Answer:
A=-2
B=-8
Step-by-step explanation:
In order for the system of linear equations to have infinitely many solution, they must be the same equation.
Ax-y=8
2x+y=B
We need to choose A and B so they are the same equation.
I notice they are both in the same form but in the second column you have opposites;
the -y and y.
So im going to multiply either equation by -1 so that part is exactly the same.
Don't choose both; choose only one.
Let's multiply the first equation by -1.
Doing this gives us the following:
-Ax+y=-8
2x+y=B
So now we can choose A and B so these equations appear exactly the same.
We need -A=2 and B=-8.
-A=2 implies A=(opposite of 2) which is -2.
Conclusion:
A=-2
B=-8
Multiply them together. The product is the answer of a multiplication process.
(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when 
and 
, and because the velocity function is continuous, you need only check the sign of 
for values on the intervals (0, 3) and (3, 6).
We have, for instance 
and 
, which means the particle is moving the positive direction for 
, or the interval (3, 6).
(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:
which follows from the definition of absolute value. In particular, if 
is negative, then 
.
The total distance traveled is then 4 ft.
(g) Acceleration is the rate of change of velocity, so 
is the derivative of :
Compute the acceleration at 
seconds:
(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)
