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its math ;)))))

Assume height above ground where arrow hits rock is s meters.  

Rock:   18.35 - s = (1/2)*9.8*t²      where t = time in seconds and accn of gravity = 9.8m/sec²

Arrow:  s = 47*t - (1/2)*9.8*t^2

Replace s in the first equation using the second equation:

18.35 - (47t - (1/2)9.8*t^2) = (1/2)*9.8*t²

18.35 - 47t + (1/2)*9.8*t^{2 =} (1/2)*9.8*t²

18.35 - 47t = 0

t = 18.35/47 ≈ 0.39 secs

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The above uses the fact that for constant acceleration situations:

distance = initial velocity*time + (1/2)*acceleration*time²

??  !!!

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You can find cot(3.5°) using the calculator on the home page here.   cot(3.5°) ≈ 16.35

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Just noticed you seem to have cot (3.5°) given (incorrectly!) on your page!!!

I assume this is cos x*(2[cos x]^2 + 1) = 0

The term in brackets can never be zero, so we must have cos x = 0

That is x = pi/2, 3pi/2 in the range between 0 and 2pi.

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Provide a specific example of what you are trying to do.

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753x654=492,462

To find that, you take your miles per lap, 1/4, and multiply by the laps, 11, so it is 1/4 times 11= 2 and 3/4 miles

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

                x   +   5

x - 4   [     x^2    + x    - 20   ]

            - [  x^2    -4x ]

                         5x   -   20

                   -  [  5x   -  20 ]

                                     0

The numerator can be factored as \((x+5)(x-4)\) so you have;

\(\frac{x^2+x-20}{x-4}\rightarrow\frac{(x+5)(x-4)}{x-4}\rightarrow x+5\)

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1/2 (1120)(40)^2 =1/2 x 1120 x 40^2=896,000

-3x+5y = 22       multiply through by 4  →   -12x + 20y = 88   (1) 

12x-10y = -8       (2)

Add (1) to (2)  and we have

10y  = 80      divide by 10

y = 8

Sub this into  -3x + 5y = 22  to find x

-3x + 5(8) = 22

-3x + 40  = 22     subtract 40 from both sides

-3x   =  - 18        divide both sides by -3

x =  6

Assuming YX is tangent to the circle, we can solve this using the secant-tangent theorem which says that  the product of the secant length and its external segment = to the square of the length of the tangent segment.....so

ZY * VY   =   (XY)^2   ......so.....

(19 + 9) * 9   = (XY)^2

28 * 9   = (XY)^2

252  = (XY)^2

sqrt(252)  = XY

sqrt (36 * 7)  = XY

6sqrt(7)   = XY  ≈ 15.87

If I have R35725 and add R700 pm to it for 17 years and get a 10% annual growth rate, what will my final lump sum be.

FV =566,768.01R - Final sum of the investment.

Subtract 440 from 600

If chords intersect in a circle, the product of their associated segments are equal.....so....

3.5 * 6   = 4 * BP       divide both sides by 4

[3.5 * 6] / 4  = BP

5.25 = BP

Interest  =  825 * .0075  = $6.19

Service charge  = $7.50

7.50  - 6.19   = $1.31 (debit)

y=x^2+16x+71    

Take 1/2 of the coefficient on x =(1/2) * 16  = 8....square this = 64....add and subtract it

x^2 + 16x + 64  + 71 - 64         factor the first three terms, simpify the last two

(x + 8)^2   + 7      this is vertex form.....the vertex is (-8, 7)

1x0.4783=0.4783

100-75/5x3+55-26= 84

That's right, never inhale carbon dioxide.  Just exhale it. 

A = 1, M = 0, S = 6, H = 4, T = 7, O = 9

20264

*       3

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60792

285+461=?                    

60792