CPhill

I learned another little "trick' to remember them...

Sin  = Oh Heck !!

Cos = Another Hour

Tan = Of Algebra !!

192 = -16 t^2 + 48t + 160

Let's move everything over to the left side......we get

16t^2 - 48t + 32 = 0     Factoring out the "16," we have

16 (t^2 - 3t + 2) = 0     Dividing by 16 on both sides

(t^2 - 3t + 2) = 0          Factoring, we get

(t -2) (t -1) = 0              And setting each factor to 0, we have

t = 2  and t = 1

Let me see how much of this I remember.......!!

The first one is  A ∩ (B U C), which, by Distributive Laws can be writtten as:

(A ∩ B) U (A ∩ C) =

({a, b, d} ∩ {b, d, e, f }) U { } =

{b, d } U { } =

{b, d}    {By, defnition, the empty set is a subset of every set}

The second one is (B’ ∩ C)’ - A  ...   which, by using De Morgan's Laws  can be written as

(B U C') - A =

({b, d, e, f} U {a, b, d, e })  - {a, b, d } =

({a, b, d, e, f} - {a, b, d}) = {e, f }

I believe that's it........but if someone else can check my answer , it would be great !!

OK

So

27 =

9 * 3 =

3 * 3 * 3 =

3³

And that's it ......

Hope that helps

8x-3y=1

-2x-3y=11

OK...let's just subtract the second equation from the first.

We have

10x = -10

 So, x = -1     and to find y, we can substitute the "-1" for x in either of the two equations.

Using the first one, we have

8(-1)  - 3y   = 1

-8 -3y = 1

-3y = 9

y = -3

So, the solution is (-1,-3)

You should check that this is correct by substituting these values into the second equation.

So we have

10 = y(5)^2

10 = y(25)

0 = 25y - 10

0 = 5(y -2)

OK...we have this

A_n = A₀ (1 + r/n) ^nt

Where

A_n = the amount accumulated at the end of the period

A₀ = the amount invested ($10000)

r= the interest rate (8.5% = .085)

n = the number of compoundings per year (12)

t = the time in years (8)

So we have

A_n = 10000(1  + .085/12)^(12*8)  = 

$${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.085}}}{{\mathtt{12}}}}\right)}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{8}}\right)} = {\mathtt{19\,691.519\: \!725\: \!320\: \!224\: \!411\: \!3}}$$

≈ $19,691.52

Just about any technical field you can name probably uses trig. That's not to say that YOU might ever need them in "real life," but....you never know !!! The job market is becoming more sophisticated all the time..........

You'd better behave, Melody.......Don't forget, that I now possess the "Power" .... and I'm not afraid to use it !!!!!

Sorry, heureka.......we were posting at the same time.......but we both arrived at  ≈ the same place !!

Thumbs Up from me.......and a green check mark !!