Answer:
The function is increasing from (- infinity , 0)
Step-by-step explanation:
Answer:
options are 3 and 4
Step-by-step explanation:
The difference of squares is defined as In option 1,
It can be written as
It is the sum of squares, therefore the option 1 is incorrect.
In option 2,
The number 40 is not a complete square of any number, therefore option 2 is incorrect.
In option 3,
It can be rewritten as
It is the difference of squares, therefore option 3 is correct.
In option 4,
It can be rewritten as
It is the difference of squares, therefore option 4 is correct.
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The sum of the volume of its part
Step-by-step explanation:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ)
Multiply by the reciprocal:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)
(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]
(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]
Distribute and simplify:
(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)
[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)
(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)
Use Pythagorean identity:
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)
(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)
Factor:
(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))
(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))
(1 + sin θ) / cos θ
4m = 12x + 40
8x + 8x + 12x + 40 + 4m = 360
28x + 40 + 12x + 40 = 360
x = 7
m = 12(7) + 40 = 124
