Answer:
angles are 80 and 100
Step-by-step explanation:
x is 20
n then solve for x
Answer:
a) p(x)=-0.0006x +21.6
b) $10.80
Step-by-step explanation:
a) Assuming that p(x) is linear, the slope can be found by:
![m=\frac{\$9-\$6}{21000-26000} \\m=-0.0006](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%5C%249-%5C%246%7D%7B21000-26000%7D%20%5C%5Cm%3D-0.0006)
Applying the point (21000; $9) to the general linear equation gives us the demand function:
![(p-p_0)=m(x-x_0)\\(p-9)=-0.0006(x-21,000)\\p(x)=-0.0006x +21.6](https://tex.z-dn.net/?f=%28p-p_0%29%3Dm%28x-x_0%29%5C%5C%28p-9%29%3D-0.0006%28x-21%2C000%29%5C%5Cp%28x%29%3D-0.0006x%20%2B21.6)
b) Revenue is given by the number of tickets sold multiplied by the price, the revenue function is:
![R(x) = xp(x)\\R(x) = -0.0006x^2 +21.6x](https://tex.z-dn.net/?f=R%28x%29%20%3D%20xp%28x%29%5C%5CR%28x%29%20%3D%20-0.0006x%5E2%20%2B21.6x)
The value of x for which the revenue function's derivate is zero is the number of spectators that yield the maximum revenue:
![\frac{dR(x)}{dx} = -0.0012x +21.6 = 0\\x=\frac{21.6}{0.0012}\\x= 18,000](https://tex.z-dn.net/?f=%5Cfrac%7BdR%28x%29%7D%7Bdx%7D%20%3D%20-0.0012x%20%2B21.6%20%3D%200%5C%5Cx%3D%5Cfrac%7B21.6%7D%7B0.0012%7D%5C%5Cx%3D%2018%2C000)
At x = 18,000, tickets price are:
![p(18,000)=-0.0006*18,000 +21.6\\p = \$10.80](https://tex.z-dn.net/?f=p%2818%2C000%29%3D-0.0006%2A18%2C000%20%2B21.6%5C%5Cp%20%3D%20%5C%2410.80)
What are the theorems we can use?
Probably the most relevant is the angle at a point on the circle subtended by a chord has a measure equal to half the arc indicated by the chord.
By the theorem,
angle AEB = angle ADB = (1/2) arc AC = (1/2) 110 = 55 deg
angle BAE = angle DBE = (1/2) arc DE = (1/2) 130 = 65 deg
angle BKD + angle KDB + angle DBK = 180 deg
angle BKD + angle ADB + angle DBE = 180 deg
angle BKD = 180 - 55 - 65 = 60 degrees
Answer: 60 degrees
Cancel x^2
Divide by 4
9/(16y)
640
128 = 1 gallon times 5 equals 640