All Answers 358147 Answers

Let the first be  x  and the second be   192 /x

And we wish to maximize

x+  (3 )  ( 192/x)

x +  576x^(-1)         take the derivative and set to 0

1  - 576x^-2   = 0

1   576 / x^2

x^2  =576

x  = 24   or x   =  -24

The second derivative is    2*576/ x^3         this will  be negative when x   = -24   so  this is a (relative)  max

So   the  numbers  are   -24   and   192/-24  =   -8

A line  perpendicular to  the  given one has a slope of  -1/2

And the equation of this line through (6,2)  is

y= (-1/2) ( x - 6) + 2

y =(-1/2) x + 3 + 2

y =(-1/2) x + 5

To find the  x coordinate of the   intersection of these lines  :

2x + 5  = (-1/2x)  + 5

x  = 0  

y=  5

And  this is the  midpoint   of (6,2)  and its reflected point

To get from   (6,2)  to (0,5)   we  had to go  to the left 6  and up 3

Applying the same movement  from  (0,5)   we get the reflected point B  =  (  -6, 8)

i think there are more to write...

total nos=24.

but, some glitches in my code. can anyone spot it?

12121

12123

12321

12323

12343

12345

32121

32123

32321

32323

32343

32345

34321

34323

34343

34345

34543

34545

*34565

*34567

54321

54323

54343

54345

54543

54545

26

python code#

total=0
f=[0]*5
for i in range(12121,54546):
  temp=i
  for j in range(5):
    f[j]=temp//(10**(4-j))
    temp%=(10**(4-j))
  #print(f[0])
  if f[0] in range(1,6,2):
    flag=0
    for k in range(1,5):
      
      if f[k]>0 and abs(f[k]-f[k-1])==1:
        flag+=1
    if(flag==4):
      print(f[0]*10000+ f[1]*1000+ f[2]*100+ f[3]*10+ f[4])
      total+=1
    flag=0  
print(total) 

f  must  be degree 5  .......multiplying it by (2x + 3)  gives a polynomial of the 6th degree

And  since the  highest  degree of g is 5,  then adding  g  to    (2x + 3)f(x)     produces a 6th degree polynomial

Very nice, textot !!!!

3mn   - 6m +  7n +  -  14

3m (n - 2)  + 7 ( n - 2)   =

(n - 2) (3m + 7)

Here's what I get......

1   2    1    2      1

1   2    1    2      3

1   2    3    2      1

1   2    3    2      3

1   2    3    4      3

1   2    3    4      5

3   2    1    2      1

3   2    1    2      3

3   2    3    2      1

3   2    3    2      3

3   4    3    4      3

3   4    5    4      5

5   4    3    2      1

5   4    3    2      3

5   4    3    4      3

5   4    3    4      5

5   4    5    4      3

5   4    5    4      5

Did I miss any  ???

C (-62, 22)

See my answer here :   https://web2.0calc.com/questions/word-problem_91#r1

Well the rectangles appear  to be squares.....

Let their side length = 1

So     the top left shading is a triangle with a base of  6 and a height of 1

So its area  =(1/2) (6)(1)   = 3

The bottom right shading  has as base of 3  and a height of 1....so its area=  (1/2)(3)(1)  =3/2

And  the two  shaded square   each have an area  of 1  so their  combined   area   = 2

And the total area = the area of 12  squares with a side  of 1  =12

So

shaded area to  total area =    ( 3 + 3/2 + 2)  /12  =   ( 6.5)  /12   =  13/24

Let me check

Base = 18    height  =  3

Correct,  geoNewbie   !!!!

Note  that if AE : EB  = 1:1, then   EB  = 1/2

And if BF : BC  = 1 :2   , then  BF  = 1/3

So the area of right triangle   EBF  =(1/2) (1/2)(1/3)  =   1/12

Similarly  FC  =2/3

And if GC : GD  =1:3    then GC  = 1/4

So the area of right triangle FGC   = (1/2)(2/3)(1/4)  =  1/12

And GD = 3/4

And if HD : HA  =1 : 4   then   HD =  1/5

So the area of right trinagle  HDG  =(1/2) (3/4)(1/5)  = 3/40

And finally    HA =4/5    and AE =1/2

So the area of  right triangle HAE  =(1/2) (1/2) (4/5)  =  1/5

So....the blue area is    area of the square  - 1/12  -1/12  -  3/40  - 1/5  =

1  - 1/12 -1/12  - 3/40 - 1/5    =   67/120

So then if I have y=4x-6, y=-2x+12 and y-axis can I calculate the area to be

1/2*b*h where b = 18, h = 3 from the graph so area = 27?

Am I approaching this the right way?

Let X, Y, and Z be points such that  XZ/XY = ZY/XY = 2.   If Y = (1,7), Z = (-1,7), then what is the sum of the coordinates of X?

There are 2 answers:

X(0.75, 6.031754163)           0.75 + 6.031754163 = 6.781754163 ≈ 6 ²⁵/₃₂

or

X(0.75, 7.968245836)           0.75 + 7.968245836 = 8.718245836 ≈ 8 ²³/₃₂

181440

The First digit is 5 as said.

Each digit after that has to be different.

There are 10 digits, so we multiply 1 less each time we move to the right.

The second digit has 9 possibilities - any digit other than 5.

The third has 8 - Any except 5 and the first digit.

And so on.

So 1*9*8*7*6*5*4*3=181440

OHHHH! 

Thank you so much!!! 

Note  that   x is in thousands  of  dollars

So  the  investment is  increasing  at    2.3 (1000)  =   $2300 per month

A graph works best  :   https://www.desmos.com/calculator/efn1vtgwgr

Note  that  this region forms  a triangle with a base of  16 - - 4 =   20

And  the intersection of these lines is (4, 4)   so   the height  of the triangle formed=  4

So  the area = (1/2)  base * height   =  (1/2) 20 *  4 =    40 units^2

Let  the final score   = x......but it  counts as  two tests, so  the  number of  points added to the t other scores will   =  2x

Number of total ponts  / number of tests  >   77        so

(72 + 67  + 82 + 79 + 2x  )   /  6   >   77        multiply  both sides by  6

72 + 67 + 82  + 79 + 2x  >  462

300 +  2x > 462

2x  >  462  -300

2x >   162      divide by 2

x  >  81         he must  make  more than an 81  on the final

The inequality  is     81  <  x  ≤ 100        (assuming that the greatest score possible is 100 )

Graph of the  inequality  :  https://www.desmos.com/calculator/arznhdoq86

So sorry, for some reason it didn't upload. I hopefully just fixed it. :D

What's the problem  ???

Connect BO  and  note  that BO = AO = CO   since they are all radii

Then   in triangle  ABO,  AO  = BO    so  angle BAO  = angle   OBA  = 30

Similarly, in triangle CBO ,  CO  = BO   so  angle  BCO  = angle  OBC  = 40

And angle ABC  =angle OBA  + angle OBC = 30 + 40  = 70

But  angle  ABC  is an inscribed  angle interceptin the same arc as central angle AOC

So     AOC  = 2 * ABC =  2 * 70    =   140°

Witness Protection Program   ????

THANK YOU SOOOOOOOOOOOOOOOOOOOOO MUCH