geno3141

If you want the calculator at this site to graph this equation, type "x/3 - 1" into the entry line (without the quotes).

Or, do you want help in doing this by hand?

How many digits?

From the numbers from 1 through 9, there are 9 digits.

From the numbers from 10 through 99, there are 90 numbers of 2 digits each = 180 digits.

From the numbers from 100 through 999, there are 900 numbers of 3 digits each = 2700 digits.

Total number of digits:  9 + 180 + 2700  =  2889 digits.

How many 7s?

From 000 to 099 there are 10 7s in the one's place and 10 7s in the ten's place = 20 sevens.

There will be 20 sevens in each of the regions 100-199, 200-299, ... 900-999 = 20 x 9 = 180 sevens.

But, in the region 700 - 799, there are 100 7s in the hundred's place.

Total of 300 7s. 

So, the probability of getting a 7:  300/2889

If all the digits from 000 through 999 were used (this includes more zeros than actually printed but won't change the sum), there would be 300 1s, 300 2s, 300 3s, ..., 300 9s.

300(0) + 300(1) + 300(2) + 300(3) + 300(4) + 300(5) + 300(6) + 300(7) + 300(8) + 300(9)  =  13,500

Let x be the number.

"twelve decreased by twice a number"   --->   12 - 2x

"8 times the sum of number and 4"   --->   8(x + 4)

12 - 2x  =  8(x + 4)

12 - 2x  =  8x + 32                    (distributive property)

12        =  10x + 32                   (add 2x to both sides)

-20       =  10x                           (subtract 32 from both sides)

x  =  -2                                      (divide both sides by 10)

8,000,000 / 20,000,000,000  =  0.0004

To turn 0.0004 into a percentage, multiply by 100   --->   0.04%

3cot(x) + 1  =  4

--->   3cot(x)  =  3

--->     cot(x)  =  1

If cot(x) = a/b, then tan(x) = b/a

--->   tan(x) = 1

--->         x  =  tan^-1(1)

--->         x  =  45^o ± n·180°

As answered previously:

To cut it into 125 congruent smaller cubes requires 5 horizontal cuts and 5 vertical cuts.

The only cubes that are painted red on one side are the interior cubes on each side. Of the 25 cubes on each side, nine of them are painted red on only one side. 9 x 6 = 54 cubes with red on only one side (9 on each side x 6 sides).

The only cubes that are not painted at all are the interior cubes; there are 3 x 3 x 3 = 27 interior cubes.

Of all the 125 cubes,

27 are interior cubes, that have no sides painted red.

54 are cubes that are painted red on only one side.

36 are cubes that are painted red on two sides.

8 are corner cubes; they are painted red on three sides.

The probability of a red side facing up:  (27/125)(0/6) + (54/125)(1/6) + (36/125)(2/6) + (8/125)(3/6)

(The first set of parentheses contains the probability of that type of cube is chosen; the second set of parentheses contains the probability of having a red side facing up; add together all these individual probabilities.)

... finish the multiplying and adding ...

ln(x) = 8     --->   x = e⁸

cos(2a) - 1/cos(a) + 1

cos²(a) - sin²(a) - 1/cos(a) + 1                        ( Use the identity:  cos(2a) = cos²(a) - sin²(a) )

[cos³(a) - cos(a)sin²(a) - 1 + cos(a)]/cos(a)       ( Write with the common denominator:  cos(a) )

[cos³(a) + cos(a) - cos(a)sin²(a) - 1]/cos(a)       ( Rearrange the terms )

[cos³(a) + cos(a)[1 - sin²(a)] - 1]/cos(a)            ( Factor out cos(a) )

[cos³(a) + cos(a)[cos²(a)] - 1]/cos(a)                ( Use the identity:  cos²(a) = 1 - sin²(a) )

[cos³(a) + cos³(a) - 1]/cos(a)                           ( Multiply)

[2cos³(a) - 1]/cos(a)                                                       

... and now I'm stuck! ...

If there is an odd number of numbers, sort the numbers in order and the middle number will be the median.

If there is an even number of numbers, sort the numbers in order and then find the mean of the middle two numbers.

Even though there are only two numbers, find the mean of the middle two numbers.

The mean of 0 and 2 is (0 + 2)/2  =  2/2  = 1.

So, the median is 1.

Write it as  x² + x - 2550  =  0

and then either factor it or use the quadratic formula.