What number is 312% of 10.5
2 answers:
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<h2>Steps:</h2>
So firstly, since we know that the coefficient of x² is 1, this means that this is our base equation:
y = x² + bx + c
Now, since we know that the roots are -7 and 1, set y = 0 and set x = -7 and 1 and simplify:
Now with this, we can set up a system of equations to solve for b and c. For this, I will be using the elimination method. For this, subtract the 2 equations:
Now that the c variable has been eliminated we can solve for b. For this, divide both sides by -8 and your first part of your answer is b = 6.
Now that we know the value of b, plug it into either equation to solve for c:
<u>Putting it together, your final answer is x² + 6x - 7 = 0.</u>
I will attach google sheet that I used to find regression equation.
We can see that linear fit does work, but the polynomial fit is much better.
We can see that R squared for polynomial fit is higher than R squared for the linear fit. This tells us that polynomials fit approximates our dataset better.
This is the polynomial fit equation:
I used h to denote hours. Our prediction of temperature for the sixth hour would be:
Here is a link to the spreadsheet (<span>https://docs.google.com/spreadsheets/d/17awPz5U8Kr-ZnAAtastV-bnvoKG5zZyL3rRFC9JqVjM/edit?usp=sharing)</span>
We can see that linear fit does work, but the polynomial fit is much better.
We can see that R squared for polynomial fit is higher than R squared for the linear fit. This tells us that polynomials fit approximates our dataset better.
This is the polynomial fit equation:
I used h to denote hours. Our prediction of temperature for the sixth hour would be:
Here is a link to the spreadsheet (<span>https://docs.google.com/spreadsheets/d/17awPz5U8Kr-ZnAAtastV-bnvoKG5zZyL3rRFC9JqVjM/edit?usp=sharing)</span>
You can solve this analytically to get
.. 55000*(1 +x/100)^10 = 108193
.. (1 +x/100)^10 = 108193/55000
.. 1 +x/100 = (108193/55000)^(1/10)
.. x = 100*((108193/55000)^(1/10) -1) ≈ 7.00
but I find it just as fast to have a graphing calculator do it.
The city's population is increasing 7% per year.
.. 55000*(1 +x/100)^10 = 108193
.. (1 +x/100)^10 = 108193/55000
.. 1 +x/100 = (108193/55000)^(1/10)
.. x = 100*((108193/55000)^(1/10) -1) ≈ 7.00
but I find it just as fast to have a graphing calculator do it.
The city's population is increasing 7% per year.