Answer:
Quad One: A
Quad Two: C
Quad Three: B
Quad Four: E
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(-)×(-)=+
-(-16)
+16
F ( x ) = 3 sim x + 3 cos x
f ` ( x ) = 3 cos x - 3 sin x
f `` ( x ) = - 3 sin x - 3 cos x = - 3 ( sin x + cos x )
The inflection points:
- 3 ( sin x + cos x ) = 0
sin x + cos x = 0
sin x = - cos x / : cos x
tan x = - 1
x 1 = 3π / 4
x 2 = 7π / 4
The function is concave up when f``(x) > 0
- 3( sin x+ cos x ) > 0
sin x + cos x < 0
tan x < - 1
f is concave up for:
x ∈ ( π/2, 3π/4 ) ∪ ( 3π/2, 7π/4)
f is concave down for:
x ∈ ( 0, π/2 ) ∪ ( 3π / 4, 3π/2 ) ∪ ( 7π / 4, 2 π ).
Answer:
<em>Zeina had 35 books and Ali had 5 books</em>
Step-by-step explanation:
<u>Equations</u>
We know Zeina has seven times as many books as Ali. If we call
x = Number of books Ali has
Then Zeina has
7x = Number of books Zeina has
We also know if Zeina gave Ali 15 books, they would have the same number of books, thus:
x + 15 = 7x - 15
Adding 15:
x + 15 +15 = 7x
Subtracting x:
15 +15 = 7x - x
Operating:
30 = 6x
Dividing by 6:
x = 30 / 6
x =5
7x = 35
Thus Zeina had 35 books and Ali had 5 books
