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olga2289 [7]
1 year ago
9

Please help, performance task: trigonometric identities

Mathematics
1 answer:
AnnZ [28]1 year ago
4 0

The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

<h3>How to solve the trigonometric equations?</h3>

<u>Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)</u>

The equation can be split as follows:

y = 1 - cos(x)

y = 2 - 2sin²(x)

Next, we plot the graph of the above equations (see graph 1)

Under the domain interval (-π, π), the curves of the equations intersect at:

(-π/3, 0.5) and (π/3, 0.5)

Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

<u>Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)</u>

The equation can be split as follows:

y = 4cos⁴(x) - 5cos²(x) + 1

y = o

Next, we plot the graph of the above equations (see graph 2)

Under the domain interval [0, 2π), the curves of the equations intersect at:

(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

Read more about trigonometry equations at:

brainly.com/question/8120556

#SPJ1

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Alexeev081 [22]

Answer:

Width is 10ft and length is 6ft.

Step-by-step explanation:

The area of a shape is the amount inside a shape. It is found using multiplication or A = l*w. Since the width is w and the length is 4ft less than its width or w - 4, use these expressions in the area formula to find their amount.

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w^2 -4w - 60 = 0\\(w-10)(w+6) = 0

Set each factor equal to 0 and solve.

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5 0
3 years ago
5 of 8
aleksandr82 [10.1K]

Given:

The mean age of 5 people in a room is 26 years.

A person enters the room. The mean age is now 33.

To find:

The age of the person who entered the room.

Solution:

Formula for mean:

\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}

The mean age of 5 people in a room is 26 years.

26=\dfrac{\text{Sum of ages of 5 people}}{5}

26\times 5=\text{Sum of ages of 5 people}

130=\text{Sum of ages of 5 people}

The mean age is now 33. It means, the mean age of 6 people is 33.

33=\dfrac{\text{Sum of ages of 6 people}}{6}

33\times 6=\text{Sum of ages of 6 people}

198=\text{Sum of ages of 6 people}

Now, the age of the person who entered the room is

Required age = Sum of ages of 6 people - Sum of ages of 5 people

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                       = 68

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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