geno3141

5^x  =  4^{x + 1}

Since 4^{x + 1}  =  4^x·4:

5^x  =  4^{x + 1}     --->     5^x  =  4·4^x

                       --->     5^x / 4^x  =  4

                       --->     (5/4)^x  =  4

Now, take the log of both sides:

                       --->     log(5/4)^x  =  log(4)

                       --->     x · log(5/4)  =  log(4)

Divide both sides by log(5/4):

                       --->     x  =  log(4) / log(5/4)

Now, use yourcalculator:

                       --->     x  =  6.21...  (approx)

One way to look at this problem:

Since the ratio of cars to trucks is 7:3, for every 10 (7 + 3 = 10) vehicles, 7 are cars and 3 are trucks.

How many groups of 10 are there?

Since there are 60 vehicles, 60 / 10 = 6   --->  there are 6 groups of 10.

Since there are 7 cars in each of the 6 groups:  6 x 7  =  42  cars

Since there are 3 cars in each of the 6 groups:  6 x 3  =  18  trucks

The only factors of 7 are 7 and 1.

There are several pairs of factors of 54, the pair that works is 3 and 18.

7x² + 3x - 54  =  (7x - 18)(x + 3)

Let's use this identity:  sin²x + cos²x  =  1     --->     sin²x  =  1 - cos²x

cosx - sin²x - 1     --->     cosx - (sin²x) - 1     --->     cosx - (1 - cos²x) - 1     --->     cosx - 1 + cos²x - 1

     --->     cos²x + cosx - 2     --->     (coxx + 2)(cosx - 1)

This will probably be easier if all the times are converted to minutes.

4 hours  =  4 x 60  =  240 minutes.

Delano  =  3/4 hour  =  3/4 x 60  =  45 minutes.

Alex  =  2/3 hour  =  2/3 x 60  =  40 minutes.

Jordan  =  3/5 hour  =  3/5 x 60  =  36 minutes.

Now lets take the 240 minutes and divide that be each of the times.

Delano:  240 / 45  =  5, remainder 15   --->  means that he made 5 signs and had 15 minutes left over.

Alex:  240 / 40  =  6, remainder 0   --->  means that he made 6 signs and had no minutes left over.

Jordan:  240 / 36  =  6, remainder 24   --->   means that he made 6 signs and had 24 minutes left over

The inverse of  log(19.1078)  is  10^19.1078.

The derivative of  cot(x)  is  - csc²(x).

So, the derivative of  8cot(x)  is  -8csc²(x).

At  x = 6,  the derivative is  -8csc²(6)  =  -8/sin²⁽6)  =  -102.4682.

Your x-values are your independent variables, your y-values are your dependent variables when your ordered pairs are in this order:  (x, y).

Let  x  =  0.54 54 54 54 54 ...

Then multiply by 100, because 100 will move the repeating digits to the left one cycle (two places):

   100 x  =  54. 54 54 54 ...     Now subtract the original value:

          x  =    0. 54 54 54 ...

     99x  =  54                         Finish by dividing by 99:

         x  =  54/99                   Reduce:

        x  =  6/11

Logs are added when the original problem was a multiplication problem.

Thus, ln(9) + ln(2)  =  ln(9 x 2)  =  ln(18)