All Answers 355923 Answers

Prodigy? Isn't that a math game? Wheres the problem btw. 

CPhill, where did 1/4 come from?!

It's 1/6 NOT 1/4

(¹/₆) / 4 = ¹/₂₄

Sam needs to read ¹/₂₄ of the book each day. 

I should open an account so I could return the favor of a down vote.  What is your answer, genius?  

30 cookies @ 50¢/cookie is 15 dollars. 

Since the selling price is the same either way, of course I'd rather my expense be 6 dollars instead of 8.  

Any integer that ends with a 6 raised to any power results in an integer that ends with a 6. 

So 196²¹³ ends with a 6.  

There's that, but the 3 is a little harder.  

Notice the last digit of the results of 3 raised to various powers.  

When "n" is:                0   1   2   3    4   5   6   7    8   9   10   11    12   13   14   15  

The last digit of 3ⁿ is:  1   3   9   7    1   3   9   7    1   3     9    7      1     3     9     7  

That's enough to show that every fourth group keeps repeating 1 3 9 7   

So divide 196 by 4 and you get 49 complete groups with no remainder. 

That means that 213¹⁹⁶ ends with a 7.  

6 times 7 is 42 so ............ the last digit of 196²¹³ times 213¹⁹⁶ is a 2.   

If this is incorrect, then my mistake was starting the table with n = 0. 

If the correct way was to start the table with n = 1, then the fourth digit in the repeating group would be 1. 

A. find Ao and by

And can you help me I really need help here

Fuckudez2fly

$2 \cdot 8 - \frac{8}{4} = 16 - 2 = \boxed{14}$

$b_p + b_g = 54$

$b_p = 5 b_g$

$6 b_g = 54$

$b_g = 9$

$b_p = 5 \cdot b_g = 5 \cdot 9 =45$

$45 - 26 = \boxed{19}$

cos 2x   =   2cos^2x  -  1

So

2cos^2x  - 1   +  4cos x  + 1   =   0

2cos^2 x  +  4cos x   =   0

cos^2x  +  2cos x   =   0

cos x  (  cos x + 2)   =  0

Setting each  factor  to  0  and solving for  x

cos x  =  0                                                                   cos x  +  2   =   0      

x = pi/2  + k *pi     where  k is  an integer                    cos x =  -2        no  solution for  x

$\frac{40}{25} \cdot 225 = 40 \cdot 9 = \boxed{360}$

Thank you sir, I appreciate very much a compliment from the top participannt.

$x = \pi k  - \frac{\pi}{2}, k \in \mathbb{Z}$

Let  the  point  be (x , 0)

We  can  solve this  equating the squares of  the distance formula

( x - - 2)^2  +  (0-0)^2     =  (0 -x)^2  + (4 - 0)^2       

(x + 2)^2    =  x^2  +  16   

x^2  + 4x  + 4   =   x^2   +  16

4x  +  4  =  16

4x  =  16 - 4

4x  =  12

x  =  3

By Vieta's, we have $r_1 + r_2 = - \frac{8}{1} = -8$ and $r_1 r_2 = \frac{4}{1} = 4.$

We also have $r_1 + r_2 = - \frac{16}{A}$ and $r_1 r_2 = \frac{B}{A}.$

Thus, we have $- \frac{16}{A} = - \frac{8}{1} \Rightarrow \frac{2}{A} = 1 \Rightarrow A = 2.$

We also have $4 = \frac{B}{A} \Rightarrow 4 = \frac{B}{2} \Rightarrow B = 8.$

$2+8 = \boxed{10}.$

I could've noted the fact that $a_{n-1} = \frac{b_{n-1}}{2},$ but visualizations are somewhat unreliable. 

This doesn't make sense. How can an x-intercept have a $y \neq 0$?

x/2  +  y/2   =   7/5

x/2 -   y/2    =  7/12               subtract  the  second equation  from the  first

y  =  7/5  -  7/12    =   [84 - 35 ]  60  =  49/60

And  using either equation

x/2  +  (49/60)/2   =  7/5              multiply through  by  2

x  + 49/60   =  14/5

x  =  14/5  -  49/60

x = 168 / 60  -  49/60   =   119 / 60

In latex, it is \div for $\div$, but in normal text, on a mac, you can do option/alt and hold and press / for ÷.