Given a triangle with a = 9, b = 11, A = 31°, what is (are) the possible length(s) of c? Round your answer to two decimal places
.
A) 16.42 or 2.44
B) 6.61
C) 14.21
D) 16.42 or 3.41
A) 16.42 or 2.44
B) 6.61
C) 14.21
D) 16.42 or 3.41
1 answer:
You can use the Law of Cosines to figure this.
a² = b² +c² -2bc×cos(A)
c² -(2b×cos(A))c +b² -a² = 0
c² -18.8577c +40 = 0 . . . . . . . substituting the given values
Then we can use the quadratic formula to find c.
c = (18.8577 ±√(18.8577² -160))/2
c = (18.8577 ±13.9861)/2 ≈ {2.44, 16.42}
The appropriate choice is ...
A) 16.42 or 2.44
a² = b² +c² -2bc×cos(A)
c² -(2b×cos(A))c +b² -a² = 0
c² -18.8577c +40 = 0 . . . . . . . substituting the given values
Then we can use the quadratic formula to find c.
c = (18.8577 ±√(18.8577² -160))/2
c = (18.8577 ±13.9861)/2 ≈ {2.44, 16.42}
The appropriate choice is ...
A) 16.42 or 2.44
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Answer:
(a) 120 choices
(b) 110 choices
Step-by-step explanation:
The number of ways in which we can select k element from a group n elements is given by:
So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:
Then each student have 120 possible choices.
On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:
1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:
2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:
3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:
So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:
50 + 50 + 10 = 110