A company's revenue from selling x units of an item is given as
R
=1700x−x^2. If sales are increasing at the rate of 45 units per day, how rapidly is revenue increasing (in dollars per day) when 290 units have been sold?
R = 1700 - x^2
dR/dt = -2x dx/dt, but we are told that dx/dt = 45 units/day
= -2(290)(45) = ....
Your equation of R = 1700 - x^2 doesn't make sense.
Why would the Revenue decrease as the sales increase?
I assume that x represents sales.
You sure it wasn't R = 1700 + x^2 ?
look into it
A company's revenue from selling x units of an item is given as R=1700x−x^2. If sales are increasing at the rate of 45 units per day, how rapidly is revenue increasing (in dollars per day) when 290 units have been sold?
I am sure that R=1700x−x^2
Let A be the area of a circle with radius r. If dr/dt=2 , find dA/dt when r=2.
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To find how rapidly the revenue is increasing when 290 units have been sold, we need to find the derivative of the revenue function with respect to time.
The given revenue function is:
R = 1700x - x^2
Let's differentiate both sides of the equation with respect to time (t):
dR/dt = d(1700x)/dt - d(x^2)/dt
dR/dt represents the rate of change of revenue with respect to time (the rate at which revenue is increasing), and dx/dt represents the rate at which units are being sold per day.
Since it is given that sales are increasing at the rate of 45 units per day (dx/dt = 45), we can substitute this value into the equation:
dR/dt = d(1700x)/dt - d(x^2)/dt
dR/dt = 1700 * dx/dt - 2x * dx/dt
dR/dt = 1700 * (dx/dt) - 2x * (dx/dt)
Now we need to find the values of x and dx/dt when 290 units have been sold.
x = 290
dx/dt = 45
Substituting these values into the equation, we can calculate the rate at which revenue is increasing:
dR/dt = 1700 * (dx/dt) - 2x * (dx/dt)
dR/dt = 1700 * 45 - 2 * 290 * 45
Simplifying this expression will give us the rate at which revenue is increasing when 290 units have been sold.