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CPhill's answer is equal to  11.59....

Try this, ACG.....

√6(3 + √3)  ≈  11.6 cm  

(4√-18)(2√-32)  =

4i√18  * 2i√32  =

4*3i√2 *  2*4i√2  =

12i√2 * 8i√2 =

96 * i^2 * 2  =

-192

Actually, is this the only answer? It's showing up wrong...

You guys (and gals) are the best!  Thanks!

The side opposite the 30°  is (1/2) of the hypotenuse  = √6 cm

The side opposite the 60° angle is  √3 times the side opposite the 30° angle  = √3 * √6

So...the perimeter is

√6 ( 1 + √3 + 2 )  =

√6 ( 3 + √3 )  cm

Thank You!!

I know a few

First one

The elevator is on the ground floor at  A  

The max upward velocity occurs at   B

Second one

C - 5 seconds

D - acceleration.....change in velocity / change in time  =

[ 18 m/s - 0 m/s ]  / 5sec =    (18/5)m/s^2 =  (3.6)m/s^2

E - Don't know this one

 F -  5 seconds

G -  acceleration  -  

[ 0 m/s - 18m/s ] / [14s - 18s ]  =  

-18m/s / [ -4sec] =  (-18/4)m/s^2  = -4.5m/s^2

H - don't know this one

I - don't know

sqrt (-49) + sqrt (-64)=

sqrt(49 x (-1))  + sqrt( 64 x (-1)

= 7 x sqrt(-1)  + 8 sqrt(-1)              (remember:  sqrt(-1)  is  i  )

= 7i + 8i

= 15 i

Thank you so much!

 x - 2               10x

_____    +    _______

x + 3              x^2  - 9

x - 2                  10x

____    +      _________

x + 3            (x + 3) (x - 3)

(x - 2) (x - 3)                10x

___________   +     ____________

(x + 3) ( x - 3)           (x + 3) ( x - 3)

[ x^2 - 5x + 6 + 10x ]

_________________

(x + 3) ( x - 3)

[ x^2 + 5x + 6 ]

_____________

{ x + 3] [ x - 3]

[ x + 2] [ x + 3]

____________

[x - 3] [ x + 3]

x + 2

____                 restriction :   x not equal to  -3 or 3

x  - 3

Angle C  = 60°

And the side opposite this  is  √3  times as long as the side opposite the 30° angle

So AB  =  6√3

So......the area is

(1/2) height * base

(1/2) AC * AB  =

(1/2) * 6 * 6√3  =

18√3  units^2

Can't see this question  ... requires login.   Are you in Little Rock, AR?

One way for triangles to be similar is that we need that the ratios of the corresponding sides to be =

That is

short side of first triangle

_____________________        =  A

short side of second triangle

Intermediate side of first triangle

__________________________        =  B

Intermediate side of second triangle

Long side of first triangle

_______________________     =   C

Long side of second triangle 

So  A = B  = C   for the triangles to be similar

So.....For 16 to be similar...we need that

23/40  = 34/55  = 36/60

23/40 = 34/55 = 3/5

None of these ratios are equal...so....not similar

For 17  to be similar....we need the sides around the equal angle need to be equal ratios

But

16/22   =  25/33  ???

8/11 = 25/33     these are not equal

For the same reason....the triangles in 19 aren't similar, either

In other words  14/9  not equal to 7/4

And the triangles in 20 are not similar because  we can't establish any AA similarity

Thank you! Sorry usually web2.0 gives me a (+1) notification when a problem has a response but for some reason I didn't get one this time I don't know why!

Thank You

√-1   is defined as  i

And  i^2  =  -1

So....we have

(i)^15  =

(i^2)^7  * i  =

(-1)^7  * i  =

-1 * i  =

-i

x^3 - x^2 + x - 1  factors as

x^2 (x -1) + 1(x - 1)  =

(x - 1)(x^2 + 1)

x^2  - 1   factors as

(x + 1) ( x - 1)

Taking all the different factors we have

(x - 1)  (x + 1) (x^2 + 1)   ⇒  second answer

  7                     7

____    +       ______

a + 8              a^2  - 64

  7                       7

_____   +     __________

 a + 8           (a + 8) (a - 8)

    7(a - 8)                         7

__________     +         _________

(a + 8) (a - 8)              (a + 8) (a - 8)

[ 7a - 56  + 7 ]

____________

(a + 8) (a - 8)

[ 7a - 49 ]

___________

(a + 8) (a - 8)

Do you EVEN go back and look at your other postings????

https://web2.0calc.com/questions/quick-responses-would-be-greatly-appreciated

Oops sorry....didn't answer #1

vf = vo + at

0 = 55.6 m/s + a(1.8)

a = - 30.9 m/s^2

He had much more time to deccelerate through the trees (18 times more) so the DEcceleration is 1/18 of the decceleration of just hitting the ground and stopping in 0.1 s

His acceleration (up to reaching terminal velocity) is just the acceleration of gravity=

9.8 m/s^2

2. Terminal velocity =   55.6 m/s     then he goes to ZERO m/s in 0.1 sec  (ouch!)

      vf = vo + at       vf = vfinal = 0 (he stopped)    vo = original velocity of 55.6 m/s

       0 = 55.6 + a(0.1)

        a = - 556 m/s^2     (this will crush you like a bug under a steamroller)

Thanks, EP  !!!

This was answered just a couple of days ago...scroll through and look for it

-8   was the answer  

15...if these are similar....we must have that

13/15  =  30/35

13/15  = 6/7      not true....so these are not similar

16.....if these were similar.....we must have that

40/60  = 23/34

2/3  =  23/34  ....not true.....so.....not similar

17  For these to be similar...we must have that

16/22  = 25 /33

8/11  = 26/33      .....not true....not similar

18 EFG  similar to EBC

Angle E  = Angle E  and

EF / EG  = EB/EC

50/60  = 20/24

5/6  = 5/6

19 Not similar

20 Not similar