Answer:
-4<n ≤ 5
Step-by-step explanation:
Answer:
Please, refer to the images below
Step-by-step explanation:
We need to solve for x in the equation
cos (x+ pi) ^2 = sin (x)
cos (x+ pi) = - cos(x)
(-cos (x)) * (-cos (x)) = sin(x)
cos(x) ^2 = sin(x)
We know that
cos(x) ^2 + sin(x) ^2 = 1
cos(x) ^2 = 1 - sin(x) ^2
1 - sin(x) ^2 = sin(x)
sin(x) ^2 + sin (x) -1 = 0
Let A = sin(x)
A^2 + A - 1 = 0
(solutions attached in picture 1)
This means that
x = arcsin(A)
(solutions attached in picture 2)
5*5*5=125
5²*5=125
5√5 is your answer
Let X be the width of the path.
The width of the path would be the width of the pool plus 2x, so 2x +16
The length of the path would be the length of the pool plus 2x, so 2x+22
The total area is 832 square feet.
Area is found by multiplying the length by the width.
So you have:
(2x+16) (2x+22) = 832
Use the Foil Method:
(2x+16) (2x+22) = 4x^2 +76x+352
Now you have:
4x^2 +76x+352 = 832
Subtract 832 from both sides:
4x^2 +76x+352-832 = 0
Simplify:
4x^2 +76x -480
Factor the left side:
4(x-5)(x+24) = 0
Divide both sides by 4:
(x-5)(x+24) = 0
Set both parenthesis to equal 0 and solve for x:
x=5 and x = -24
The width of the path cannot be a negative number, so the width is 5 meters.
3 because the x value has been repeated