The table shows weight for different US coins Allen has one each coin in his hand.round each weight to the nearest whole gram.th
en estimate total weight of the coins in allen's hand
1 answer:
You might be interested in
Answer:
m∠A ≈ 43°
m∠B ≈ 55°
mBC ≈ 20
Step-by-step explanation:
Law of Sines:
Step 1: Find m∠B
Step 2: Solve for ∠B
29sinB = 24sin82°
sinB = 24sin82°/29
B = sin⁻¹(24sin82°/29)
B = 55.038°
Step 3: Find m∠A
180 - (55.038 + 82)
180 - 137.038
m∠A = 42.962°
Step 4: Find BC
Step 5: Solve for BC
29sin42.962° = BCsin82°
BC = 29sin42.962°/sin82°
BC = 19.9581
Answer:
For the set X = {a, b, c}, the following three relations satisfy the required conditions in (a), (b) and (c) respectively.
(a) R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)} is reflexive and symmetric but not transitive .
(b) R = {(a, a), (b, b), (c, c), (a, b)} is reflexive and transitive but not symmetric .
(c) R = {(a,a), (a, b), (b, a)} is symmetric and transitive but not reflexive .
Step-by-step explanation:
Before, we go on to check these relations for the desired properties, let us define what it means for a relation to be reflexive, symmetric or transitive.
Given a relation R on a set X,
R is said to be reflexive if for every .
R is said to be symmetric if for every .
R is said to be transitive if and
, then
.
(a) Let R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)}.
Reflexive:
Therefore, R is reflexive.
Symmetric:
Therefore R is symmetric.
Transitive: but but (a,c) is not in R.
Therefore, R is not transitive.
Therefore, R is reflexive and symmetric but not transitive .
(b) R = {(a, a), (b, b), (c, c), (a, b)}
Reflexive:
Therefore, R is reflexive.
Symmetric:
Therefore R is not symmetric.
Transitive: and
.
Therefore, R is transitive.
Therefore, R is reflexive and transitive but not symmetric .
(c) R = {(a,a), (a, b), (b, a)}
Reflexive: but (b, b) and (c, c) are not in R
R must contain all ordered pairs of the form (x, x) for all x in R to be considered reflexive.
Therefore, R is not reflexive.
Symmetric: and
Therefore R is symmetric.
Transitive: and
.
Therefore, R is transitive.
Therefore, R is symmetric and transitive but not reflexive .