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expand the numerator

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880 miles=distance
8hours=time
speed=distance/time
each one travelled half the distance
so speed=440/8=55 mph

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angular velocity (w)=35 radians/min=35/60 rad/second=0.5833 rad/s
diameter=38 feet
hence radius (r)=19 feet
velocity?

v=0.5833(19)=11.0833
=11.1 feet/s(rounding off)

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sure,post the questions and we'll get to them

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1 quart ------------ 9(10)=90
?? quarts ------------ 10(12)=120
cross multiply
x(90)=1(120)
x=120/90=4/3=1.33 quarts of paint required

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a. A cable 200 ft. long is cut into two pieces so that one piece is 12 ft. longer than the other. How long is each piece?
let the first pc be x ft long
then second piece is (x+12)
together they make up 200 feet
so x+x+12=200
2x+12=200
2x=200-12=188
x=188/2=94

b. A boat travels 24 miles upstream in 3 hours. It then takes 3 hours to go 36 miles downstream. Find the speed of the boat in still water and the speed of the current.
let speed of boat in still water be x,and speed of current downstream be y
then upstream the speed of the boat will be (y-x) miles per hour
distance=24 miles in 3 hours at speed of (y-x)
speed=(y-x)=distance/time=24/3=8
speed downstream is (x+y)
speed=(x+y)=dstnce/time=36/3=12
so we have 2 equations and 2 variables,
y-x=8 AND x+y=12
y=8+x AND y=12-x
y=8+x=12-x
8+x=12-x
x+x=12-8
2x=4
x=2
so speed of boat is 2 mph
y=8+x=10 mph which is speed of current

c. A service station wishes to mix 40L of a 78% antifreeze solution. How many liters of a 75% solution and a 90% solution should be used in forming the mixture?
let x litres be taken of the 75% solution
let y litres be taken of the 90% solution
then (x+y)=40 as we need 40litres of the solution
so y=40-x
now we can write our equation as,
x(75%)+y(90%)=40(78%)
x(75/100)+y(90/100)=40(78/100)
75x+90y=40(78)
75x+90y=3120
75x+90(40-x)=3120
75x+90(40)-90x=3120
-15x+3600=3120
-15x=3120-3600
-15x=-480
x=32
y=40-x=8
so you need 32 litres of 75% solution,and 8liters of 90% solution

Hope this helps,
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1, 1/2, 1/4, 1/8,…

What is r, the ratio between 2 consecutive terms?
second term=1/2
third term=1/4
ratio r=third/second=(1/4)/(1/2)=(1/2)

Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.

a=1,n=10,r=0.5
sum for n terms=
=
=
=
=
=1.998046875
=1.9980(rounding off)

Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.

a=1,n=12,r=0.5
sum for n terms=
=
=
=
=
=
=1.99951171875
=1.9995(rounding off)

What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
The number will approach 2.
It will reach 1.999999999999999999999999....upto infinity, but it will always be smaller than 2

Hope this helps,
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1.
we know that
OR
therefore,

so we get,
x=8(1/2)=4
2. logx (1/16)=-2
take x to the other side,so we get




therefore,x=4
3. log(x)=square root log(x)
square both sides,
[log(x)]^2=[log(x)]
using property of logs we get,
2logx=logx
2logx-logx=0
logx=0


now look at this,
log8 to the base 2=*3*
so 8=2 raised to *3*
instead of 3 if we put 0,instead of 8 we will get 1
so any number raised to zero becomes one,so we get
x=1

hope this helps,
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you have provided the data,what is the question?

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-(x+6)+4x=3(x-1)+7
opening brackets,
-x-6+4x=3x-3+7
3x-6=3x+4
take everything to one side
3x-3x-6-4=0
0-10=0
-10=0
which cannot be true

please check your question,then post again
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when it says to write a rule for each function,
you have to write an expression which will give you the required value for f(x) when you substitute x

meaning,
x f(x)
-1 -9
0 -5
1 -1
2 3

So here you should put (-1) in the expression and you should get (-9)
So you would have to multiply by 9

Sample functions are below,please try to find other ways of doing this as well,because the same expression can be written in at least 3 different ways

x y f(x)
-1 -9 (9x)
0 -5 (x-5)
1 -1 (-x)
2 3 (x-1)

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-(1/4)x=3/4 OR (-1)/4x=3/4

-(1/4)x=3/4
if you mean negative one-fourth of x,then we get,
-1x=3 [multiplying through out by 4]
then x=-3

if you mean -1x divided by 4,then we get,
-1x=(3/4)*4
-1x=3
x=-3

luckily both answers work out to the same
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let length be x cm,breadth be y cm,height be z cm

then volume=x*y*z=7500
then surface area=2(xy*yz*zx)=2600

We only get 2 equations,please check your question for any missing data or assumptions you are required to make,and post again
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3(x-4)=2(x-8)+5x
open the brackets
3x-12=2x-16+5x
3x-12=7x-16
taking everything to one side
3x-12-7x+16=0
remember on taking terms to the other side,their sign reverses
now we get
-4x+4=0
-4x=-4
x=1

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g(x)= 2x^2-5x-7
to find g(-1), substitute x=-1
so we get
g(-1)=2(-1)^2-5(-1)-7(-1)
=2(1)+5+7=14
g(2)=2(4)-5(2)-7=8-5-10=-7
and so on
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6000x-2000y+136000=0 (4< x < 18)
where x=4 corresponds to 1994

It reduces to y=3x+68.

x=4,y=3(4)+68=12+68=80
x=5,y=3(5)+68=15+68=83
x=6,y=86
x=7,y=89
x=8,y=92------------->(a)
x=9,y=95
x=10,y=98
x=11,y=101
x=12,y=104
x=13,y=107
x=14,y=110----------->(b)
x=15,y=113
x=16,y=116
x=17,y=119
x=18,y=122

If you substitute x=0,we get y=68.Multiply this by 1000 and we get a credible figure,considering it as 1990. Then for x=18,y=122 ie in the year 2008, a figure of $122000 seems to make sense.

That would make 1998 and 2004 your answers,though of course we have no logical reasoning to back this up.

If this is a valid question,and you do manage to solve this,drop a mail at:
xcentaur[at]hotmail[dot]com
Hope this helps,
xC

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-a^2+9a-2a^2-9-10a
group like terms
(-a^2-2a^2)+(+9a-10a)+(-9)
-3a^2-a-9

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x+4=t over 7
x+4=t/7
7(x+4)=t
7x+28=t
7x+28-t=0

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Hi I am having some trouble with this problem from my College pre-calculus class.
Given the following rational function, Complete each of the following:
a. Find the zeros of the function.
b. Find the y-intercepts.
c. Find the horizontal and vertical asymptotes.



Thats all well and good,but what's the function?
If you'd like a more general answer,please post again or try Google

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(2sqrt5-2sqrt3)(sqrt10+sqrt6)
opening the brackets,

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"5/sqrt7+sqrt3"
do you mean,

OR

Please check your question, and post again
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let the number be x
Five divided by the difference of a number and 7 equals the quotient of 10 and the sum of the number and 6
5/(x-7)=10/(x+6)
cross multiply
5(x+6)=10(x-7)
5x+30=10x-70
100=5x
x=20

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x+y=-1......[1]
3x-y=-7.....[2]

Take the first equation,substitute x=0,-1,1,2,-2 and so on, and calculate y
you will have all these values of x and y as pairs
x=0,y=-1
x=-1,y=0
x=1,y=-2
and so on
plot these on the graph as (x,y)=(0,-1),(-1,0),(1,-2) etc
Then draw a straight line through the points,connecting them

Repeat for the second equation

The lines will meet at a particular point.From the graph paper,look up the co-ordinates of the point,and there you have your solution. It should work out to (x,y)=(-2,1)

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xC

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(a+b)(c-d) = ac-ad+bc-bd
Opening the brackets we get,

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y=5 means that for all values of x,y will take on value '5'
meaning x could be 0,-1,1,2,-2,etc but y will always be 5
try to imagine this on a graph paper
if you manage to,you will see this becomes a straight line passing through the y-axis at the point y=5
Like this,

So it would be a straight line parallel to the x-axis passing through point 5 on the positive y-axis

Hope this helps,
xC

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m+5n-(3m+4n)
m+5n-3m-4n
-2m+n

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7p+q-(7q-6p)
7p+q-7q+6p
13p-6q

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-b^2-b+7b+2b^2-6b
group like terms
(-b^2+2b^2)+(-b+7b-6b)
b^2+0
b^2

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-2(5u+v)-v
-10u-2v-v
-10u-3v

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(2, 3) and (8, 1) ==> (a,b) and (c,d)
Midpoint is given by:
( (a+c)/2,(b+d)/2 )

So we get,
(5,2)

Hope this helps,
xC

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7r+3(s-2r)
7r+3s-6r
r+3s