A cable with mass 0.5 kilograms per meter (kg/m) is used to lift 150 kg of coal up a mine shaft 50 meters deep. Set up the integral that will calculate the work needed to lift the load one quarter of the way up the shaft. (Set up the integral only, no need to compute its value.)

Explanation:

the integral for the work is:

the work is against the gravitational force. While the coal is going up, M(y) is changing due to the length of the cable is lower. We can describe this by using the following formula

Thus , the integral for the work is:

hope this helps!!

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.