To find the average change per hour, divide the total change by the total time:
-9.9 inches / 2.25 hours = -4.4 inches per hour.
Completing the squares tells us exactly what square root we will need to calculate our answer.
Using the formula below you can find these answers:
![A(x-h)^2 + K = 0 (x-5)^ 2 = - K/A ](https://tex.z-dn.net/?f=A%28x-h%29%5E2%20%2B%20K%20%3D%200%0A%28x-5%29%5E%202%20%3D%20-%20K%2FA%0A)
Does this make sense?
9514 1404 393
Answer:
34
Step-by-step explanation:
The graph shows the vertex of the feasible region that is farthest from the origin is (2, 4). These are the values of (x, y) that maximize P.
P = 5(2) +6(4) = 10 +24 = 34
The maximum value of P is 34.
_____
<em>Additional comment</em>
The feasible region is entirely contained within the first quadrant. We have left off the x ≥ 0 and y ≥ 0 constraints to leave the inequalities uncomplicated.
The graph shows the line 34 = 5x +6y so you can see that it only intersects the feasible region (doubly-shaded area) at the vertex where the objective function is maximized.
Answer:
<h3> 1.)
![x_1=\dfrac{7+\sqrt{13}}{2}\,,\qquad x_2=\dfrac{7-\sqrt{13}}{2}](https://tex.z-dn.net/?f=x_1%3D%5Cdfrac%7B7%2B%5Csqrt%7B13%7D%7D%7B2%7D%5C%2C%2C%5Cqquad%20x_2%3D%5Cdfrac%7B7-%5Csqrt%7B13%7D%7D%7B2%7D)
</h3><h3> 2.)
![x_1=-\dfrac13\,,\qquad x_2=-3](https://tex.z-dn.net/?f=x_1%3D-%5Cdfrac13%5C%2C%2C%5Cqquad%20x_2%3D-3)
</h3>
Step-by-step explanation:
1.)
![x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b=-7\,,\ c = 9\\\\\\x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{7\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}{2}\\\\x_1=\dfrac{7+\sqrt{13}}{2}\,,\qquad x_2=\dfrac{7-\sqrt{13}}{2}](https://tex.z-dn.net/?f=x%5E2%20-%207x%20%2B%209%20%3D%200%5Cquad%5Cimplies%5Cquad%20a%3D1%5C%2C%2C%5C%20b%3D-7%5C%2C%2C%5C%20c%20%3D%209%5C%5C%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B7%5Cpm%5Csqrt%7B%28-7%29%5E2-4%5Ccdot1%5Ccdot9%7D%7D%7B2%5Ccdot1%7D%3D%5Cdfrac%7B7%5Cpm%5Csqrt%7B49-36%7D%7D%7B2%7D%5C%5C%5C%5Cx_1%3D%5Cdfrac%7B7%2B%5Csqrt%7B13%7D%7D%7B2%7D%5C%2C%2C%5Cqquad%20x_2%3D%5Cdfrac%7B7-%5Csqrt%7B13%7D%7D%7B2%7D)
2.)
![3x^2 + 10x = -3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b=10\,,\ c = 3\\\\\\x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-10\pm\sqrt{10^2-4\cdot3\cdot3}}{2\cdot3}=\dfrac{-10\pm\sqrt{100-36}}{6}=\dfrac{-10\pm\sqrt{64}}{6}\\\\x_1=\dfrac{-10+8}{6}=\dfrac{-2}6=-\dfrac13\,,\qquad x_2=\dfrac{-10-8}{6}=\dfrac{-18}{6}=-3](https://tex.z-dn.net/?f=3x%5E2%20%2B%2010x%20%3D%20-3%5C%5C%5C%5C3x%5E2%2B10x%2B3%3D0%5Cquad%5Cimplies%5Cquad%20a%3D3%5C%2C%2C%5C%20b%3D10%5C%2C%2C%5C%20c%20%3D%203%5C%5C%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-10%5Cpm%5Csqrt%7B10%5E2-4%5Ccdot3%5Ccdot3%7D%7D%7B2%5Ccdot3%7D%3D%5Cdfrac%7B-10%5Cpm%5Csqrt%7B100-36%7D%7D%7B6%7D%3D%5Cdfrac%7B-10%5Cpm%5Csqrt%7B64%7D%7D%7B6%7D%5C%5C%5C%5Cx_1%3D%5Cdfrac%7B-10%2B8%7D%7B6%7D%3D%5Cdfrac%7B-2%7D6%3D-%5Cdfrac13%5C%2C%2C%5Cqquad%20x_2%3D%5Cdfrac%7B-10-8%7D%7B6%7D%3D%5Cdfrac%7B-18%7D%7B6%7D%3D-3)
q<13
Step-by-step explanation:
2q is less than 26 so 1q has to be less than half of 26 or 13.
q<13