geno3141

A right-angled scalene triangle cannot have legs that measure 4 inches and 5 inches if the hypotenuse measures 6 inches ...

Let side a = 4 and side b = 5 with side c = 6 (hypotenuse).

The Pythagorean Theorem demands that a² + b²  = c²

But ...............                                       4² + 5²  ≠ 6²                (16 + 25 = 41, not 36)

Is (5^x)2  =  5^x·2 ?

If so, since m(x) = 1:  1  =  5^x·2 

   divide by 2:         1/2  =  5^x

--->                log(1/2)  =  log(5^x)

--->                log(1/2)  =  x·log(5)

--->   log(1/2) / log(5)  =  x

--->  x  =  -0.43067...

Or does (5^x)2  =  (5^x)^{2 ?}

If so,    1  =  (5^x)² 

--->     1  =  5^2x

--->  log(1)  =  log(5^2x)

--->  log(1)  =  2xlog(5)

--->  log(1) / log(5)  =  2x

--->  0  =  2x

--->  x  =  0

9⁴ / 9⁶  =  9^-2       (when dividing numbers with the same base, subtract exponents)

9^-2  =  1/9²  =  1/81  =  0.012345679012...

Or:  9⁴ / 9⁶  =  6561/531441  =  1/81  =   0.012345679012...

1 2/4  =  1 1/2  =  3/2

You can set up a proportion:  (1/4) / (3/2)  =  x / 1

Cross multiply:  1 · (1/4)  =  (3/2) · x

--->                          1/4  =  (3/2)x

Multiply both sides by 2/3:  (2/3)·(1/4)  =  (2/3)·(3/2)x

--->                                              2/12  =  x

--->                                               1/6  =  x

--->   Answer:  1/6^th of a cup

If you wish to find the angle that has a cosine value of .5000 with this calculator:

Press (2nd)  

Press (acos)

Enter .5

Press

It will give the answer 60°

On the unit circle, the coordinates of a 270° angle are (0, -1).  

At this point x-value = 0, y-value = -1, r-value (the distance from the origin to the point) = 1.

sin = y/r          cos = x/r        tan = y/x        csc = r/y        sec = r/x        cot  =  x/y

sin(270°)  =  -1/1  =  -1                            csc(270°)  =  1/-1  =  -1

cos(270°)  =  0/1  =  0                              sec(270°)  =  1/0  =  undefined

tan(270°)  =  -1/0  =  undefined               cot(270°)  =  0/-1  =  0

These are terms in a geometric sequence because:  18/54 = 1/3  and  6/18 = 1/3

The common ratio is  1/3.

To find the n^th term, you can use the formula:  t_n  =  a·r^n-1

[a = first term = 54; r = common ratio = 1/3; n is the number of the term that you want = 9]  

--->   t₉  =  54·(1/3)^9-1  =  54·(1/3)⁸  =  54/6561  =  2/243

Calculator time!

Add/subtract the like terms:

(11x - 3) + (4x - 1)  =  11x - 3 + 4x - 1  =  11x + 4x - 3 - 1  =  15x - 4

To find the mass of each one, divide the total mass by the number of hamburgers.

--->   3.25 kg / 25  =  0.13 kg per hamburger.