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Note that we can confirm this by writing x^-1   as 1/x

So

log 1/x    = log 1 - log x   =  0 - log x    =  - log x

Note that the combined rates of the ttains  = 120kph  = 1/30 km / s

And the length of the trains are 1/2 km ......and the other is 2/3 as long = 1/3 km,...so....

The problem boils down to the number of seconds it takes the rear of the longer train to travel [ 1/2 + 1/3] km  = 5/6 km

And   D /R  = T     ....so....        [5/6]km / [ 1/30 km/ s]   =  [5 * 30 ] / 6     =   25 seconds to completely pass each other

Look here

Simplify the following:
(2 x^2+3 x-20)/(x^2+6 x+8)

The factors of 8 that sum to 6 are 4 and 2. So, x^2+6 x+8 = (x+4) (x+2):
(2 x^2+3 x-20)/(x+4) (x+2)

Factor the quadratic 2 x^2+3 x-20. The coefficient of x^2 is 2 and the constant term is -20. The product of 2 and -20 is -40. The factors of -40 which sum to 3 are -5 and 8. So 2 x^2+3 x-20 = 2 x^2+8 x-5 x-20 = 4 (2 x-5)+x (2 x-5):
4 (2 x-5)+x (2 x-5)/((x+4) (x+2))

Factor 2 x-5 from 4 (2 x-5)+x (2 x-5):
(2 x-5) (x+4)/((x+4) (x+2))

((2 x-5) (x+4))/((x+4) (x+2)) = (x+4)/(x+4)×(2 x-5)/(x+2) = (2 x-5)/(x+2):
Answer: |(2x - 5) / (x + 2)

wot is the power of 147

\({\color{blue}"The \ power \ of \ 147" means \ to \ raise \ a \ number, }\)

\({\color{blue}a \ term, \ a \ variable, \ a \ constant \ into \ the \ 147th \ power.}\)

  !

This is a whole number and there is no rounding involved. If it had a decimal such as:12345.89, then you could round to the nearest tenth =12345.9.

You can't round that to the nearest tenth. You can round it to the nearest ten though, which would be 173610.

Enter your number first, then press the key"+,-" just to the right of zero.

if x + x + x = 30 ; x + 2y + 2y = 18 and 2y - 2z = 2 how much is y + x * z

So  simplifying, we have

3x = 30  →  x = 10

And

x + 4y  = 18   →   10 + 4y = 18   →  4y  = 8  →   y = 2

And

2y - 2z   = 2  →   y - z  = 1   →   2  - z  = 1   →  z = 2 - 1   =  1

So

y + x * z  =  2 + 10 * 1   = 2 + 10  = 12

x = 10 and y = 2 and z = 1

how much is y + x * z =2 + 10*1= 12

X+X+X=30

3x=30

x=10

x+2y+2y=18

(10)+2y+2y=18

10+4y=18

4y=8

y=2

2y-2z=2

(2*2)-2z=2

4-2z=2

-2z=-2

z=1

y+x*z

2+10*1

2+10

12

Just multiply: 9 x Pi =Circumference.

You use the formula 2rpi, or dpi, so you would go 3.14(recomended for pi) and multiply that by 9, and you would get 9*3.14 = 28.26.

pie to the power of 7 multiplied by 23

\({\color{blue}{\pi}^7\times 23=69466.7442389}\)   !

1) a. Sum =F x (1 - r^n) / (1 - r), F=First term, r=common ratio, n=number of terms.

     b.Sum of infinite series =F / (1 - r ), variables same as above.

2) a. Given partial sums, it follows that the first term =3

    b. The common ratio is 1/3

    c. The 5th term will be: 1/27

This is an infinite series which sums to 4.5.

If you wish to use Algebra to solve it, then see the example here by Mr. CPhill, which is very nicely solved and explained: http://web2.0calc.com/questions/arithmetic-sequence_52513

Looks like you got it right:

Expand the following:
((7 a)/(9)+(9 b)/(7))^2-a b

((7 a)/(9)+(9 b)/(7)) ((7 a)/(9)+(9 b)/(7)) = ((7 a)/9) ((7 a)/9) + ((7 a)/9) ((9 b)/7) + ((9 b)/7) ((7 a)/9) + ((9 b)/7) ((9 b)/7) = (49 a^2)/(81)+a b+a b+(81 b^2)/(49) = (49 a^2)/(81)+2 a b+(81 b^2)/(49):
(49 a^2)/(81)+2 a b+(81 b^2)/(49)-a b

Grouping like terms, (49 a^2)/(81)+2 a b+(81 b^2)/(49)-a b = (81 b^2)/(49)+(2 a b-a b)+(49 a^2)/(81):
(81 b^2)/(49)+(2 a b-a b)+(49 a^2)/(81)

2 (a b)-a b = a b:
Answer: |(81 b^2)/(49)+ab+(49 a^2)/(81)

Possible derivation:
d/dx(x^x)
Express x^x as a power of e: x^x = e^(log(x^x)) = e^(x log(x)):
 = d/dx(e^(x log(x)))
Using the chain rule, d/dx(e^(x log(x))) = ( d e^u)/( du) 0, where u = x log(x) and ( d)/( du)(e^u) = e^u:
 = (d/dx(x log(x))) e^(x log(x))
Express e^(x log(x)) as a power of x: e^(x log(x)) = e^(log(x^x)) = x^x:
 = x^x d/dx(x log(x))
Use the product rule, d/dx(u v) = v ( du)/( dx)+u ( dv)/( dx), where u = x and v = log(x):
 = log(x) d/dx(x)+x d/dx(log(x)) x^x
The derivative of x is 1:
 = x^x (x (d/dx(log(x)))+1 log(x))
The derivative of log(x) is 1/x:
 = x^x (log(x)+1/x x)
Simplify the expression:
Answer: |= x^x (1+log(x))

Just divide 45,000/150=            and 90,000/150 =               The answers you get give you the number of tickets that have to be sold.

I'M FINE, TNX, AND YOU?

You can find the series by using symbolic Algebra. But in this case, it is not necessary because it is very obvious: -2, 4, 10, 16, 22, 28..........etc. The common difference=6, so that:

-2 + 4 +10 =12, and

-2 x 4 x 10 =-80

If 635a is divisible be 3, find all possible values of a 

a=1, 4, 7. If you wish to go beyond 1-digit answer, then you can continue by adding 3 to 7, so that you would have: 10, 13, 16, 19.......and so on.

correct

what is the are of a rectangle that is square root of 70 by square root of 28. in its simplest form

rectangle: square root of 70 by square root of 28

\(\sqrt{70} \times \sqrt{28} =\sqrt{70\times 28}\)      !

\(A=\sqrt{1960} =44.272\)            !

How do you solve this problem x/3 - (3-x)/6 - (x+2)/8 = (3x-1)/6 ?

\(\frac{x}{3}-\frac{3-x}{6}-\frac{x+2}{8}=\frac{3x-1}{6} \)  

                                           \(Common \ denominator = 24\)

\(\frac{x\times 8-4\times (3-x)-3\times (x+2)}{24} =\frac{4\times (3x-1)}{24} \)

\(8x-12+4x-3x-6=12x-4 \)

\(-3x=14\)

\({\color{blue}x=-\frac{14}{3}}\)

\({\color{blue}x=- 4 \frac{2}{3}}\)

\({\color{blue}x=-4.666\overline{6}}\)      !