please help me to find the Q value…. Transcribed Image Text: Tc = l00+ 5Q+ -5Q- 180 Q² ginen function. ?c= lo0 t 5 Q to Q -2 480Q² + (5)Q’-+ (-2)Q O-1 -2-1 mQ = marginal Revenue marginal 480 = o + sQ t Q (-2 480 -3 Tc=Toral ecof l = 5Q- Q MC- 240 MR =TC 30 50-%0 -3 5Q-Q fomr nd, 240 50 5Q Q to 240 30 what is answer for Q ? plzase expluin. explnin.
To find the value of Q, we need to solve the given equation: Tc = 100 + 5Q – 5Q².
Let’s rearrange the equation to obtain a quadratic equation in terms of Q:
-5Q² + 5Q + 100 – Tc = 0 (Equation 1)
To find the Q value, we need to solve this quadratic equation. We can use various methods such as factoring, completing the square, or using the quadratic formula.
In this case, the quadratic equation is not easily factorable, so we will use the quadratic formula:
Q = (-b ± √(b² – 4ac)) / (2a)
Comparing Equation 1 with the general quadratic equation (ax² + bx + c = 0), we can identify that a = -5, b = 5, and c = 100 – Tc.
Substituting these values into the quadratic formula, we have:
Q = (-(5) ± √((5)² – 4(-5)(100 – Tc))) / (2(-5))
Simplifying the equation further:
Q = (-5 ± √(25 + 20(100 – Tc))) / -10
Q = (-5 ± √(25 + 2000 – 20Tc)) / -10
Q = (-5 ± √(2025 – 20Tc)) / -10
Q = (-5 ± √(2025 – 20Tc)) / -10
Now let’s simplify the expression inside the square root:
2000 – 20Tc = 20(100 – Tc)
2000 – 20Tc = 2000 – 20Tc
Since the equation simplifies to 0 = 0, we can conclude that the expression inside the square root is equal to 0, which means we have a single real root for Q.
Now, we have:
Q = (-5 ± √0) / -10
Since the square root of 0 is 0, we get:
Q = (-5 ± 0) / -10
Q = -5 / -10
Q = 1/2
Hence, the value of Q is 1/2.
To explain the process, we started with the given equation for Tc and rearranged it to obtain a quadratic equation. We then used the quadratic formula to solve the equation and find the value of Q. By simplifying the expression inside the square root, we identified that it is equal to 0, which resulted in a single real root. Finally, we calculated the value of Q as 1/2.