---
2.
The leg and cast in Figure P4.18 weigh 270 N, with the center of mass as indicated by the blue arrow in the diagram. The counterbalance w1 weighs 135 N. Determine the weight w2 and the angle needed so that no force is exerted on the hip joint by the leg plus cast.
N
°

Figure P4.18

3. Two packing crates of masses m1 = 10.0 kg and m2 = 6.50 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.26. The 6.50 kg crate lies on a smooth incline of angle 43.0°. Find the acceleration of the 6.50 kg crate.
m/s2 (up the incline)
Find the tension in the string.
N

Figure P4.26
6.
A 2.00 kg block is held in equilibrium on an incline of angle = 70° by a horizontal force applied in the direction shown in Figure P4.50. If the coefficient of static friction between block and incline is µs = 0.300, determine the following.

Figure P4.50
(a) the minimum value of
N
(b) the normal force exerted by the incline on the block
N

7.
A block of mass m = 2.00 kg rests on the left edge of a block of length L = 3.00 m and mass M = 8.00 kg. The coefficient of kinetic friction between the two blocks is µk = 0.300, and the surface on which the 8.00 kg block rests is frictionless. A constant horizontal force of magnitude F = 10.0 N is applied to the 2.00 kg block, setting it in motion as shown in Figure P4.52a.

Figure P4.52
(a) How long will it take before this block makes it to the right side of the 8.00 kg block, as shown in Figure P4.52b? (Note: Both blocks are set in motion when the force is applied.)
s
(b) How far does the 8.00 kg block move in the process?
m

8 In Figure P4.30, m1 = 10.0 kg and m2 = 4.5 kg. The coefficient of static friction between m1 and the horizontal surface is 0.50 while the coefficient of kinetic friction is 0.30.

Figure P4.30
(a) If the system is released from rest, what will its acceleration be?
m/s2
(b) If the system is set in motion with m2 moving downward, what will be the acceleration of the system?
m/s2

2.) If " S " is the set of all "x" such that 0≤x≤1, what points, if any, are points of accumulation of both "S" and C(S)?
3.) Prove that any finite set is closed.
5.) Prove that, if "S" is open, each of its points is a point of accumulation of "S".
1.) Suppose "S" is a set having the number "M" as its least up

Below are four bivariate data sets. (Note that each scatter plot is displayed on the same scale.) Each data set is made up of sample values drawn from a population.
x y = Figure 1
--- ---
1.0 8.0
2.0 4.8
3.0 9.8
4.0 6.2
5.0 2.0
6.0 4.8
7.0 8.9
8.0 4.0
9.0 9.7
10.0 6.7
u v

I am having a problem drawing the table for the following system: Define a universal set U as the set of counting numbers. Form a new set that contains all possible subsets of U. This new set of subsets together with the operation of set intersection forms a mathematical system. Then I have to tell which properties that we did

Introduce slack variables as necessary, and then write the initial simplex tableau for each linear programming problem.
1). Find x1 ≥ 0 and x2 ≥ 0 such that
X1 + x2 ≤ 10
5x1 + 3x2 ≤ 75
and z = 4x1 + 2x2 is maximized
2. Production -Knives The Cut-Right Company sells set of kitchens knives. Th

I have these problems from Topology of Surfaces by L.Christine Kinsey: the problems I require assistance with are 2.26, 2.28, 2.29, and 2.32. These are stated below.
PROBLEM (Exercise 2.26). Describe what stereographic projection does to
(1) the equator,
(2) a longitudinal line through the north and south poles,
(3) a tr

? Let X:={a,b,c} be a set of three elements. A certain topology of X contains (among others) the sets {a}, {b}, and {c}. List all open sets in the topology T.
? Let X':={a,b,c,d,e} be a set of five elements. A certain topology T' on X' contains (among others) the sets {a,b,c}, {c,d} and {e}. List any other open set in T' which