Math Is Fun Forum

you have two choices ,
1. factor it as  x^2+x-6=(x+3)(x-2) , then it would be x+3 =5
2. apply L'hosp...(spelling XD) rule, take derivative 2x+1=5

Here's my work

I'll do the first one

If A+B< 10 , the solutions is A+B=C  (1,2,3) (1,3,4), so on..............
If A+B>or = 10 ,  AAA+BBB would be 4 digits, so it wont work

Can I prove it like this
Consider, a, b two vectors

|a+b| is the length of the 3rd side of triangle consisted of a and b

|a| ,|b| are length of side a and side b

sum of two sides always larger than the other one
and when the two vectors are parallel they equal

For the second one,

actually, if you know that DB+AD=350 , you could change it to  AD=x/tan32 , DB=x/tan54
AD+DB = x( 1/tan32+1/tan54)=350 , your work looks fine, I think there might be some minor error

The vol of nitric acid at the beginning is 200x0.5%=1
The rate of flow in nitric acid is constant 6x20%=6/5
The escaping rate of nitric acid should be  v=8x(temp density of nitric acid) = 8x (amount of acid)/(total volume)

The speed of the change of volume of Nitric acid
Total volume = 200-2t 

To question 2:

Density = V/(total volume)

How do I put  Double integration over a region D, the code \iint doesn't seem to work?

6. was he born in Asia (from middle east to Japan)?

It was my mistke， N,O take the value of 6,4 , I put it wrong, , just a minor mistake