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1) Compute 

 

2) One day, I decide to run to the park. On the way there, I run at a rate of  miles per hour for  hours. On the way back, I take the same path and jog at a slower rate of  miles per hour so that it takes me  hours to get home. Given that , what is ? Express your answer as a common fraction.

 

3) 

 

4) 

Find a non-zero value for such that  ax^2+8x+4=0 has only one solution.

 

Thanks!🙏🏼

 Jul 10, 2018
 #1
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0

Is your 2nd question missing some numbers?

 Jul 10, 2018
 #2
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+1

3)

 

Simplify the following:
2 + i - 4 - i + 2 + 4 i

Group like terms in 2 + i - 4 - i + 2 + 4 i.
2 + i - 4 - i + 2 + 4 i = (2 - 4 + 2) + (i - i + 4 i):
(2 - 4 + 2) + (i - i + 4 i)

Evaluate 2 - 4 + 2.
2 - 4 + 2 = 0:
i - i + 4 i

Add like terms in i - i + 4 i.
i - i + 4 i = 4 i:
4 i

 

1) Just evaluate by any calculator:

(2011^2 - 2006^2) / (2010^2 - 2007^2)

=5 / 3

 Jul 10, 2018
edited by Guest  Jul 10, 2018
 #5
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0

Hey, I think you made a little mistake at the begining...

I think the equation should be (2+i)-(-4)+(-i)+(2+4i)...

Guest Jul 11, 2018
 #3
avatar+98197 
+1

Here's  (1)   without a calculator....note that the numerator and  denomonator  are  both just the difference of squares...so we have :

 

(2011 + 2006) ( 2011  - 2006)       

_______________________    =

(2010 + 2007) ( 2010 - 2007)

 

 

 

(4017) (5)

_________  =

(4017) (3)

 

 

 5

__

 3

 

cool cool cool

 Jul 10, 2018
 #4
avatar+98197 
+1

Here's  4

 

ax^2   + 8x  +  4   = 0 

 

If this has only one solution.....then it will be true  that the  discriminant given by  (8)^2  - 4 (a) (4)  will = 0

 

So we have

 

(8)^2  - 4 (a) (4)   =  0   simplify

 

64  - 16a    = 0      add   16a  to both sides

 

64   = 16a        divide both sides by 16

 

4  =  a 

 

 

cool cool cool

 Jul 10, 2018

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