the answer will be -0.8, if i helped thank you
Answer:
x = 3/8 +/- i(√5)/8.
Step-by-step explanation:
I can't see any list by this is the solution of the equation:
x^2 - 3/4x = -1/4
x^2 - 3/4 x + 1/4 = 0
Multiply by 4 to remove the fractions:
4x^2 - 3x + 1 = 0
x = [-(-3) +/- sqrt(3)^2 - 4*4*1)] / 8
x = 3/8 +/-√ (-5) / 8
x = 3/8 +/- √5 i / 8
We have a circumference that is given by the following equation:
We can write this equation in its standard form as follows:
On the other hand, the linear function is given as the following table:
![x \ \ \ \ \ \ \ \ g(x) \\ -1 \ \ -9.2 \\ 0 \ \ \ \ \ -9 \\ 1 \ \ \ \ \ -8.8](https://tex.z-dn.net/?f=x%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20g%28x%29%20%5C%5C%20-1%20%5C%20%5C%20-9.2%20%5C%5C%200%20%5C%20%5C%20%5C%20%5C%20%5C%20-9%20%5C%5C%201%20%5C%20%5C%20%5C%20%5C%20%5C%20-8.8)
To check if the circle and the line intersects, let's substitute the equation of the line into the equation of the circle to see if there is a real solution, so:
![x^{2}+(0.2x-9)^{2}=49 \\ \\ \therefore x^{2}+0.04x^{2}-3.6x+81=49 \\ \\ \therefore 1.04x^{2}-36x+32=0 \\ \\ Solving \ for \ x: \\ x_{1}=33.70 \\ x_{2}=0.91 \\ \\ Solving \ for \ y: \\ y_{1}=0.2(33.70)-9=-2.26 \\ y_{2}=0.2(0.91)-9=-8.18](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B%280.2x-9%29%5E%7B2%7D%3D49%20%5C%5C%20%5C%5C%20%5Ctherefore%20x%5E%7B2%7D%2B0.04x%5E%7B2%7D-3.6x%2B81%3D49%20%5C%5C%20%5C%5C%20%5Ctherefore%201.04x%5E%7B2%7D-36x%2B32%3D0%20%5C%5C%20%5C%5C%20Solving%20%5C%20for%20%5C%20x%3A%20%5C%5C%20x_%7B1%7D%3D33.70%20%5C%5C%20x_%7B2%7D%3D0.91%20%5C%5C%20%5C%5C%20Solving%20%5C%20for%20%5C%20y%3A%20%5C%5C%20y_%7B1%7D%3D0.2%2833.70%29-9%3D-2.26%20%5C%5C%20y_%7B2%7D%3D0.2%280.91%29-9%3D-8.18)
Finally the intersects are:
![P_{1}(33.70, -2.26) \ and \ P_{2}(0.91, -8.18)](https://tex.z-dn.net/?f=P_%7B1%7D%2833.70%2C%20-2.26%29%20%5C%20and%20%5C%20P_%7B2%7D%280.91%2C%20-8.18%29)
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The amount of electricity required to run the manufacturing operations and lighting is given by: y = 12 x + 24.
When no parts are manufactured : x o= 0.
y o = 12 * 0 + 24
y o = 24
Answer:
( x o, y o ) = ( 0, 24 )
When no parts are manufactured, 24 watts is used ( only for lighting the facility ).