Given:
The height of a golf ball is represented by the equation:
![y=x-0.04x^2](https://tex.z-dn.net/?f=y%3Dx-0.04x%5E2)
To find:
The maximum height of of Anna's golf ball.
Solution:
We have,
![y=x-0.04x^2](https://tex.z-dn.net/?f=y%3Dx-0.04x%5E2)
Differentiate with respect to x.
![y'=1-0.04(2x)](https://tex.z-dn.net/?f=y%27%3D1-0.04%282x%29)
![y'=1-0.08x](https://tex.z-dn.net/?f=y%27%3D1-0.08x)
For critical values,
.
![1-0.08x=0](https://tex.z-dn.net/?f=1-0.08x%3D0)
![-0.08x=-1](https://tex.z-dn.net/?f=-0.08x%3D-1)
![x=\dfrac{-1}{-0.08}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-1%7D%7B-0.08%7D)
![x=12.5](https://tex.z-dn.net/?f=x%3D12.5)
Differentiate y' with respect to x.
![y''=(0)-0.08(1)](https://tex.z-dn.net/?f=y%27%27%3D%280%29-0.08%281%29)
![y''=-0.08](https://tex.z-dn.net/?f=y%27%27%3D-0.08)
Since double derivative is negative, the function is maximum at
.
Substitute
in the given equation to get the maximum height.
![y=(12.5)-0.04(12.5)^2](https://tex.z-dn.net/?f=y%3D%2812.5%29-0.04%2812.5%29%5E2)
![y=12.5-0.04(156.25)](https://tex.z-dn.net/?f=y%3D12.5-0.04%28156.25%29)
![y=12.5-6.25](https://tex.z-dn.net/?f=y%3D12.5-6.25)
![y=6.25](https://tex.z-dn.net/?f=y%3D6.25)
Therefore, the maximum height of of Anna's golf ball is 6.25 units.
Answer:
Step-by-step explanation:
5n-53
Hope it helps
Mark me as brainiest pls begging you
Answer:
5
Step-by-step explanation:
First figure out the equation:
We know this is a linear equation because it appears to have a constant slope
Its y-intercept is where it passes in the y-axis, so it's -8
Furthermore, you should also figure out the slope. Notice that the y value increments by 3 every 1 x-value. Rise/Run is 3/1 = 3. Thus, the slope is 3
So your equation is g(x) = 3x - 8
Now we find our inverse function, which is just swapping the x-y values.
Thus, inverse of g(x) ==> y = 3x - 8 ==> x = 3y - 8 ==> x+8 = 3y ==> ![\frac{x+8}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B8%7D%7B3%7D)
Plug in 7 for x and you get 5
210/35% in the calculator it’s 135.50
Relationship is going to work out so 72728