Answer:
Explanation:
Given a square Piece whose side is 12 inches
Now square pieces are cut from each corner to make it a open box
Suppose x is the length of square piece at each corner
then
base square has a length of 
Dimension of new box is 
Volume 

For maximum volume differentiate with respect to x we get

we get x=6 and 4 but at x=6 volume becomes zero therefore x=4 is valid



Answer:
5.71428571422 m/s
Explanation:
u = Initial velocity = 20 m/s
v = Final velocity
s = Displacement
a = Acceleration
Time taken = 15-1 = 14 s
Distance traveled in 1 second = 


The speed as she reaches the light at the instant it turns green is 5.71428571422 m/s
<u>We are given:</u>
Mass of the Steelhead(m) = 9 kg
Velocity of the Steelhead(v) = 16 m/s
<u>Calculating the Kinetic Energy:</u>
KE = 1/2mv²
replacing the variables
KE = 1/2 * 9 * (16)²
KE = 1152 Joules
Since Astronaut and wrench system is isolated in the space and there is no external force on it
So here momentum of the system will remain conserved
so here we can say

initially both are at rest
so here plug in all values


so here the astronaut will move in opposite direction and its speed will be equal to 0.20 m/s