Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the trian
gular region enclosed by the lines y = 0, y = 2x, and x + 2y = 1; rho(x, y) = x
1 answer:
Answer:
m=1/300 du
Step-by-step explanation:
we have that m=∫∫rho(x,y)dA for this we must find the limits of integration (according to the graph1)
On the x axis: if y=2x and x+2y=1 then y=2x and y=(1-x)/2 ⇒ 2x=(1-x)/2 ⇒ 4x=1-x ⇒ 5x=1 ⇒ x=1/5; on the y axis y=0 and y=1/2
m=∫∫rho(x,y)dA (view the graph 2)
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Answer:
The number are and
.
Step-by-step explanation:
Given as :
The difference between the squares of two number = 3
And , Twice the square of the first number increased by the square of the second number is 9
Now, Let The first number = F
And The second number = S
So , According to question
F² - S² = 3 .......A
2 F² - S² = 9 ........B
Now, solving the equations
( 2 F² - S² ) - ( F² - S² ) = 9 - 3
Or, ( 2 F² - F² ) + ( S² - S² ) = 6
Or, F² + 0 = 6
∴ F =
Putting the value of F in eq A
So, ( )² - S² = 3
Or, 6 - 3 = S²
Or, S² = 3
∴ S =
So, The number are ,
Hence The number are and
. Answer