geno3141

Formula for the area of a circle:  A  =  π·r²

--->   A  =  π·2²

--->   A  =  4π

This answer is irrational because π is irrational and any rational number (like the number 4) times an irrational number has an irrational answer. (Irrationality wins!)

50 cookies with 45 of them giving you a stomach-ache ...

and 5 to give to me, becase I'm hungry and I like cookies ...

Set up the proportion:  height/shadow  =  height/shadow

4'6"  =  4.5'     and     3'4"  =  3.25'

--->   x / 100  =  4.5 / 3.25

Cross-multiply:

--->   3.25x  =  4.5·100

--->   3.25x  =  450

--->   x  =  450 / 3.25

--->   x  =  138.5 feet (approx)

The standard form for the equation of a circle is:  (x - h)² + (y - k)²  =  r²

where the center is the point (h, k) and the radius is r.

e^6x · e^x  =  e²¹  

Add exponent:  6x + x  =  7x

e^7x  =  e²¹  

The only way that the left side can equal the right side, is for  7x  =  21  --->   x  =  3

y = 2sin(x²)          and         y = 2sin(2x - π/2)

--->   2sin(x²)  =  2sin(2x - π/2)     --->   sin(x²)  =  sin(2x - π/2)     --->   x²  =  2x - π/2

--->   x² - 2x + π/2  =  0   

--->   (using the quadratic formula with a = 1, b = -2, and c = π/2)   --->  x  =  [2 + √(4 - 4(1)(π/2)]/2

--->   x  =  [2 + √(4 - 2π)]/2   --->  non-real answer

However, since sin(x) = sin(π-x), let's change  x²  =  2x - π/2  to  x²  =  π - [2x - π/2]

--->   x²  =  -2x + 3π/2

--->   x² - 2x - 3π/2  =  0

Again, using the quadratic formula:  x  =  [2 + √(4 - 4(1)(-3π/2)]/2

--->   x  =  [2 + √(4 +6π)]/2   --->  x = 1.39 (approx)  (by symmetry, also x = -1.39)

Using a period of 2π:  x²  =  3π - [2x - π/2]    (replace π wirh 3π)

--->   x²  =  -2x + 7π/2

--->   x² - 2x - 7π/2  =  0

Again, using the quadratic formula:  x  =  [2 + √(4 - 4(1)(-7π/2)]/2

--->   x  =  [2 + √(4 +14π)]/2   --->  x = 2.46 (approx)  (by symmetry, also x = -2.46)

A formula for the circumference of a circle is:  C  =  π · d

--->   C  =  π · (7 4/5)

--->   C  =  39/5 · π

--->   C  ≈  24.50 

Using the method of linear combinations:

   -3x + 3y  =  4   --->                                 -3x + 3y  =  4

     -x +  y  =  3   --->   multiply by -3   --->   3x - 3y  =  -9

Add down the columns:                                 0  +  0  =  -5      --->   0  =  -5

This is impossible to solve.

If you were to graph these two equations, you would get a pair of parallel lines. Since the solution to a pair of equations occurs where the two lines cross and since parallel lines don't cross, there is no solution. 

IQR is the interquartile range.

0/0  is an "indeterminate" expression, meaning that it has no fixed value.

Depending upon the problem that created the value 0/0, the answer can be any number ...

it might be 3, or -6, or 0, or -√2, or π, or any other number. It can also could be ∞ or -∞.

Take calculus, and this will be explained to you ...