<span>The two points that are most distant from (-1,0) are
exactly (1/3, 4sqrt(2)/3) and (1/3, -4sqrt(2)/3)
approximately (0.3333333, 1.885618) and (0.3333333, -1.885618)
Rewriting to express Y as a function of X, we get
4x^2 + y^2 = 4
y^2 = 4 - 4x^2
y = +/- sqrt(4 - 4x^2)
So that indicates that the range of values for X is -1 to 1.
Also the range of values for Y is from -2 to 2.
Additionally, the ellipse is centered upon the origin and is symmetrical to both the X and Y axis.
So let's just look at the positive Y values and upon finding the maximum distance, simply reflect that point across the X axis. So
y = sqrt(4-4x^2)
distance is
sqrt((x + 1)^2 + sqrt(4-4x^2)^2)
=sqrt(x^2 + 2x + 1 + 4 - 4x^2)
=sqrt(-3x^2 + 2x + 5)
And to simplify things, the maximum distance will also have the maximum squared distance, so square the equation, giving
-3x^2 + 2x + 5
Now the maximum will happen where the first derivative is equal to 0, so calculate the first derivative.
d = -3x^2 + 2x + 5
d' = -6x + 2
And set d' to 0 and solve for x, so
0 = -6x + 2
-2 = -6x
1/3 = x
So the furthest point will be where X = 1/3. Calculate those points using (1) above.
y = +/- sqrt(4 - 4x^2)
y = +/- sqrt(4 - 4(1/3)^2)
y = +/- sqrt(4 - 4(1/9))
y = +/- sqrt(4 - 4/9)
y = +/- sqrt(3 5/9)
y = +/- sqrt(32)/sqrt(9)
y = +/- 4sqrt(2)/3
y is approximately +/- 1.885618</span>
<span>Sum of Interior Angles: Formula: (n-2) * 180
-Pentagon: 540</span>°<span>
-Hexagon: 720</span>°<span>
-Octagon: 900</span>°<span>
-Nonagon: 1260</span>°<span>
-Decagon: 1440</span>°<span>
-Dodecagon: 1800</span>°
Each interior Angle: Formula: [(n-2)*180] / n
-Pentagon: 108°
-Hexagon: 120°
-Octagon: 135°
-Nonagon: 140°
-Decagon: 144°
-Dodecagon: 150°
The sum of the exterior angles of each polygon stated above is equal to 360 degrees. Using the formula: (180-interior angle) * n
The central angle is formed by making a circle in the middle and divide it by the number of sides. Therefore, CA = 360 /n
-Pentagon: 72°
-Hexagon: 60°
-Octagon: 45°
-Nonagon: 40°
-Decagon: 36°
-Dodecagon: 30°
Answer:
D (2,0), (3,0)
Step-by-step explanation:
Sorry if it's wrong
Answer:
∆WUV⁓∆SRT
Step-by-step explanation:
Answer:
48 km/h
Step-by-step explanation:
80/50*30=48 km/h