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The  volume of the  cone shaped  box =  (scale factor)^3  * (volume of candle)

2500 = (5/3)^3  * volume of the candle

2500 = (125/27)^3  *  volume of candle

2500 *  (27/125)  = volume of candle

540  (cm^3)    =  volume of candle

The area of the rectangle  = 4 * 2 =  8      (1)

And the area of triangle ABD is 1/2 of this =  4     (2)

O is the  center of the  rectangle =  (2,1)

The  slope of the line containing DB  = 2/4 = 1/2

So....the slope of the line containing QP   =   -2

And this line passes through  O,   so the equation of this line  is

y =   -2 ( x -2) + 1

y  = -2x  +  4 + 1

y= -2x + 5

We can find the x coordinate of Q  by  letting y = 0  

0  = -2x + 5

-5 = -2x

x = -5/-2 =  2.5

So the area   of triangle  DOQ =  (1/2) DQ * height =  (1/2) (2.5) (1) = 1.25  (3)

So....the area of the yellow region =   (1)  -(2) - (3)  = 

8  - 4  -  1.25   =

8  - 5.25  =

2.75  

1^2 - 5             -4

_____   =      _____ =    -1

1 +  3               4

-2 ( x + h)^2   - 5(x + h)  + 5  =

-2 (x^2 + 2xh + h^2)  - 5x - 5h  +  5  =

-2x^2 - 4xh -2h^2  - 5x  - 5h  +  5 

x*2   -  8x

The domain is all real numbers  

This is a parabola that turns upward

The  x coordinate of the  vertex =   8/ (2*1)   8/2  = 4

And the y coordinateof the vertex  is   4^2 - 8(4)  =  16 -32 =  -16

So...the range is [-16,  infinity )

From the circle I am getting 

16 = a² - b²

and from the hyperbola I am getting

36 = a² + b²

solving these 2 equations gets

20 = 2b²

b = \(\sqrt{10}\)

a = \(\sqrt{26}\)

however when I try to graph it, it looks nothing like your graph

https://www.desmos.com/calculator/qeszzqvt5h

ok. thx

I would like to see someone answer this too.   

Thank you!

[CBOQ] = 2.75 square units

Thank you, Melody!

Circumference = 2piR

Circumference=30pi

660pi/30pi=22 rotations

gcf(12,8)=4

The largest side possible is 4 feet.

The x^2 doesn't matter (or x for that matter) since it is 1

So we have -2+3i-7-2i+37-13i

Simplifying we get 28-12i

Thank you Chris! I expected it to be something with permutations! Much thanks to the reply above, MooMooooMooM! I have to go for the night, have a great day/night/morning/noon/evening wherever you are!

This is equivalent to the  number  of  distinguishable  "words" we can make from  BBBKKAA   =

                    (Number  of Letters ) !

____________________________________________=

(Number of Bs)! * ( Number of Ks)! * (Number of As)!

                                 7!

                _________________  =

                   3!   *   2!    *   2!

                          5040

                      ________  =           210  identifiable orders

                           24

2/8 is less than 4/8

2/8<4/8

There are 7! ways to order 7 objects but there are repeats

Divide 7! by 3! because there are 3  bananas and you can order 3 items 3! ways

Do the same with the other two fruits

Let O  be the center of the  circle

Angles OQP  and ORP both =  90°

Then  in quadrilateral PQOR.....angle  QOR is supplemental to angle QPR  =140°

So   the smaller angle inscribed angle QSR    =    (360 -140)/2 =  220/2   = 110° 

And  the larger angle QSR = 360 - 110  =   250°

And  in quadrilateral  PQSR  the  sum of angles  PQS + PRS =   360  - 40 -250  =   

360  -  290  =

70°

Just  find the  common denominator of  6  and  8

6 = 2 * 3

8  = 2^3

Taking   the  product of each unque  number with its greatest exponent  =

3 * 2^3   = 

3 * 8   =  

24

See the pic here :

Let A  =  (0,0)     D =  (0,46)

B=  (13 cos (-30)  , 13sin (-30)  )  =   (13sqrt (3)/2 , -13/2)  =  ( 6.5 sqrt (3)  , -6.5)

The  slope beteen  A and  B  =   (-6.5)/(6.5 sqrt (3) )  =   -1/sqrt (3)

A perpendicular line   to this  segment trhrough B  has the equation

y= sqrt (3)  ( x -  6.5 sqrt (3) )  - 6.5

y = sqrt (3) x  - 26

The x coordinate of the  intersection  of  this  line with the line y=  46   can be found as

sqrt (3)x  -26 =  46

sqrt (3)x  =  72

x =  72/sqrt (3)   =   24sqrt (3)  =  sqrt (1728)

C = ( 24sqrt (3) , 46 )

So......AC =    sqrt  [  (sqrt (1728))^2  + 46^2  ]   =   sqrt [1728 + 2116 ] = sqrt  (3844)   =   62  

24   would be 4 paks of cars and 3 paks of gliders .

It will be of the form   ...xxxxxxxxxxxx7,xxx.