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Anna007 [38]
4 years ago
5

Analyze the diagram below and complete the instructions that follow.Find m

Mathematics
1 answer:
vladimir2022 [97]4 years ago
3 0
Answer: 70.5°

Solution:

Call B, the measure of the angle CBA

cos(B) = adjacent-leg / hypotenuse = 3 / 9 = 1 / 3

=> B = arc cos (1/3) ≈ 70.5°

I will calculate other measures for you, trying to cover the most common ratios: sine, cosine, tangent

1) (segment CA)^2 + (segment BC)^2 = (hypotenuse)^2

=> (segment CA )^2 = (hypotenuse)^2 - (segment BC)^2 = 9^2 - 3^2 = 81 - 9 = 72

=> segment CA = √72 = 6√2

2) sin(B) = opposite-leg / hypotenuse = 6√2 / 9 =2√2 / 3

3) sin(A) = cos(B) = 1/3

4) cos(A) = sin(B) = 2√2 / 3

5) tan(B) = opposite-leg / adjacent-leg = (2√2 / 3 ) / 3 = 2√2 / 9

6) tang(A) = 3 / (2√2 /3) = 9 /( 2√2) = 9√2 / 4

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If p q r is prime numbers such that pq+r=73, what is the least possible value of p+q+r
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The answer to this question would be: p+q+r = 2 + 17 + 39= 58

In this question, p q r is a prime number. Most of the prime number is an odd number. If p q r all odd number, it wouldn't be possible to get 73 since
odd x odd + odd= odd + odd = even
Since 73 is an odd number, it is clear that one of the p q r needs to be an even number. 

There is only one odd prime number which is 2. If you put 2 in the r the result would be:
pq+2= 73
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There will be no solution for pq since 71 is prime number. That mean 2 must be either p or q. Let say that 2 is p, then the equation would be: 2q + r= 73

The least possible value of p+q+r would be achieved by founding the highest q since its coefficient is 2 times r. Maximum q would be 73/2= 36.5 so you can try backward from that. Since q= 31, q=29, q=23 and q=19 wouldn't result in a prime number r, the least result would be q=17
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