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The minimum value of x - y is 2.

z = 5 - 2i.

For this to occur either the  1st  2nd  or  3rd  must be a Wednesday

   which would make Halloween (the 31 st) be a   Friday   Thursday or Wednesday  respectively

We can write -4 in exponential notation as 4e^(pi*i), so the equation is z^4 = 4e^(pi*i).

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.

a calculator can do this fast recommend mathway for this problem, but the answer is positive or negative the fourth root of positive 4 or negative 4.

Well ....you will first need to graph it....here is a graph.....the area is a triangle     area = 1/2 base * height   

  Can you take it from here ?

Verifique se os ângulos abaixo são côngruos. Valor:1,0
a) 30° e 150°
b) 5π/2 e π

dave puts a collection of 15 books on the shelf in a random order. Among the books are 2 fiction and 13 non-fiction books. what is the probability that the two fiction books will be together on the left side of the shelf and the 13 non-fiction all together on the right side of the shelf?

Here is my best guess

total number of ways books can be arranged    15 !

  two fictions together have two ways to be arranged while the remaining slots   13!

2 * 13! / 15!

What is the size of the projected shadow of a 40 m high building, when the angle of
elevation of the Sun is 50 ° ?

tan 50°  =  40 /  shadow length

shadow length =  40  / tan 50°  ≈  33.6 m

Note  the   last  digit pattern  for  powers of  7

7^1  =  7

7^2  =  9

7^3  =  3

7^4  =  1       and  this  pattern  repeats 

So   5515  mod 4   =  3

This indicates  the  3rd  entry in the pattern  =   3   =  ending digit

\(c(g^2+p)^2+q\\=c(g^4+2g^2p+p^2)+q\\=cg^4+2cg^2p+p^2c+q\)

Set up system of equation according to corresponding coefficients:

\(c=1\\ 2cp=18\\ p^2c+q=24\\ \)

Substitute first equation to second:

\(2(1)p=18\\p=9\)

Lastly, substitute first and second equation to third equation:

\(9^2(1)+q=24\\q=\boxed{-57}\)

I hope this helps (❁´◡`❁)

ok bye

(3 ¹/₂) / 3 = (7/2) / 3 = 7/6

In mathematics number system is primarily divided into real numbers , integers , natural number , whole numbers , rational numbers and irrational numbers. Addition is the only property on numbers which is valid on all the categories of numbers. 

Subtraction of two irrational numbers may be a rational number too e.g. 

√2−√2=02-2=0

which is a rational number. Product of two irrational numbers can be rational or irrational number. For example √2 √3 = √6 ∈ Qc and √2 √2 = 2 ∈ Q.

Let the number of times (4+8) to be added be n. 

Therefore 

n(4+8)=40

⇒ n(12)=40

⇒ n = 40/12

⇒ n = 3.5

Hence we have to add (4+8) at least 4 times to get 40.

  Brian = 8 + 8m

 Jerry = 9m                         m = minutes

When are they equal?

8+ 8m  = 9m    subtract 8m from both sides

8 = m                   in 8 minutes they will have the same amount       8 + 8m = 8 + 8(8) = 72 cards each

Mental toughness and fortitude.

Connect  AC

AC  is parallel  to  WT  and PS 

Area  of  triangles  ADC   and   ABC    =  180

Triangle WDT  is similar to triangle ADC

Triangle PBS is similar  to triangle ABC

Area  of  triangle WDT  =  (2/3)^2  * area  of  triangle ADC =   (4/9) triangle  ADC

Area  of  triangle PBS  =  (2/3)^2  *  area  of ytiangle  ABC  =  (4/9) triangle ABC

So

(4/9) [ ADC] + (4/9) [ ABC ] + shaded area  =  180

(4/9)  (  [ ADC ]  +  [ ABC ] )   +  shaded  area  =  180

(4/9)  [ 180 ]  +  shaded area  =  180

80  + shaded area  =  180

shaded  area  =  180  -  80   =   100

Will do

The   y  intercepts occur  when  x  = 0

So

0  =  1  +  2sin (t)   rearrange  as

2sin (t)   =  - 1

sin (t)  =   -1/2

This   occurs  when   t   =   7pi/6     

The  y  intercept    =   2 + 6 [cos  ( 7pi/6) ]^2  =  2+ 6 (-sqrt (3)  / 2)^2  =  2 + 6 (3/4)  = 2 + 9/2  = 6.5

Here's a graph : https://www.desmos.com/calculator/oumasnrvgu 

The  side  of  the square  =  42/sqrt 2   inches

So.....the number of feet of trim  needed  =    4 * 42  / sqrt 2   ≈  118.8  inches = 118.8/12  =  9.9 ft

The sq ft  of   glass  needed =   4 * (1/2) 21^2  =  2 * 21^2   = 882 sq in   =  882/12^2  = 6.125 ft^2

Thanks  to EP  for spotting  my  earlier errror  !!!!!

Are you sure you have the correct numbers in your posted Question?

15 x 43 = 645 beads

You could have 14 bags with 39 beads      and one bag with 99 beads

(x-r₁  ) ( x - r₂ )           plug in your roots (which ae not included in your question) and expand ....

x = origianl amount

x -120   after spending 120

   spend 4/7 of this leaves 3/7   

      (x-120) * 3/7    =   1/9 x                        Can you solve this for 'x'  ?

The answer is B, just took the test.

From a circular piece of paper with radius BC, Jeff removes the unshaded sector shown. Using the larger shaded sector, he joins edge BC to edge BA (without overlap) to form a cone of radius 18 centimeters and of volume 432*pi cubic centimeters. What is the number of degrees in the measure of angle ABC of the sector that is not used?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Cone radius    r = 18

Cone volume    V = 432pi

Knowing this, we can calculate the height of a cone:

V = 1/3(r²pi*h)

Cone height    h = 4

Cone slant height     s = sqrt(r² + h²) = 2√85

Note that slant height s is also radius BC.

The length of major arc AC is also the length of the circumference of a base of a cone.

So, the bottom line is:

Angle  ABC = 8.572658425º