Maurice and three other volunteers work at the hospital every week. if the number of hours each volunteer works is always the sa
2 answers:
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Answer:
We consider a triangle ABC as attached in the answer.
We draw a line parallel to AB that passes through point C.
Angles C and C' are vertical angles, therefore ∠C = ∠C'.
Angles B and B' are corresponding angles, therefore ∠B = ∠B'.
Angles A and A' are corresponding angles, therefore ∠A = ∠A'.
it can be seen that angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'.
The three angles A', B', and C' form together a straight angle so, their angle sum is 180°. But then the angle sum ∠A + ∠B + ∠C must also be 180°.
This proofs that sum of angles of a triangle is equal to 180.
Answer for the first box: 20
Answer for the second box: 6
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Explanation:
The notation a(1) represents the first term of the sequence given. The first term is 20, so thats why a(1) = 20.
The notation a(n) = a(n-1) + ____ means we add some term to the previous term to get the next. This process happens over and over. In this case, we add 6 to each term to get the next
- term1 = 20
- term2 = term1 + 6 = 20 + 6 = 26
- term3 = term2 + 6 = 26 + 6 = 32
- term4 = term3 + 6 = 32 + 6 = 38
and so on...
So we write a(n) = a(n-1) + 6
This value of 6 can be found by selecting any term and subtracting off the previous term, so we could say any of the following below
- term2 - term1 = 26 - 20 = 6
- term3 - term2 = 32 - 26 = 6
- term4 - term3 = 38 - 26 = 6
That's how we end up with
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Extra info:
The common difference is d = 6 and the first term is a = 20
We can use these two facts to find the nth term a(n)
a(n) = a + d*(n-1)
a(n) = 20 + 6*(n-1)
a(n) = 20 + 6n - 6
a(n) = 6n + 14
Then note how plugging in n = 1 leads to
a(n) = 6*n + 14
a(1) = 6*1 + 14
a(1) = 20
and n = 2 leads to
a(n) = 6*n + 14
a(2) = 6*2 + 14
a(2) = 26
and so on
This allows us to plug in any value of n we want, without having to generate the previous terms before it. So for instance, you could plug in n = 100 to jump directly to the 100th term. If you use the recursive definition in the last section, then you have to generate the first 99 terms first before you can get to the 100th term.