Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
sin(x)^4 - sin(x)^2 = cos(x)^4 - cos(x)^2
sin(x)^2 = 1 - cos(x)^2:
sin(x)^4 - 1 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2
-(1 - cos(x)^2) = cos(x)^2 - 1:
cos(x)^2 - 1 + sin(x)^4 = ^?cos(x)^4 - cos(x)^2
sin(x)^4 = (sin(x)^2)^2 = (1 - cos(x)^2)^2:
-1 + cos(x)^2 + (1 - cos(x)^2)^2 = ^?cos(x)^4 - cos(x)^2
(1 - cos(x)^2)^2 = 1 - 2 cos(x)^2 + cos(x)^4:
-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = ^?cos(x)^4 - cos(x)^2
-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = cos(x)^4 - cos(x)^2:
cos(x)^4 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2
The left hand side and right hand side are identical:
Answer: (identity has been verified)
Step-by-step explanation:
oh, come on. you can just use common sense.
a local minimum is a point where the curve goes down to, and then turns around and starts to go up again. that point in the middle, where it turns around and does not go down any further, is the minimum.
for the maximum the same thing applies, just in the other direction (the curve goes up and turns around to go back down again).
a)
the local minimum values (y) are
-2, -1
b)
the values of x where it had these minimum values are
-1, +3
The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².
<h3>How to derive the equation of the parabola from the locations of the vertex and focus</h3>
Herein we have the case of a parabola whose axis of symmetry is parallel to the x-axis. The <em>standard</em> form of the equation of this parabola is shown below:
(x - h) = [1 / (4 · p)] · (y - k)² (1)
Where:
- (h, k) - Coordinates of the vertex.
- p - Distance from the vertex to the focus.
The distance from the vertex to the focus is 1 / 8. If we know that the location of the vertex is (0, 0), then the <em>standard</em> form of the equation of the parabola is:
x = 2 · y² (1)
The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².
To learn more on parabolae: brainly.com/question/4074088
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Answer:
2.5 pi
Step-by-step explanation:
Comment
If you were trying to get the area of a whole circle, you would use
Area = pi r^2
You have to modify the formula to show that just part of the circle has an area that you are interested in.
The new formula is
Area = (theta/360) pi r^2
Givens
r = 30 cm
theta = 100
Solution
Area = (100 / 360) * pi * r^2 Substitute the givens into this formula
Area = (5 / 18) * pi * 3^2 Expand
Area = (5 / 18) * pi * 9 Cancel 9 into 18
Area = 5/2 * pi
Area = 2.5 * pi
Hello!
Answer:
|2x - 5| = 4
Solve for the negative and positive expressions:
2x - 5 = 4
2x = 9
x = 9/2
------------
-(2x - 5) = 4
-2x + 5 = 4
-2x = -1
x = 1/2.
Therefore, the solutions are x = 1/2 and 9/2.
