add d to both sides
c(a+b) = f + d
divide away c
a+b = (f+d)/c
subtract b from both sides:
a=[(f+d)/c]-b
here's the solution,
first term (a) = -5x
common difference (d) = (8x + 4) - (-5x - 1)
= 13x + 5
now, we know,
=》
![nth \: term = a + (n - 1) \times d](https://tex.z-dn.net/?f=nth%20%5C%3A%20term%20%3D%20a%20%2B%20%28n%20-%201%29%20%5Ctimes%20d)
=》
![11th \: \: term = - 5x + (11 - 1) \times (13x + 5)](https://tex.z-dn.net/?f=11th%20%5C%3A%20%20%5C%3A%20term%20%20%3D%20%20-%205x%20%2B%20%2811%20-%201%29%20%5Ctimes%20%2813x%20%2B%205%29)
=》
![11th \: \: term = - 5x + 130x + 50](https://tex.z-dn.net/?f=11th%20%5C%3A%20%20%5C%3A%20term%20%20%3D%20%20-%205x%20%2B%20130x%20%2B%2050)
=》
![11th \: \: term = 125x + 50](https://tex.z-dn.net/?f=11th%20%5C%3A%20%20%5C%3A%20term%20%20%3D%20125x%20%2B%2050)
Answer:
4 meters
Step-by-step explanation:
Given a quadratic equation in which the coefficient of
is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.
Since the divers height, y is modeled by the equation
![y= -x^2 + 2x + 3](https://tex.z-dn.net/?f=y%3D%20-x%5E2%20%2B%202x%20%2B%203)
Step 1: Determine the equation of symmetry
In the equation above, a=-1, b=2, c=3
Equation of symmetry, ![x=-\dfrac{b}{2a}](https://tex.z-dn.net/?f=x%3D-%5Cdfrac%7Bb%7D%7B2a%7D)
![x=-\dfrac{2}{2*-1}\\x=1](https://tex.z-dn.net/?f=x%3D-%5Cdfrac%7B2%7D%7B2%2A-1%7D%5C%5Cx%3D1)
Step 2: Find the value of y at the point of symmetry
That is, we substitute x obtained above into the y and solve.
![y(1)= -1^2 + 2(1) + 3=-1+2+3=4m](https://tex.z-dn.net/?f=y%281%29%3D%20-1%5E2%20%2B%202%281%29%20%2B%203%3D-1%2B2%2B3%3D4m)
The maximum height of the diver is therefore 4 meters.