Take the derivative twice then substitute t=3 into the equation

x'  = -12sin(5t) + 4cos(5t)

x" = -12cos(5t) - 4sin(5t)

    = -12cos(15) -4sin(15)

    = -12.62  units/time^2       I think.

Guest is right....Thanx for the correction !

x' = - 60 sin (5t) + 20 cos(5t)

x" = - 300 cos (5t) - 100sin (5t)

when t = 3     then x" = -315.66

You might think, but you're wrong.

The derivative of sin (5t), (for example) is 5cos (5t), not simply cos (5t).

That's as reduced as it can go as a FRACTION.

USE THE CALCULATOR DUMBHEAD

Reduced :-)

it really isnt that hard just do it 

What do you want done with it? Solve for what?

a^2-2-(3b+a)=a^2 - 2 -3b - a

Just the same as dividing any other number: Example: divide 1/4 by 15:

Enter 1 then press / then 4, then / again and finally  enter 15 and press = key.

 Look at the top of the calculator, you should see the answer of 1/60.

Take the derivative twice then substitute t=3 into the equation

x'  = -12sin(5t) + 4cos(5t)

x" = -12cos(5t) - 4sin(5t)

    = -12cos(15) -4sin(15)

    = -12.62  units/time^2       I think.

10000000000000000000000000000000000000000000000000+my d**k = 10000000000000000000000000000000000000000000000000

Stupid.

Simplify it first       73.0 (9.8)  /(2*(38^2)) = sin (theta)

.247715 = sin(theta)

Arcsin (.247715) = theta = 14.34 degrees

Guest, you are right. But your last line isn't truthful. 

Thank You ALAN!.

In our Indian style Acceleration better as, say: a. I don't want to say that you are wrong.

sqrt(563 = 23.7276210354093442

3z/4+30=180

3z+120=720

3z=600

z=200

If  "e" is a variable, then we have:

5=20/e  cross multiply

5e=20  divide both sides by 5

e=4

 x = at^2-bt^3  

The first derivative will be the velocity  v=  2at - 3bt^2 

The second derivative will be the acceleration= 2a - 6bt    

   SInce t= 2 in this question,  Acceleration(@t=2) = 2a-12b

ncr(n,k) calculates the number of combinations taken k at a time from n.

ncr(n,k)  = n!/(k!*(n-k)!)

. 

I assume the first term is meant to be (t-1)^2.  If so:

(t - 1)^2 + 12 = -7(t-1)

Add 7(t -1) to both sides:

(t - 1)^2 + 7(t - 1) + 12 = 0

This factors as

(t - 1 + 3)(t - 1 + 4) = 0

or (t + 2)(t + 3) = 0

so t = -2  or  t = -3

.

I should have used a different letter for acceleration above, so as not to confuse it with the constant  a.

Acceleration better as, say:    acc = 2a - 6bt.

.

Displacement:   x = at^2 - bt^3

Velocity:            v = 2at - 3bt^2                  Velocity is rate of change of displacement with time

Acceleration:    a = 2a - 6bt                       Acceleration is rate of change of velocity with time.

.

x/y = 2/3    y/z = 5/7     Multiply the two together to get   x/z = 10/21

Can express y/z as 15/21

So:  x:y:z  =  10:15:21

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Like so:

You could try the online Desmos graphing calculator.