Since opening night, attendance at Play A has increased steadily, while Play B first rose then fell. Equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. On what day(s) was the attendance the same at both plays and what was the attendance?
To find the day(s) when the attendance was the same at both plays, we need to set the attendance equations equal to each other and solve for x.
The equation for Play A is: y = ax + b
The equation for Play B is: y = cx^2 + dx + e
Setting these equations equal to each other, we have:
ax + b = cx^2 + dx + e
Rearranging the terms to form a quadratic equation:
cx^2 + (d - a)x + (e - b) = 0
Now we can solve this quadratic equation to find the values of x (the number of days) when the attendance was the same at both plays.
Once we have the values of x, we can substitute them back into either equation to find the attendance (y) at that particular day.
To find the day(s) when the attendance was the same at both plays, we need to set the two equations equal to each other and solve for x.
The equation for Play A is:
y = ax + b
The equation for Play B is:
y = cx^2 + dx + e
Setting the two equations equal to each other, we get:
ax + b = cx^2 + dx + e
To simplify further, we can rearrange the equation and bring all terms to one side:
cx^2 + (d-a)x + (e-b) = 0
Now, we have a quadratic equation in terms of x. To solve for x, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the coefficients are:
a = c
b = d-a
c = e-b
We can substitute these values into the quadratic formula to find the value(s) of x when the attendance was the same at both plays. Plugging in the values, we get:
x = (-(d-a) ± √((d-a)^2 - 4c(e-b))) / (2c)
By solving this equation, we will get one or two values of x, which represent the day(s) when the attendance was the same at both plays.
Once we have the value(s) of x, we can substitute them back into either of the original equations (y = ax + b or y = cx^2 + dx + e) to find the corresponding attendance (y) at that day.
No equations.
Set both y's = to each other.