Answer: A. (2, 5), (3, 6), (6,9)
Step-by-step explanation:
Each value of x maps onto only one value of y.
Answer:
A + B + C = π ...... (1)
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L.H.S.
= ( cos A + cos B ) + cos C
= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C
= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C
= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }
= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)
= 1 + 4 sin(A/2) sin(B/2) sin(C/2)
= R.H.S. ............................. Q.E.D.
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In step (2), we used the Factorization formula
cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given
The attached triangle
Required
Find x and y
From the triangle; the angle sign in x and 52 means;
3y and 15 are congruent sides
So:
By definition of conditional probability,
Assuming a standard 6-sided fair die,
- if , then means ; otherwise,
- if , then .
Both outcomes are mutually exclusive with probability each, hence total probability .
Of the 36 possible outcomes, there are 6 ways to sum the integers 1-6 to get 7:
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
and so a sum of 7 occurs of the time.
Then the probability we want is