Answer:
the car would have to be going under 5mph
Step-by-step explanation:
Answer:
y = 3(x + 2) + 2 and y = -3(x + 2) + 2
Step-by-step explanation:
* Lets revise the equation of the hyperbola with center (h , k) and
transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1
- The coordinates of the vertices are (h , k ± a)
- The coordinates of the co-vertices are (h ± b , k)
- The coordinates of the foci are (h , k ± c) where c² = a² + b²
- The equations of the asymptotes are ± a/b (x - h) + k
* Lets solve the problem
∵ The equation of the hyperbola is (y - 2)²/9 - (x + 2)² = 1
∵ The form of the equation is (y - k)²/a² - (x - h)²/b² = 1
∴ h = -2 , k = 2
∴ a² = 9
∴ a = √9 = 3
∴ b² = 1
∴ b = √1 = 1
∵ The equations of the asymptotes are y = ± a/b (x - h) + k
∴ The equations of the asymptotes are y = ± 3/1 (x - -2) + 2
∴ The equations of the asymptotes are y = ± 3 (x + 2) + 2
* The equations of the asymptotes of the hyperbola are
y = 3(x + 2) + 2 and y = -3(x + 2) + 2
Answer:
y = 3x -1
Step-by-step explanation:
It is convenient to choose two points that have x-values 1 unit apart when computing the slope of the line (m). Here, we choose the points (-1, -4) and (0, -1).
... m = (change in y)/(change in x) = (-1-(-4))/(0-(-1)) = 3/1 = 3
The point (0, -1) tells you that the y-intercept (b) is -1.
Now you have the information you need to fill in y = mx + b:
... y = 3x -1
To determine the centroid, we use the equations:
x⁻ =
1/A (∫ (x dA))
y⁻ = 1/A (∫ (y dA))
First, we evaluate the value of A and dA as follows:
A = ∫dA
A = ∫ydx
A = ∫3x^2 dx
A = 3x^3 / 3 from 0 to 4
A = x^3 from 0 to 4
A = 64
We use the equations for the centroid,
x⁻ = 1/A (∫ (x dA))
x⁻ = 1/64 (∫ (x (3x^2 dx)))
x⁻ = 1/64 (∫ (3x^3 dx)
x⁻ = 1/64 (3 x^4 / 4) from 0 to 4
x⁻ = 1/64 (192) = 3
y⁻ = 1/A (∫ (y dA))
y⁻ = 1/64 (∫ (3x^2 (3x^2 dx)))
y⁻ = 1/64 (∫ (9x^4 dx)
y⁻ = 1/64 (9x^5 / 5) from 0 to 4
y⁻ = 1/64 (9216/5) = 144/5
The centroid of the curve is found at (3, 144/5).