Answer:
A. (-∞ , 0)
B. x = 0 triple root
C. The function tends to infinity
Step-by-step explanation:
For the function f(x) = x^3 we have:
Negative intervals:
(-∞ , 0)
The roots of this function is:
x = 0
The final behavior of this function tends toward infinity
A graphic is attached below
For this problem, we are given the graph of an ellipse, and we need to determine its expression in the standard form.
The standard equation of an ellipse is given below:
![\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D%2B%5Cfrac%7B%28y-k%29%5E2%7D%7Bb%5E2%7D%3D1)
Where (h,k) is the center of the ellipse, a is the horizontal radius and b is the vertical radius.
The center of the ellipse on our problem is (-2,2), the vertical radius is 2 and the horizontal radius is 3. We have:
![\begin{gathered} \frac{(x+2)^2}{3^2}+\frac{(y-2)^2}{2^2}=1 \\ \frac{(x+2)^2}{9}+\frac{(y-2)^2}{4}=1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%28x%2B2%29%5E2%7D%7B3%5E2%7D%2B%5Cfrac%7B%28y-2%29%5E2%7D%7B2%5E2%7D%3D1%20%5C%5C%20%5Cfrac%7B%28x%2B2%29%5E2%7D%7B9%7D%2B%5Cfrac%7B%28y-2%29%5E2%7D%7B4%7D%3D1%20%5Cend%7Bgathered%7D)
In order to calculate the Foci, we need to first find the eccentricity of the ellipse, which is given by the following formula:
![\begin{gathered} e=\sqrt{a^2-b^2} \\ e=\sqrt{3^2-2^2} \\ e=\sqrt{9-4}=\sqrt{5} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20e%3D%5Csqrt%7Ba%5E2-b%5E2%7D%20%5C%5C%20e%3D%5Csqrt%7B3%5E2-2%5E2%7D%20%5C%5C%20e%3D%5Csqrt%7B9-4%7D%3D%5Csqrt%7B5%7D%20%5Cend%7Bgathered%7D)
The coordinates of the foci are given by:
![\begin{gathered} F(h+e,k)=(-2-\sqrt{5},2) \\ F^{\prime}(h-e,k)=(-2+\sqrt{5},2) \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20F%28h%2Be%2Ck%29%3D%28-2-%5Csqrt%7B5%7D%2C2%29%20%5C%5C%20F%5E%7B%5Cprime%7D%28h-e%2Ck%29%3D%28-2%2B%5Csqrt%7B5%7D%2C2%29%20%5Cend%7Bgathered%7D)
The coordinates for the foci are: (-2-sqrt(5), 2) and (-2+sqrt(5), 2).
Answer: DB=31.66and EC=49.32
Step-by-step explanation:
Hello :
<span>−5x+cy=−5
cy = 5x - 5.... </span> whether there exists a constant c : c <span>≠0
y = (5/c)x - 5/c.... form : y ax+b a is the slope
the slope is : (5/c)
5/c = - 6
c = -5/6</span>