CPhill

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1.00 /  120  =   x  / 2370          cross-multiply

2370  = 120 x              divide both sides by 120

19.75 = x  =  US dollars  and cents

Yeah....I see I can get something larger

9.7  + 8.6    =  18.3   maybe  ???

3. If a,b ,c ,d and  are four different digits from 1 to 9 , inclusive, then what's the largest possible value for the decimal a.bc + 0.d?

Less sure about this one...I get

    9.86

 + 0.7

_______

  10.56

1. If a,b ,c ,d and  are four different digits from 1 to 9 , inclusive, then what's the largest possible value for the decimal a.b + c.d?

9.8   +  7.6    =  17.4

2. If a,b ,c ,d and  are four different digits from 1 to 9 , inclusive, then what's the largest possible value for the decimal a.b - c.d?

9.8  - 1.2  =  8.6

-0.123      -0.0123      0.112233       0.1223     0.123     0.125      0.13

   0.125

-  0.0123

________

   0.1127

The   amplitude  = 8

Here is a possible function :   https://www.desmos.com/calculator/2cbend58si

We can divide  the figure into two triangles

Each have a base of 13

One has a height of 6  and the other has a height of  8

The area is    (1/2) (13)  ( 6 + 8)  =  7 * 13  =  91 units^2

We  have  an ellipse

The  focal points are (-1,0)  and (1,0)

Using symmetry, the center is (0, 0)

c  = the distance from the  center to either foci  =   1

The  sum of the distances from any point on the ellipse to the focal points = 2a

So

2a  = 6

a  =  3   ⇒   a^2  =  9

b^2  =  a^2  - c^2  =   9  - 1  =  8

The equation is

x^2/a^2   + y^2/b^2  = 1       .....so.....

x^2 / 9   +   y^2 / 8   =   1

We  have  that

8 / 4  = (x + 3)  / ( x  - 4)     

2  =  ( x + 3)  / ( x - 4)

2 ( x - 4)  =  x + 3

2x   - 8  = x  +  3

2x  -  x   =   8 + 3

x  = 11