Answer:
The solutions of the equation are 0 , π
Step-by-step explanation:
* Lets revise some trigonometric identities
- sin² Ф + cos² Ф = 1
- tan² Ф + 1 = sec² Ф
* Lets solve the equation
∵ tan² x sec² x + 2 sec² x - tan² x = 2
- Replace sec² x by tan² x + 1 in the equation
∴ tan² x (tan² x + 1) + 2(tan² x + 1) - tan² x = 2
∴ tan^4 x + tan² x + 2 tan² x + 2 - tan² x = 2 ⇒ add the like terms
∴ tan^4 x + 2 tan² x + 2 = 2 ⇒ subtract 2 from both sides
∴ tan^4 x + 2 tan² x = 0
- Factorize the binomial by taking tan² x as a common factor
∴ tan² x (tan² x + 2) = 0
∴ tan² x = 0
<em>OR</em>
∴ tan² x + 2 = 0
∵ 0 ≤ x < 2π
∵ tan² x = 0 ⇒ take √ for both sides
∴ tan x = 0
∵ tan 0 = 0 , tan π = 0
∴ x = 0
∴ x = π
<em>OR</em>
∵ tan² x + 2 = 0 ⇒ subtract 2 from both sides
∴ tan² x = -2 ⇒ no square root for negative value
∴ tan² x = -2 is refused
∴ The solutions of the equation are 0 , π
Answer:
yes es correcto ya que 70 es igual a 4 metros
The total length of the fence is 48 m if the rectangular swimming pool measures 7.5 m by 4.5 m.
<h3>What is rectangle?</h3>
It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that:
A rectangular swimming pool measures 7.5 m by 4.5 m.
It is completely surrounded by a fence parallel to each edge of the pool and at a distance of 3 m from each edge of the pool.
The total length of the fence = 2(7.5+3×2 + 4.5+3×2)
The total length of the fence = 2(7.5+6 + 4.5+6)
The total length of the fence = 2(24)
The total length of the fence = 48 m
Thus, the total length of the fence is 48 m if the rectangular swimming pool measures 7.5 m by 4.5 m.
Learn more about the rectangle here:
brainly.com/question/15019502
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You can tell which animal is faster by pacing
Answer:
4 / 9
Step-by-step explanation:
There are 4 reds out of 9 so the probability would be 4 out of 9 or 4 / 9.