Answer:
D
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant
Using the distance formula
= | y + 1 |
Squaring both sides
(x + 5)² + (y - 5)² = (y + 1)^2 , that is
(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides
(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify
y² + 2y + 1 - y² + 10y - 25 = (x + 5)²
12y - 24 = (x + 5)² ← factor left side
12(y - 2) = (x + 5)² ← divide both sides by 12
y - 2 = 
(x + 5)² ← add 2 to both sides
y = (x + 5)² + 2
or
f(x) = (x + 5)² + 2 → D
We know, Circumference of a Circle = 2πr
In mathematical form, You can write it as:
2πr₁ = 3(2πr₂)
2π(12) = 6πr₂
24π = 6πr₂
r₂ = 4 m
In short, Your Answer would be: 4 meter
Hope this helps!
Answer:
Step-by-step explanation:
Before we find x, we need to set up this triangle a little more. We need to find the triangle's altitude before we can solve for x. We will use the heartbeat method to find the altitude.
Let altitude = y; solve for y:
Now that we know the altitude, we can use the Pythagorean Theorem to find the hypotenuse (x).
Since c and x are the same; c is just the hypotenuse in the Pythagorean Theorem.
Answer:
y = 3
Step-by-step explanation:
We need to find the slope. We do so by choosing any two points and dividing the change in the y-coordinates (their difference) by the change in the x-coordinates (their difference). Let's just choose (1, 3) and (0, 3). The slope is: . So, the slope is 0.
We want to write a line in slope-intercept form, which is: y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis). Here, the slope m = 0. Looking at the graph, we see that the y-intercept is (0, 3), so b = 3. Then, our line is: y = 0x + 3 ⇒ y = 3.
Another note is that this is a horizontal line. One thing to remember is that all horizontal lines have slopes of 0, so their function is simply y = k, where k is a constant through which the line cuts through.
Answer:
Step-by-step explanation:
