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160:15 The ratio of snow to rain, or: 160 / 15 =10 2/3 : 1. So that you would have:

[4,250 x 15] / 160 =398.4375 mm of rain equivalent.

We know that f(3) = 5.

so f(f(3)) = f(5) = 8.

f(f^(-1)(4)) is just 4.

f^(-1)(f^(-1)(5)):

f^(-1)(5) = 3

f^(-1)(3) = 2

so f^(-1)(f^(-1)(5)) = 2.

Add them up: 8 + 4 + 2 = 14. :D

most likely, it is arranged in this way...

A --------- B

|               |

|               |

D-----------C

Just think that it is a trapezoid... lol

because AB||CD, angle B + angle C = 180 deg.

because angle C = 3 angle B, 4 angle B = 180 deg, which means angle B = 45 deg.

sin( 7·pi / 4 )  =  - sqrt(2) / 2

2 · sin( 7·pi / 4 )  =  - sqrt(2) / 2 · 2  =  -sqrt(2)

SUM = (F + L) / 2 * N, where F=First term, L=Last term, N=Number of terms.

160 = (F - 30) / 2 * 20, solve for F

160 = 10 (F - 30)

160 = 10 (F - 30) is equivalent to 10 (F - 30) = 160:
10 (F - 30) = 160

10F - 300 = 160

10F = 160 + 300

10F = 460 divide both sides by 10

F = 460 / 10

F = 46 - First term.

Let f(x) = 4x-5 and g(x) = 3x, find (f-g)(x)

I think that it is just f(x)-g(x)

=4x-5-3x

=x-5

8/3-(sqrt(6))

I assume you mean

8/[3-sqrt(6)]

you have to multiply by the conjugate of the denominator.

\(\frac{8}{3-\sqrt6}\\ =\frac{8}{3-\sqrt6}\times \frac{3+\sqrt6}{3+\sqrt6}\\ =\frac{8(3+\sqrt6)}{9-6}\\ =\frac{24+8\sqrt6}{3}\\\)

If I was to be a moderator, I would personally put you as the best answer 

1-((1-0.7)^110)

1 - ((0.3)^110)

1 - (3.0432527221 7045370863 7199325153 0170531786 7470666370 49 x  10^-58)

=0.9999999999 9999999999 9999999999 9999999999 9999999999 9999999695 6747277829 5462913628 0067484698 2946821325 2933362951.

Are you happy now??!!

This one is easy to see! The first sequence is the result of evaluating the second sequence, which is called the Leibniz's formula for Pi. That is: 1- 1/3 + 1/5 -1/7 + 1/9 -1/11 + 1/13 - 1/15.......to infinity = Pi/4. So if we divide Pi by 4 =0.78539816339744830961566084581988.....except in your first sequence the "decimal point" has been removed to make a little more difficult to recognize. However, this Leibniz's formula converges extremely slowly. To get the first ten accurate digits, you will have to evaluate about 5 billion terms!!.

g( f(x) )  =  5 - 4x

We want to find  g(4)  , that is, we want to find  g  when...

f(x)  =  4

                             Since  f(x)  =  2x - 3  , we can replace  f(x)  with  2x - 3  .

2x - 3  =  4

                             Add  3  to both sides.

2x  =  7

                             Divide both sides by  2  .

x  =  7/2

Now we know that when  x = 7/2  , f(x)  =  4 .

g( f(x) )  =  5 - 4x

                                              Replace every instance of  x  with  7/2  .

g( (f(7/2) )  =  5 - 4(7/2)

                                              Since  f(7/2)  =  4 , we can say...

g(4)  =  5 - 4(7/2)

g(4)  =  -9

Composing answer . . .

Let Kathy's age = k, then we have:

The mother's age =3k + 1, but:

k + 3k + 1 = 57

4k =57 - 1

4k = 56 divide both sides by 4

k =56 / 4

k = 14 - Kathy's age, and 3*14 + 1 =43 - her mother's age.

Very nice Hectictar :)

Most calculators would do this or maybe just say error because the number is too small to display.

\(y=2 ^{ -100000000000}\\ log(y)=log(2 ^{ -100000000000})\\ log_{10}(y)= -100000000000log_{10}(2)\\ log_{10}(y)= -30102995000\\ y=10^{-30102995000}\\ y=\frac{1}{10^{30102995000}}\\ y\approx 0 \)

Let m = mother's age.

m = 3k + 1      (1)

m + k = 57      (2)

from (2) we have m = 57 - k.    (3)

Replace the m in (1) using (3)

57 - k = 3k + 1

Subtract 1 from both sides

56 - k = 3k

Add k to both sides

56 = 4k

Divide both sides by 4

14 = k     (or just k = 14)

.

Here's a visual representation:

.

3\(\sqrt{}1331\)=11

Here's some thoughts on it...

Let's define it as "n".

2/0  =  n           Multiply both sides by  0   .

2  =  0n

So...what is  n ? Any number times  0  is equal to 0 .

So, there is no possible number for  n  that makes the equation true.

But...what about  0/0   ?

Let's say...

0/0  =  x           Multiply both sides by  0  .

0  =  0x

Now we can see that any number for  x  makes this equation true.

So x is undefined, because it can be any number.

Let p(x) = 2x^3 - 113 and let q be the inverse of p. Find q(137)

Note that the inverse just reverses the original coordinates

So the coordinates of the inverse are ( 137, x)

So....putting 137 into the inverse sends us back to the otiginal "x"

So....the original coordinates were  ( x, 137 )

And x will equal  q (137)

So...all we need to do is to set p = 137 and solve to find this otiginal x

2x^3 - 113  = 137   add 113 to both sides

2x^3 = 250  divide both sides by 2

x^3  = 125   take the cube root of both sides

x = 5   and this is q(137)

Proof...I won't derive it but the inverse q  is   ∛ [ ( x + 113) / 2 ]

And  q (137)  =  5

x^2−8=√(4x^2)   square both sides

x^4 -16x^2 + 64  = 4x^2

X^4 - 20x^2 + 64 = 0     factor as

(x^2  - 16) ( x^2 - 4)  = 0

(x - 4) ( x + 4) (x - 2) ( x + 2)  = 0

Setting each factor to 0 and solving for x we have the possible solutions 

x = ± 2   and x = ± 4

Only the second pair actually solve the original equation....the other two are extraneous due to squaring both sides

Moves

1, 1

6, 7

2, 7

2, 3

7, 9

3, 9

3, 5

3 ,1

8, 7

4, 7

4, 3

9, 9

5, 9

1, 9

1, 5

1, 1  and the cycle  starts again......

So...it  visits 15 different points

Add the two values  =  8.3

Divide by 2  =  4.15

Because angle CBA is bisected, we have the following relationship :

BC / AB  =  CD / AD

20 / 15  = CD / AD = 4 / 3

So....CD  is the longer  segment  of  side  AC

And it's 4/7 the length  of AC  =   (4/7) * 10  =  40/7 units  ≈  5.7 units

Here's a pic :

Let the number of hours per week =H
3.5H + 4.10 =5.25H - 11, solve for H
4.10 + 11.00 =5.25H - 3.5H
15.10 =1.75H
H = 15.10 / 1.75
H =8.629 hours per week that Francis and Bella work to have the same amount of money.