All Answers 358516 Answers

z³ =   1 / 343        take the cube root of both sides

z = 1/ 7

The horizontal distance =  sqrt ( d²  - 8800² )

(8x⁸)(6x⁹)  =

(8 * 6) ( x⁸ * x⁹)   =

48 x¹⁷

Solve for x:
sin(5 x) = sin(3 x)

Take the inverse sine of both sides:
5 x = pi-3 x+2 pi n_1  for  n_1  element Z
   or  5 x = 3 x+2 pi n_2  for  n_2  element Z

Add 3 x to both sides:
8 x = pi+2 pi n_1  for  n_1  element Z
   or  5 x = 3 x+2 pi n_2  for  n_2  element Z

Divide both sides by 8:
x = pi/8+(pi n_1)/4  for  n_1  element Z
   or  5 x = 3 x+2 pi n_2  for  n_2  element Z

Subtract 3 x from both sides:
x = pi/8+(pi n_1)/4  for  n_1  element Z
   or  2 x = 2 pi n_2  for  n_2  element Z

Divide both sides by 2:
Answer: | 
| x = pi/8+(pi n_1)/4  for  n_1  element Z
   or  x = pi n_2  for  n_2  element Z

343^1/3=7

z=7

((x^4)-20(x^2)) - ((x^4)+2(x^3))

=-2x^3 - 20x^2

(27/512)^1/3=3/8 of a foot of each side or

3/8 X 12=4.5 inches each side

The side  will =  +cube root [27 / 512]    =  [3 / 8 ]  ft

sin(3x)  = sin(4x -x )  = sin4xcosx - sinxcos4x

sin(5x)  = sin(4x + x)  = sin4xcosx + sinxcos4x     .......so....

sin4xcosx + sinxcos4x  =  sin4xcosx - sinxcos4x

2sinxcos4x  = 0      divide both sides by 2

sinxcos4x = 0     

So either  

sinx  = 0     which happens at 0 + nPi    where n is an integer

or

cos(4x)  = 0

cos(x)  = 0   at   pi/2 and  3pi/2

So.....dividing each angle by 4 we have that

cos(4x)  =  0   at    pi/8 + n(pi/4)   where n is an integer

And   at    3pi/8 + n(pi/4).....however  the previous solution covers this one as well....so we have.......pi/8 + n(pi/4)

Here's the graph  of the intersection points [ in degrees].......https://www.desmos.com/calculator/jv5zqyexum

  K= +4/7     or    K=  - 4/7

The first thing you should recognize about 16/49 is that both the numerator and denominator of that fraction are perfect squares. Which means you can very easily take the square root ... like this:

\({k}^{2} = \frac{16}{49} \)

\(\sqrt{{k}^{2}} = k = \frac{\sqrt{16}}{\sqrt{49}} = \frac{4}{7}\)

The final asnwer is 4/7. (or -4/7)

K^2=16/49 take the sqrt of both sides

K=4/7

Good work LambLamb,

I got exactly the same answer.

But

are you going to show how you did it? 

-4

sin(5x) = sin(3x)

general solution in radians:

x = 0 + πn

x=π/8 + πn/4

2 plus 2 equal to 4.

whats 19 divided 1 over 15,

19 /  (1/15) Is this what you want or mean? if yes then,

19 X 15=285 You can  take your pick, whatever you meant.

The distance to be closed in each case is the same.........=  k   km

And it will obviously take more time for the faster rider to catch the slower when they go in the same direction than when they close this distance traveling in the opposite direction

So......let S be the rate of the faster cyclist and s  be the rate of the slower

When they are going in the same direction, the effective rate rate of closure = S - s........when they are closing the distance from the opposite direction, the effective rate of closure  = S + s

And we have

k  km       =     k km

And Rate * Time   = Distance......... so.......

[S  - s] r    =   [ S + s] t

Sr - sr =  St + st

Sr - St  =  st + sr

S[r - t]  = s[r + t]

S/s   = [r + t ] / [ r - t ]

OK. That DOES make sense!. Because I gave you the answer as 2/3m!!!!!!. And, of course, 2/3 of a meter is:2/3 X 100cm=66 2/3cm.

-1.7+h=-2.2-3.4 isolate h

h=-2.2 - 3.4 +1.7

h= -3.9

yes?

yes?

I think you maybe misreading the answer, because a model is almost ALWAYS much smaller than the real thing. Also, remember that 2/3=.6666666.........etc. You Cannot get 66 2/3 from 50 and 75. The only way you could get 66 2/3 is:

50/75 X 100=66 2/3?????. But, where did the 100 come from? Remember, sometimes the answers in the book are wrong.

Isnt it 50x75=3,750?

I think it's 1 4/15