Answer:
Step-by-step explanation:
![y'' + y' − 2y = 0, y(0) = a, y' (0) = 1](https://tex.z-dn.net/?f=y%27%27%20%2B%20y%27%20%E2%88%92%202y%20%3D%200%2C%20y%280%29%20%3D%20a%2C%20y%27%20%280%29%20%3D%201)
Auxialary equation is
![m^2+m-2=0\\m=-2,1](https://tex.z-dn.net/?f=m%5E2%2Bm-2%3D0%5C%5Cm%3D-2%2C1)
General solution is
![y=Ae^{-2x} +Be^x](https://tex.z-dn.net/?f=y%3DAe%5E%7B-2x%7D%20%2BBe%5Ex)
![y(0) = A+B =a](https://tex.z-dn.net/?f=y%280%29%20%3D%20A%2BB%20%3Da)
![y'(0) = -2Ae^{2x} +Be^x = -2A+B = 1](https://tex.z-dn.net/?f=y%27%280%29%20%3D%20-2Ae%5E%7B2x%7D%20%2BBe%5Ex%20%3D%20-2A%2BB%20%3D%201)
Eliminate B to get
3A =a-1
We know that y tends to 0 when x tends to infinity for any finite A
i.e. a should be a finite real number.
The answer is 10, you would multiply 8 by 2 because 8 represents N , it would be 16-6
Answer: OPTION A.
Step-by-step explanation:
Given the following function:
![h(x)=-\frac{1}{4}x^2+\frac{1}{2}x+\frac{1}{2}](https://tex.z-dn.net/?f=h%28x%29%3D-%5Cfrac%7B1%7D%7B4%7Dx%5E2%2B%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B1%7D%7B2%7D)
You know that it represents the the height of the ball (in meters) when it is a distance "x" meters away from Rowan.
Since it is a Quadratic function its graph is parabola.
So, the maximum point of the graph modeling the height of the ball is the Vertex of the parabola.
You can find the x-coordinate of the Vertex with this formula:
![x=\frac{-b}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%7D%7B2a%7D)
In this case:
![a=-\frac{1}{4}\\\\b=\frac{1}{2}](https://tex.z-dn.net/?f=a%3D-%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5Cb%3D%5Cfrac%7B1%7D%7B2%7D)
Then, substituting values, you get:
![x=\frac{-\frac{1}{2}}{(2)(-\frac{1}{4}))}\\\\x=1](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7B%282%29%28-%5Cfrac%7B1%7D%7B4%7D%29%29%7D%5C%5C%5C%5Cx%3D1)
Finally, substitute the value of "x" into the function in order to get the y-coordinate of the Vertex:
Therefore, you can conclude that:
<em> The maximum height of the ball is 0.75 of a meter, which occurs when it is approximately 1 meter away from Rowan.</em>
Answer:
I am not 100% about this, but I think that Z=46 Y=30 and X=45
Step-by-step explanation:
Answer:
<u>The correct answer is 15.72 or 6 ∛18</u>
Step-by-step explanation:
Let's calculate the cube root of 216 * 18
∛(216 * 18)
216 = 8 * 27
8 = 2³; 27 = 3³
18 = 9 * 2 or 3² * 2
∛(8 * 27 * 18)
Simplifying:
∛(2³ * 3³ * 3² * 2)
∛(2³ * 3³ * 3² * 2)
2 * 3 ∛(3² * 2
<u>6 * 2.62 = 15.72 or 6 ∛18</u>