Answer:
D
Step-by-step explanation:
A polynomial of degree 2 has 2 roots, either real or complex
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
Answer:
A
Explanation:
For functions to be inverse, it must be true that f( g(x) ) = x and g( f(x) ) = x.
But for F( G(x) ), we have √( G(x) - 3 ) + 8
= √( (x+8)² - 3 - 3 ) + 8
= √( (x+8)² - 6 ) + 8
This -6 part should be cancelled out for functions to work out but we cannot do that, therefore F(x) and G(x) are not inverse.
Answer:
Class second have higher score and have greater spread.
Step-by-step explanation:
For first box plot
For second box plot
First class has greater minimum value, it means first class has lower grades.
First quartile of both classes are same, it means equal number students in both classes have less than 62 marks.
First class has greater median.
second class has greater third quartile.
Second class has greater Maximum value. It means second class have higher score than first class.
Second class has greater range. It means the data of second class has greater spread.
Second class has greater inter quartile range. It means the data of second class has greater spread.
Therefore, the class second have higher score and have greater spread.
Answer:
592
Step-by-step explanation: