Answer:
the sum of the values should be -14
Step-by-step explanation:
-12+3-5=-14
Answer:
Step-by-step explanation:
Answer:
Since
, the superhero makes it over the building.
Step-by-step explanation:
The height is given by the following function:
![f(x) = -16x^{2} + 200x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-16x%5E%7B2%7D%20%2B%20200x)
Will the superhero make it over the building?
We have to find if there is values of x for which f(x) = 612.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:
![x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D)
![x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20%5Cfrac%7B-b%20-%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D)
![\bigtriangleup = b^{2} - 4ac](https://tex.z-dn.net/?f=%5Cbigtriangleup%20%3D%20b%5E%7B2%7D%20-%204ac)
If
, the polynomial has no solutions.
In this question:
![f(x) = -16x^{2} + 200x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-16x%5E%7B2%7D%20%2B%20200x)
![-16x^{2} + 200x = 612](https://tex.z-dn.net/?f=-16x%5E%7B2%7D%20%2B%20200x%20%3D%20612)
![16x^{2} - 200x + 612 = 0](https://tex.z-dn.net/?f=16x%5E%7B2%7D%20-%20200x%20%2B%20612%20%3D%200)
We have to find ![\bigtriangleup](https://tex.z-dn.net/?f=%5Cbigtriangleup)
We have that
. So
![\bigtriangleup = (-200)^{2} - 4*16*612 = 832](https://tex.z-dn.net/?f=%5Cbigtriangleup%20%3D%20%28-200%29%5E%7B2%7D%20-%204%2A16%2A612%20%3D%20832)
Since
, the superhero makes it over the building.
Yes it would be cause it has a constant rate of change
If
is the first number in the progression, and
is the common ratio between consecutive terms, then the first four terms in the progression are
![\{x,xr,xr^2,xr^3\}](https://tex.z-dn.net/?f=%5C%7Bx%2Cxr%2Cxr%5E2%2Cxr%5E3%5C%7D)
We want to have
![\begin{cases}xr^2-x=12\\xr^3-xr=36\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dxr%5E2-x%3D12%5C%5Cxr%5E3-xr%3D36%5Cend%7Bcases%7D)
In the second equation, we have
![xr^3-xr=xr(r^2-1)=36](https://tex.z-dn.net/?f=xr%5E3-xr%3Dxr%28r%5E2-1%29%3D36)
and in the first, we have
![xr^2-x=x(r^2-1)=12](https://tex.z-dn.net/?f=xr%5E2-x%3Dx%28r%5E2-1%29%3D12)
Substituting this into the second equation, we find
![xr(r^2-1)=12r=36\implies r=3](https://tex.z-dn.net/?f=xr%28r%5E2-1%29%3D12r%3D36%5Cimplies%20r%3D3)
So now we have
![\begin{cases}9x-x=12\\27x-3x=36\end{cases}\implies x=\dfrac32](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D9x-x%3D12%5C%5C27x-3x%3D36%5Cend%7Bcases%7D%5Cimplies%20x%3D%5Cdfrac32)
Then the four numbers are
![\left\{\dfrac32,\dfrac92,\dfrac{27}2,\dfrac{81}2\right\}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cdfrac32%2C%5Cdfrac92%2C%5Cdfrac%7B27%7D2%2C%5Cdfrac%7B81%7D2%5Cright%5C%7D)