### Upper and lower bounds 2

```Upper and Lower Bounds 2
- Calculations
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Two ropes, A and B, have lengths:
A = 36m to the nearest metre
B = 23m to the nearest metre.
35.5  A  36.5
22.5  B  23.5
1 What are the upper and lower bounds
for A + B?
35.5  A  36.5
22.5  B  23.5
35.5  22.5  A  B  36.5  23.5
58  A  B  60
Subtraction
2 What are the upper and lower bounds
for A - B?
35.5  A  36.5
22.5  B  23.5
35.5  23.5  A  B  36.5  22.5
12  A  B  14
Multiplication
Area = wh = ?
h = 6.4cm (nearest mm)
w = 11.7cm (nearest mm)
What are the upper and lower bounds of the area of the rectangle?
11.65  w  11.75
6.35  h  6.45
11.65  6.35  wh  11.75  6.45
73.9775  wh  75.7875
74.00  wh  75.79
Division
What are the upper and lower
bounds of the angle x?
h = 4cm
(nearest cm)
x
w = 7cm (nearest cm)
3.5  h  4.5
h
tan x 
w
6.5  w  7.5
3.5  7.5  tan x  4.5  6.5
0.4666...  tan x  0.6923...
25.01689...  x  34.69515...
25.0  x  34.7
Summary
LB  A  A  UB  A
LB  B   B  UB  B 
LB  A +LB  B   A  B  UB  A +UB  B 
LB  A - UB  B   A  B  UB  A - LB  B 
LB  A  LB  B   A  B  UB  A   UB  B 
LB  A  UB  B   A  B  UB  A  LB  B 
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