For these questions to be true and the equation of the tangent to have an equal y to the equation of the parabola i guess there has to be a "c" and in that case integrate the equation of the tangent you will have a = 5 and b = -18 then you substitute in the equation of the parabola with the point you have you will find that "c" = 21 and so the equation of the parabola becomes y = 5x^2 - 18 x +21
Answer:
James is 58 and Tyson is 39 years old.
Step-by-step explanation:
x + y = 97
x - y = 19 +
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2x = 116
x = 58
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y = 97 - 58
y = 39
Answer:
50 in total, 45 were eaten
Step-by-step explanation:
If there's only 10% left and 10% is 5 cookies, then that means for every 10% is 5 cookies so 90 x 5 = 45
I'm guessing the repeating part is 89 at the end, so that
![x=0.8967\overline89\implies10^4x=8967.\overline{89}](https://tex.z-dn.net/?f=x%3D0.8967%5Coverline89%5Cimplies10%5E4x%3D8967.%5Coverline%7B89%7D)
Then
![10^4x=8967+\displaystyle89\sum_{i=1}^\infty\frac1{100^i}](https://tex.z-dn.net/?f=10%5E4x%3D8967%2B%5Cdisplaystyle89%5Csum_%7Bi%3D1%7D%5E%5Cinfty%5Cfrac1%7B100%5Ei%7D)
![10^4x=8967+89\left(\dfrac1{1-\frac1{100}}-1\right)](https://tex.z-dn.net/?f=10%5E4x%3D8967%2B89%5Cleft%28%5Cdfrac1%7B1-%5Cfrac1%7B100%7D%7D-1%5Cright%29)
![10^4x=8967+\dfrac{89}{99}](https://tex.z-dn.net/?f=10%5E4x%3D8967%2B%5Cdfrac%7B89%7D%7B99%7D)
![x=\dfrac{8967}{10^4}+\dfrac{89}{99\cdot10^4}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B8967%7D%7B10%5E4%7D%2B%5Cdfrac%7B89%7D%7B99%5Ccdot10%5E4%7D)
![x=\dfrac{443911}{495000}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B443911%7D%7B495000%7D)
###
An arguably quicker way without using geometric series:
![10^4x=8967.\overline{89}](https://tex.z-dn.net/?f=10%5E4x%3D8967.%5Coverline%7B89%7D)
![10^6x=896789.\overline{89}](https://tex.z-dn.net/?f=10%5E6x%3D896789.%5Coverline%7B89%7D)
![10^6x-10^4x=887822](https://tex.z-dn.net/?f=10%5E6x-10%5E4x%3D887822)
![x=\dfrac{887822}{10^6-10^4}=\dfrac{443911}{495000}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B887822%7D%7B10%5E6-10%5E4%7D%3D%5Cdfrac%7B443911%7D%7B495000%7D)