Find M A. 17 B. 16 C. 18 D. 20
1 answer:
Answer:
A. 17
Step-by-step explanation:
using the cosine rule (also see attached for reference):
AB² = BC² + AC² - 2·AC·BC cos C
2·AC·BC cos C = BC² + AC² - AB²
Given that AC = 18, AB = 12 and BC = 18, substituting these into the formula
2(18)(28) cos C = 28² + 18² - 12²
1008 cos C = 964
cos C = 964/1008
cos C = 0.9563
C = cos⁻¹ 0.9563
C = 16.99 ( = 17° rounded to nearest degree)
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Part A:
Let the length of one of the sides of the rectangle be L, then the length of the other side is obtained as follow.
Let the length of the other side be x, then
Thus, if the length of one of the side is x, the length of the other side is 8 - L.
Hence, the area of the rectangle in terms of L is given by
Part B:
To find the domain of A
Recall that the domain of a function is the set of values which can be assumed by the independent variable. In this case, the domain is the set of values that L can take.
Notice that the length of a side of a rectangle cannot be negative or 0, thus L cannot be 8 as 8 - 8 = 0 or any number greater than 8.
Hence the domain of the area are the set of values between 0 and 8 not inclusive.
Therefore,
Let the length of one of the sides of the rectangle be L, then the length of the other side is obtained as follow.
Let the length of the other side be x, then
Thus, if the length of one of the side is x, the length of the other side is 8 - L.
Hence, the area of the rectangle in terms of L is given by
Part B:
To find the domain of A
Recall that the domain of a function is the set of values which can be assumed by the independent variable. In this case, the domain is the set of values that L can take.
Notice that the length of a side of a rectangle cannot be negative or 0, thus L cannot be 8 as 8 - 8 = 0 or any number greater than 8.
Hence the domain of the area are the set of values between 0 and 8 not inclusive.
Therefore,