Answer:
-1/3
Step-by-step explanation:
Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
5^11 + 5^10
------------------- =
5^10 - 5^8
48,828,125 + 5^10
-------------------------- =
5^10 - 5^8
48,828,125 + 9,765,625
--------------------------------- =
5^10 - 5^8
48,828,125 + 9,765,625
----------------------------------- =
9,765,625 - 5^8
48,828,125 + 9,765,625
--------------------------------- =
9,765,625 - 390,625
58,593,750
------------------------------ =
9,765,625 - 390,625
58,593,750
------------------ =
9,375,000
answer: 6.25
5.
-4=r/20-5
First add 5 to both sides
1=r/20
Then multiply both sides by 20
20=r
Final answer: r=20
7.
(v+9)/3=8
First multiply both sides by 3
v+9= 24
Subtract 9 from both sides
v=15
Final answer: v=15