Find the mass of the triangular lamina with vertices $( 0,0 ) , ( 20,40 ) \text {, and } ( 40,0 ) \text { for }$ the density $\rho=k$
A)401k
B)809k
C)800k
D)400k
E)805k

Question

Quizplus · Accepted Answer

The mass of the lamina can be found by integrating the density over the area of the triangle. The area of the triangle with vertices $(0,0), (20,40), \text{ and } (40,0)$ can be calculated using the formula for the area of a triangle, $\frac{1}{2} \times \text{base} \times \text{height}$. Here, the base is $40$ (the length along the x-axis from $(0,0)$ to $(40,0)$) and the height is $40$ (the maximum y-value). Thus, the area $A$ is $\frac{1}{2} \times 40 \times 40 = 800$. Since the density $\rho$ is constant and equal to $k$, the mass $m$ of the lamina is the product of the area and the density: $m = A \times \rho = 800 \times k = 800k$.

Find the Mass of the Triangular Lamina with Vertices (0,0),(20,40), and (40,0) for ( 0,0 ) , ( 20,40 ) \text {, and } ( 40,0 ) \text { for }(0,0),(20,40), and (40,0) for

Find the Mass of the Triangular Lamina with Vertices $( 0,0 ) , ( 20,40 ) \text {, and } ( 40,0 ) \text { for }$