![h(t)=-4.9t^{2}+34.3t+1 \\h'(t)=(-4.9t^{2}+34.3t+1)'=-9.8t+34.3 \\h'(t)=0 \\-9.8t+34.3=0 \\ \\t= \frac{34.3}{9.8} =3.5 \\ \\h_{max}=h(3.5)=-4.9\times3.5^{2}+34.3\times3.5+1=61.025](https://tex.z-dn.net/?f=h%28t%29%3D-4.9t%5E%7B2%7D%2B34.3t%2B1%0A%5C%5Ch%27%28t%29%3D%28-4.9t%5E%7B2%7D%2B34.3t%2B1%29%27%3D-9.8t%2B34.3%0A%5C%5Ch%27%28t%29%3D0%0A%5C%5C-9.8t%2B34.3%3D0%0A%5C%5C%0A%5C%5Ct%3D%20%5Cfrac%7B34.3%7D%7B9.8%7D%20%3D3.5%0A%5C%5C%0A%5C%5Ch_%7Bmax%7D%3Dh%283.5%29%3D-4.9%5Ctimes3.5%5E%7B2%7D%2B34.3%5Ctimes3.5%2B1%3D61.025)
The ball reaches its maximum height after 3.5 seconds, and the maximum height is 61.025 meters.
Answer:
non-linear: C, E, F
Step-by-step explanation:
Choices A, B, D are linear functions, so the rest are non-linear: C, E, F
the system has no solution.
Option C is correct.
Step-by-step explanation:
We need to solve the system of equations by substitution
![x - y = 6\,\,\,eq(1)\\x = y + 2\,\,\,eq(2)](https://tex.z-dn.net/?f=x%20-%20y%20%3D%206%5C%2C%5C%2C%5C%2Ceq%281%29%5C%5Cx%20%3D%20y%20%2B%202%5C%2C%5C%2C%5C%2Ceq%282%29)
Putting value of x from eq(2) into eq(1)
![(y+2)-y=6\\y+2-y=6\\0+2=6\\0=6-2\\0\neq4](https://tex.z-dn.net/?f=%28y%2B2%29-y%3D6%5C%5Cy%2B2-y%3D6%5C%5C0%2B2%3D6%5C%5C0%3D6-2%5C%5C0%5Cneq4)
As as 0≠4is not true, we cannot find the value of y so the system has no solution.
Option C is correct.
Keywords: System of equations
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Answer:
The system of the equations has no solution; the two lines are parallel.
Step-by-step explanation:
The equations have the same slope. In standard form, this can be seen as the same coefficients for x and y. We will multiply the second equation by -12 to reveal this.
![\frac{1}{4} x-\frac{1}{3}y=1 \\-12(\frac{1}{4} x-\frac{1}{3}y=1)\\\frac{-12}{4} x-\frac{-12}{3}y=-12\\-3x+4y=-12](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20x-%5Cfrac%7B1%7D%7B3%7Dy%3D1%20%5C%5C-12%28%5Cfrac%7B1%7D%7B4%7D%20x-%5Cfrac%7B1%7D%7B3%7Dy%3D1%29%5C%5C%5Cfrac%7B-12%7D%7B4%7D%20x-%5Cfrac%7B-12%7D%7B3%7Dy%3D-12%5C%5C-3x%2B4y%3D-12)
This means the equations are parallel and will never cross. There is no solution.
Answer:
There are no expressions provided in the question.