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Also, 99% of all greek stories have a moral, and if you are into this, there are many Greek mythology podcasts on Spotify. Some are PG13 bc back then tales were a bit vulgar

OMG I love Greek myths and would love to suggest u some

here's my top 3

ICARUS

PANDORAS BOX

PENELOPE AND HADES

Also Hercules but that's too stereotypical

Thanks,

-DBZ

We want to solve this

11200 = 5600e^(.059t)      divide both sides by 5600

11200/5600 = e^(.059t)

2 = e^(.059 t)     take the natural log of both sides

Ln 2 = Ln e^(.059 t)      and we can write

Ln 2 = (.059 t) * Ln e            Ln e = 1 so we can ignore this

Ln 2 =  .059 t           divide both sides by .059

Ln 2 /  .059 = t ≈  11.74 years  =  12 years

This is really straighforward.....  

15 < 4+x     now   subtract 4 from both sides

15-4   <  4-4 + x

11 < x  

x> 11

Look at this carefully, PF

When x = 1    f(x) = g(x).....so the graphs intersect at (1, 3)

So...x = 1 is a solution

Now....at  which other x value  is f(x) =  g(x)???

I see the number 3! Is that the only one?

-4x + 2 > 26      subtract 2 from both sides

-4x > 24         divide both sides by -4 and reverse the inequality sign (since we divide by a negative)

x < -6

You left an "x" out of the original equation

Last one

AA Similarity Postulate

Polygon Similarity Postulate

Addition Property of Equality

ax-b = c, for x

Add b to both sides

x = b + c         

Divide both sides by a

x = ( b + c) /   a

a=h(a+b)/2, for h

Multiply both sides by 2

2a = h (a + b)       

Divide both sides by (a + b)

2a / ( a + b)  = h

First one

P(x) = x^2 ( x - 1)^2(x - 5/2)^2   =

x^2 ( x^2 - 2x + 1) ( x - 5/2)^2  =

(x^4 - 2x^3 + x^2)  (x^2 - 5x + 25/4)  =

x^6 - 7 x^5 + (69 x^4)/4 - (35 x^3)/2 + (25 x^2)/4

First graph....

Odd is correct....the x axis is "cut" 5 times

The sign of the leading coefficient is negative because it is UP on the left and DOWN on the right

Second graph....Even is correct....tthe x axis is cut 6 times

The lead coefficient is positive because it is UP  on both sides of the y axis

ok thank you so much for helping!

I don't know the answer to that YEEEEEET.....I suppose it depends upon what we are given

We can always set the r's equal......but.....the resulting equation may (or may not) be easy to solve algebraically

Let  n = x

Look at the graphs of      1/x^3    and 1/x^5     here : https://www.desmos.com/calculator/h6g3vll7f0

Note that they intersect at x = -1  and x = 1

But....they do NOT intersect at x = 0

So....x = n =  0       is not a solution

ah ok thank you 

one more question: does this method apply to all polar graphs such as when you have to solve tan and sin or is there a different method to do so

Notice that -pi/3  =  -60°   =   360 - 60 =    300°  =    5pi / 3

lim               sin 5x

x →0           _____   

                    sin 8x

Note that we can write

lim               sin (5x)

x → 0        _________   

                        x

            _______________              and we   can  also write

                   sin (8x)

                  ______

                       x 

lim               5sin (5x)

x →0           _______

                      5x

              _____________

                  8sin (8x)

                  ________

                    8x

Note that  using a limit property   .....if we let 5x , 8x =  θ  

lim                 sin  θ

 θ →0          _______  =   1

                         θ

So we have

5(1)           5 

___   =     ___  

8(1)           8

can you please explain how you find out -pi/3 = 5pi/3