CPhill

As can be seen here : https://www.desmos.com/calculator/yhtjmyvehq

This function has no local max or min

The volume of each of the candies is given by

(1/3) *base area * (height)    = (1/3) (12^2)(15) = 720mm^3

So .....100 of them have a volume of  72000 mm^2

So.....we want to solve this

72000 = pi (75)^2 * height              ......divide both sides by pi(75)^2

72000 / [ pi * (75)^2 ]  =  height ≈  4.07 mm

-3x > 12       divide both sides by -3 and reverse the inequality sign

x < -4

Thanks, heureka  !!!

Refresh my memory.....

How is   f_xy    calculated   ???

This is just the difference between the area of the wall and the area of the headboard =

7*9   -      6 *5 

63    -     30     =

33 sq ft 

6 8 1 9 4

First find the mean =    [ 6 + 8 + 1 + 9 + 4 ] / 5   =  28 / 5

Take the sum of the squared differences from each data value and the mean  and take the average of these

So we have

 [(6 - 28/5)^2 + ( 8 - 28/5)^2 + (1 - 28/5)^2 + (9 - 28/5)^2 + (4 - 28/5)^2 ]  / 5  =

206 /25   =

8.24 = the variance

\(x\le y\le z\)

\( sqrt{x} + sqrt{y} + sqrt{z} = 10\)

\(x + y + z = 38\)

\(sqrt{xyz} = 30\)

Let sqrt x  = a, sqrt y = b  and sqrt z = c...so we have

a + b + c  = 10      

a^2 + b^2 + c^2 = 38

abc = 30  ⇒ c =  30 / [ ab]    

c is an integer > a, b    

By inspection,  the system  will be true  when a = 2 and b = 3

And c = 30 / [2 * 3 ]  =  5

So

The solutions  are  (a, b, c)    = ( 2, 3 , 5)

So

(x , y , z)   =  (a^2, b^2,c^2) =    (4, 9, 25)

Taking the Guest's answer from here :

3x^2 - 10x + 3 = 0

We can use a factoring "trick" to solve this.....write  - 10x  as  -9x - x

3x^2 - 9x - x + 3  = 0     factorby grouping

3x ( x - 3) - 1(x - 3)  = 0

(x - 3) ( 3x - 1) = 0

Setting both factor to 0 and solving for x produces

x = 3  or  x  = 1/3

Thanks, Melody

Here's an algebraic solution

We have  the form

(x - h)^2           (y - k)^2

_______    -    ________     =   1

   a^2                  b^2

The center    is (h, k)       =   ( 3, 17)

Since "x" comes first in this form.....the foci will lie on the horizontal axis

The focal point with the larger x coordinate is given by

(  3  + √ [ a^2 + b^2 ] , 17 )     = ( 3 + √ [5^2 + 12^2], 17 ) =  ( 3 + 13, 17) =

(16, 17 )

Well here's a possibility

2x + y  - z    =  5

5x - 3y + 4z = 7

-6x -7y + 2z = -19