The top view of a table, with weight W_t, is shown in the figure. The table has lost the leg at ( L_x, L_y), in the upper right corner of the diagram, and is in danger of tipping over. Company is about to arrive, so the host tries to stabilize the table by placing a heavy vase (represented by the green circle) of weight W_v at ( X, Y). Denote the magnitudes of the upward forces on the table due to the legs at (0, 0), ( L_x, 0), and (0, L_y) as F_0, F_x, and F_y, respectively.

1. Find F_x, the magnitude of the upward force on the table due to the leg at ( L_x, 0). Express the force in terms of W_v, W_t, X, Y, L_x, and/or L_y. Note that not all of these quantities may appear in the answer.

2. Find F_y, the magnitude of the upward force on the table due to the leg at (0, L_y). Express the force in terms of W_v, W_t, Y, X, L_y, and/or L_x. Note that not all of these quantities may appear in the final answer.

3. Find F_0, the magnitude of the upward force on the table due to the leg at (0, 0).

Express the force in terms of W_v, W_t, F_x, F_y, L_x, L_y, X, and/or Y. Note that not all terms may appear in the answer.

While the host is greeting the guests, the cat (of weight W_c) gets on the table and walks until her position is (x,y)=(L_x,L_y)

4. Find the maximum weight W_max of the cat such that the table does not tip over and break the vase. Express the cat's weight in terms of W_v, X, Y, L_x, and L_y.

1. Find F_x, the magnitude of the upward force on the table due to the leg at ( L_x, 0). Express the force in terms of W_v, W_t, X, Y, L_x, and/or L_y. Note that not all of these quantities may appear in the answer.

2. Find F_y, the magnitude of the upward force on the table due to the leg at (0, L_y). Express the force in terms of W_v, W_t, Y, X, L_y, and/or L_x. Note that not all of these quantities may appear in the final answer.

3. Find F_0, the magnitude of the upward force on the table due to the leg at (0, 0).

Express the force in terms of W_v, W_t, F_x, F_y, L_x, L_y, X, and/or Y. Note that not all terms may appear in the answer.

While the host is greeting the guests, the cat (of weight W_c) gets on the table and walks until her position is (x,y)=(L_x,L_y)

4. Find the maximum weight W_max of the cat such that the table does not tip over and break the vase. Express the cat's weight in terms of W_v, X, Y, L_x, and L_y.

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