Based on the given puzzle above by crafty grandma Edith and was answered by her six-year-old granddaughter, the correct answer would be 3. 9183 is equals to 3. Hope this is also the answer that you are looking for. Have a great day!
Answer: Vertical Stretch
Step-by-step explanation:
Given: The cost of manufacturing x refrigerators is given by the function :![f(x)=2x^2+6000](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2%2B6000)
If the cost doubles fr the year 2011 owing to higher raw material prices, then we multiply the given function by 2, then we get a new function :
which represents a vertical stretch in the graph.
∵ 2 is a positive constant greater than 1 which is multiplied to the parent function f(x). So by the definition of vertical stretch the parent function will be vertically stretched .
Lead and ski are adverbs, skier is the adjective.
Answer:
<em>The aircraft has a height of 1000 m at t=2 sec, and at t=8 sec</em>
Step-by-step explanation:
<u>Finding Exact Roots Of Polynomials</u>
A polynomial can be expressed in the general form
The roots of the polynomial are the values of x for which
![P(x)=0](https://tex.z-dn.net/?f=P%28x%29%3D0)
Finding the roots is not an easy task and trying to find a general solution has been discussed for centuries. One of the best possible approaches is trying to factor the polynomial. It requires a good eye and experience, but it gives excellent results.
The function for the trajectory of an aircraft is given by
![\displaystyle h(x)=0.5(-t^4+10t^3-216t^2+2000t-1200)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20h%28x%29%3D0.5%28-t%5E4%2B10t%5E3-216t%5E2%2B2000t-1200%29)
We need to find the values of t that make H=1000, that is
![\displaystyle 0.5(-t^4+10t^3-216t^2+2000t-1200)=1000](https://tex.z-dn.net/?f=%5Cdisplaystyle%200.5%28-t%5E4%2B10t%5E3-216t%5E2%2B2000t-1200%29%3D1000)
Dividing by -0.5
![\displaystyle t^4-10t^3+216t^2-2000t+1200=-2000](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%5E4-10t%5E3%2B216t%5E2-2000t%2B1200%3D-2000)
Rearranging, we set up the equation to solve
![\displaystyle t^4-10t^3+216t^2-2000t+3200=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%5E4-10t%5E3%2B216t%5E2-2000t%2B3200%3D0)
Expanding some terms
![\displaystyle t^4-8t^3-2t^3+200t^2+16t^2-1600t-400t+3200=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%5E4-8t%5E3-2t%5E3%2B200t%5E2%2B16t%5E2-1600t-400t%2B3200%3D0)
Rearranging
![\displaystyle t^4-8t^3+200t^2-1600t-2t^3+16t^2-400t+3200=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%5E4-8t%5E3%2B200t%5E2-1600t-2t%5E3%2B16t%5E2-400t%2B3200%3D0)
Factoring
![\displaystyle t(t^3-8t^2+200t-1600)-2(t^3-8t^2+200t-1600)=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%28t%5E3-8t%5E2%2B200t-1600%29-2%28t%5E3-8t%5E2%2B200t-1600%29%3D0)
![\displaystyle (t-2)(t^3-8t^2+200t-1600)=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28t-2%29%28t%5E3-8t%5E2%2B200t-1600%29%3D0)
This produces our first root t=2. Now let's factor the remaining polynomial
![\displaystyle t^2(t-8)+200(t-8)=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%5E2%28t-8%29%2B200%28t-8%29%3D0)
![\displaystyle (t^2+200)(t-8)=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28t%5E2%2B200%29%28t-8%29%3D0)
This gives us the second real root t=8. The other two roots are not real numbers, so we only keep two solutions
![\displaystyle t=2,\ t=8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%3D2%2C%5C%20t%3D8)