The graphs of the inequalities are , , and .
Graph the inequalities , , and .
Observe the graph :
on .
Moments and center of mass of a planar lamina :
Let and be continuous functions such that on , and consider the planar lamina of uniform density bounded by the graphs of and .
The moments about the -and -axes are .
.
The center of mass is and , where is the mass of the lamina.
Find the area of the region .
Substitute .
Apply derivative on each side with respect to .
.
Substitute and .
Substitute and .
The area of the region is .
Find .
.
Find .
Since the graph is symmetrical about the -axis, center of mass lies on the axis of symmetry.
The center of mass is and .
Substitute and in .
.
Substitute and in .
.
The centroid of the region is .
The centroid of the region is .
"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett |
"Your site is amazing! It helped me get through Algebra." Charles |
"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease |