geno3141

If the whole expression  1 + 5x  is under the square root sign:

          1 + x  =  √(1 + 5x)

Remove the square root sign by squaring both sides:

          ( 1 + x )²  =  ( √(1 + 5x )²

      1 + 2x + x²   =   1 + 5x

Subtract 1 + 5x from both sides and rearranging:

              x² - 3x  =  0

        x ( x - 3 )  =  0

So  x = 0  or  x = 3

But these are only possibilities! They must be checked!

         1 + 0  =  √(1 + 5·0)     --->   1  =  √1      Yes!

         1 + 3  =  √(1 + 5·3)      --->  4  =  √(16)  =  4     Yes!

So, both  0  and  3  work.

If the problem is:  1 - -49/81, the problem can be simplified because                                                                                                                      subtracting a negative can be replaced by adding a positive:

                           1 + 49/81  =  1 49/81.

If the problem is:  (1 - -49) / 81,  then it reduces to  (1 + 49)/81  that is  50/81.

I'm not sure exactly what you mean, but I'll take a stab at this:

If you want to simplify  √(4/9)  

write it as the square root of the numerator divided by the square root of the denominator, as:

    √(4/9)  =  √4 / √9  =  2/3

Also:  √(17/36)  =  √17 / √36  =  √17 / 6

If this doesn't answer your question, post back and include some problems. Thanks.

Let  n  =  50.8383838383838 ...

Since the number of digits that repeat is two multiply the both sides by 100 and subtract the original equation from the new equation:

   100 n  =  5083.838383838383 ...

      -   n  =     50.838383838383 ...

   -------  =  ---------------------------

     99 n  =  5033                      (Everything after the decimal point subtracts out.)

-->    n  =  5033/99

If only one digit repeated, multiply by 10; if three digits repeated, multiply by 1000; etc.

Since  cot(x)  =  cos(x)/sin(x),  the  cot(x)  will be undefined whenever  sin(x) = 0  and these are the locations of the asmyptotes of the function. 

sin(x) = 0  at  0  radians,  ± π radians,  ± 2π  radians,  ...

Changing all of them into decimals:

9 / 6    =  1.5

2 / 3    =  0.6666...

3 / 2    =  1.5

1 1/2   =  1.5

18/12  =  1.5

The answer is approximately 15 680 . 324 

Hi Tori!

Since the function is secant and secant = 1 / cosine, the period of secant will be the same as the period of cosine.

In a function like  f(x) = cos( at )  (where t is the variable and a is a constant), the period of that function is found using:  period  =  2π / a.

In your problem, the value for a = π/5, so the period will be (2π) / (π/5).

     2π ÷ (π/5)   =   2π · (5/π)   =   10 seconds, 

which agrees with the problem that says "it completes one rotation every 10 seconds."

"dms" means "degrees, minutes, and seconds".

There are 60 minutes in each degree and 60 seconds in each minute.

18.75°  means that you hae 18 full degrees plus another .75 of a degree.

Since there are 60 miutes in a degree, .75° can be changed into minutes by:  .75 x 60  =  45 minutes.

18.75°  =  18 degrees and 45 minutes  =  18° 45'

Since it came out to 45 minutes without any remaining decimal, we don't have to change the remaining decimal part into seconds. If there were a remaining decimal, multiply that decimal times 60 to get seconds.

The exponent is -2/3.

The negative sign means that the problem belongs in the denominator with a positive exponent.

(-125) ^ (-2/3)  =  1 / [ (-125) ^ (2/3) ]

An exponent of 2/3:

  ---  the numerator of 2 means that you need to square the number

  ---  the denominator of 3 means that you need to find the cube root of the number

and you can do these two operations in eiter order. 

If you square first, you get:  1 / [ (15625) ^ (1/3) ]

Now, finding the cube root:  1 / ( 25)  =  1 / 25.

If you find the cube root first, you get:  1 / [ (-5) ^ 2 ]

Now, squaring:  1 / (25)  =  1 / 25.

Generally, if you find the root first, you will be working with smaller numbers.