Alan

You should be able to do a 3x1 vector - it's the default when you switch into the vector/matrix mode!

I think there's a bug in the calculator that prevents the A^-1*B option working directly.  I've sent a message to Admin about it.   ADMIN HAS NOW FIXED THIS!

I wouldn't use Cramer's rule for anything more than a 3x3.  I wouldn't expect anyone to do a 4x4 or bigger by hand!  Get hold of some software that will do this for you.  There is a free download program called SMath Studio Desktop that should do this. 

"...get the inverse matrix and then multiply it with the constants matrix to get the solution to the systems of equations problem but using a matrix instead of doing it by hand...."

You could do this all in one step here, by changing B to vector and entering the appropriate values, then changing the + sign to a * sign.

No! That doesn't work!  For some reason the calculator here tries to calculate A^-B if you do that!!  You'll have to do it in two separate stages (i.e. find A^-1 first then reenter that as a new A and multiply by B).

You can use the constant acceleration formula: v = u + at

v is  final velocity (0 m/s)

u is initial velocity (20 m/s)

a is acceleration (-4/3 m/s²: the minus sign shows it is decelerating)

t is the time (in seconds)

So:

0 = 20 - (4/3)*t

Rearrange:

(4/3)t = 20

t = 20*3/4

t = 15 seconds

You need to supply the values for Cp1, Cp2, t1 and t2.

You can do it on the calculator here.  First select vectors/matrices from the right side of the input bar. Then choose 3x3 matrix for A and B.  Enter your coefficients in A.  keep zeros in B. Select ^-1 for A and + for combining the matrices, then press =.  A little cumbersome, but it works!

You can start by assuming that, if it factors nicely, it will be in the form

(ax + b)(cx + d) where a, b, c and d are nice whole numbers (positive or negative).

Expanding these brackets we get:

(ax + b)(cx + d)  =  a*c*x² + a*d*x + b*c*x + b*d = a*c*x² + (a*d + b*c)*x + b*d 

Now compare this with the left-hand side of your equation 6x² - 5x - 4

A. From the constant term we must have b*d = -4, so the magnitudes of b and d must be 1 and 4 or 2 and 2.

B. From the x²  term a*c = 6 so the magnitudes of a and c must be 1 and 6 or 2 and 3

C. From the x term we must have a*d + b*c = -5

Now you have to try various combinations of a, b, c and d from A and B until you get C correctly (you'll have to include the possiblity that the signs are positive or negative as well).  This sounds like a lot of combinations, but actually there aren't that many to try and you'll find the right values fairly quickly.

If no combinations fit it means the equation doesn't factorize nicely and you would have to use the quadratic formula.

Alternatively, you could use the quadratic formula right away! 

One way is first to make the denominators the same, so make (3x + 2)/3 = 2*(3x + 2)/6

Now we can add the two terms:  [2*(3x + 2) + 4x - 1]/6

Distribute the 2 over the first set of brackets (6x + 4 + 4x - 1)/6

Collect like terms (10x + 3)/6 

or 10x/6  +  3/6

or 5x/3 + 1/2

6x² - 5x - 4 factors nicely into (2x + 1)(3x - 4)

For this to be zero we must have x = -1/2  or  x = 4/3

For 2) conservation of momentum says m1*v1 = (m1+m2)*v2where m1 is mass of woman and m2 is mass of boat.  From this we get v2 = v1*m1/(m1+m2), so v2 is smaller than v1.  It is in the same direction.

For 16) when you calculate v = x/t you are calculating the average velocity, but you need the final velocity and the initial velocity as the acceleration is given by (final velocity - initial velocity)/t.  

The initial velocity is easy enough - it is zero.

average velocity = (initial velocity + final velocity)/2 so:  x/t = (0 + final velocity)/2

Rearrange to get: final velocity = 2*x/t.

So acceleration = (final velocity - initial velocity)/t

or 1.62 = (2*2/t - 0)/t

1.62 = 4/t²

t = √(4/1.62)

t = 1.57 s  ≈ 1.6 s