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See my answer, here :

https://web2.0calc.com/questions/help_93576

You obviously don't want 'help' ....you want someone to spoonfeed you the answers.....don't play on cphill's willingness to help !!!

OK...didn't realize that  .....we don't want to encourage  cheating....

CPHill help

You know you are cheating and that is not fine!

 Express your answer as a decimal rounded to the nearest tenth.

Although i dont understand why, if you guys have an agreement not to solve aops questions that is fine

Chris, this is an art of problem solving questions, we have a loose agreement not to answer these.

  36    =  -16t^2 + 80 t

-16t^2 +80t -36 = 0        use quadratic formula to find values of  t

a = -16    b = 80   c = -36

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)                         the smaller 't' value will be the FIRST time it is at 36 ft 

                                                               the other 't' value will be when it is on the way down

OK.....

Prime factor the integer  under  the radical

Call  the  index of the radical, n

If  n  does not evenly divide  every  exponent in the prime factorization, then  we have an irrational result

Two examples

²√ 16  =   ²√2^4      2 divides 4 evenly,,,so we have a rational answer  because   √16  = 4

³√ 32  =  ³√ 2^5      since 3 does not evenly divide 5, we have an irrational answer  =  2³√2^2  = 2³√4

Thanks!

Multiplying  the original equation through by  12  we get

3x  + y =  12      rearrange as

y  =  -3x  + 12

m = -3     b  =12

x intercept....set y=  0

0 = -3x + 12

-12 = -3x

-12/-3 = 4   = x intercept  = a

a + b + m  = 

4  + 12   -  3   =

13

From the center of the  circle (call it O )  connect    OB

Then  OB  = OA  = 18

So angle BAO  =angle ABO   = 42°

Then angle AOB =  180  - 2(42)  = 180 - 84 =  96°  

Using the Law of Cosines

AB^2 = (OA)^2  + (OB)^2   -2 (OA * OB) cos (AOB)

AB^2  =  (18)^2  + (18)^2  - 2(18*18) cos (96)

AB  = sqrt [  (18)^2  + (18)^2  - 2(18*18) cos (96) ]

AB = sqrt (715.7)  ≈   26.75

Is there a way to solve this without using a calculator? I know that with the Law of Cosines I have to do the arccos to get the angle, but that requires a calculator (at least for arccos(4/5)) and I want to try and solve it without using one.

3^2 + 4^2   = x^2

9  +  16  = x^2

25   =  x^2       take the positive root

5  = x

Note  that rhe line rises from right to left  and  y changes  by  2  when x changes by -1

So.... (9,0)  will  be a lattice point   and (0,18) will be a lattice point

So....the number of lattice points =    [ 9 - 0 ] + 1  =   10 lattice points

Here's a graph : https://www.desmos.com/calculator/drzzupjy3g

unlikely

improbable  

I knew that I was being hilarious just kidding online.