A summer camp cookout is planned for the campers and their families. There is room for 200 people. Each adult costs $4, and each
camper costs $3. There is a maximum budget of $750. Write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers.
A.
B.
C.
D.
A.
B.
C.
D.
2 answers:
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Answer:
Ix = Iy = a^4 / 12
Ixy = a^4 / 24
Step-by-step explanation:
Solution:-
- Sketch the right angled isosceles triangle as shown in the attachment.
- The density (ρ) is a multivariable function of both coordinates (x and y).
ρ ( x, y ) = k*(x^2 + y^2)
Where, k: coefficient of proportionality.
- The lamina and density are symmetrical across the line y = x. (see attachment). The center of mass must lie on this line.
- The coordinates of centroid ( xcm and ycm) are given by:
- The coordinates of xcm = ycm, they lie on line y = x.
- Calculate the mass of lamina (m):
- Calculate the Moment (My):
- Calculate ( xcm = ycm ):
xcm = ycm = ( ka^5 /15 ) / ( ka^4/6) = 2a/5
- Now using the relations for Ix, Iy and I: We have:
Ix = bh^3 / 12
Iy = hb^3 / 12
Where, h = b = a .... (Right angle isosceles)
Ix = Iy = a^4 / 12
Ixy = b^2h^2 / 24
Ixy = a^4 / 24
