/3
Happy Calculating!!!
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Polynomials-and-rational-expressions/61893: I need some help please
Find all zeros of f(x)=3x^2(x-5)(2x+9)^3(x-4) and their multtiplicatee
thank you
1 solutions
Answer 42640 by funmath(2925) on 2006-11-17 17:01:53 (Show Source):
You can put this solution on YOUR website!f(x)=3x^2(x-5)(2x+9)^3(x-4)
Set each factor = to 0 and solve for x to find the 0's.
:
x-5=0
x-5+5=0+5
x=5
:
2x+9=0
2x+9-9=0-0
2x/2=-9/2
x=-4.5
:
x-4=0
x-4+4=0+4
x=4
:
I'm not sure what you mean by multipliatee.
The zeroes are: x={0,5,-4.5,4}
Happy Calculating!!!
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logarithm/61833: Exponential and Logarithmic Functions
(1)Let f(x) = 2^x , g(x) = (1/8)^x, and h(x) = log sub 2(x). Find each of the following:
f(3)
f(-2)
f(1/2)
g(2)
g(-1)
g(1/3)
h(2)
h(1/2)
(2) Solve each of the following equations for the given variable
(a) 2^a = 16
(b) 3^z = 1/9
(c) 9^n = 3
(d) (1/5)^x = 25
1 solutions
Answer 42635 by funmath(2925) on 2006-11-17 15:21:55 (Show Source):
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Functions/61665: Could someone helo me please
Find the domain and range of Y=squaree root of 8+5x
thx
1 solutions
Answer 42624 by funmath(2925) on 2006-11-17 14:22:03 (Show Source):
You can put this solution on YOUR website!Find the domain and range of.
[DOMAIN IS EVERYTHING THE X'S CAN BE, THE RANGE IS EVERYTHING THE Y'S CAN BE BECAUSE OF X]
:
You can't have a real number solution for a negative number, so:
 <--domain
At x=-8/5, y=0
when x gets really big, y gets big too, so the range is 
:
Happy Calculating!!!
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logarithm/61801: This question is from textbook
Please help with the following problem: e^x = 2^x+1
1 solutions
Answer 42616 by funmath(2925) on 2006-11-17 13:34:57 (Show Source):
You can put this solution on YOUR website!e^x = 2^(x+1)
ln(e^x)=ln(2^(x+1))
xln(e)=(x+1)ln(2)
x(1)=(x+1)ln(2)
x=xln(2)+ln(2)
x-xln(2)=ln(2)
x(1-ln(2))=ln(2)
x(1-ln(2))/(1-ln(2))=ln(2)/(1-ln(2))
x=ln(2)/(1-ln(2))
x=2.258891353 approximatlely.
Happy Calculating!!!
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