Math Is Fun Forum

Ecologists estimate that when the population of a certain city is p thousand persons, the average level L of carbon monoxide in the air above the city will be L ppm (parts per million), where L=10+0.4p+0.0001p². The population of the city is estimated to be p=752+23t+0.5t² thousand persons t years from the present.

a)Find the rate of change of carbon monoxide with respect to time.

I got: L=10+4(752+23t+0.5t²)+0.0001(752+23t+0.5t²)²

dL/dt = 4(23+t)+0.0002((752+23t+0.5t²)(23+t)
        =(23+t)(4.1504+0.0046t+0.0001t²)

b)Find the time rate of change of the population (the rate of change of the population with respect to time)

I got: dp/dt = 23+t

c)How fast (with respect to time) is the carbon monoxide level changing at time t=2?

You would use the dL/dt right and substitute 2 in for t? I got the answer of 104 ppm/yr but I think that sounds high so I'm not sure.

Any help is appreciated!

Find the equation of the tangent line to the graph x³y^9 = 1 at the point (64, .25) and (64, -.25).

I found the correct equation for the first point, but I can't figure out the second point (64,-.25).

I got y= (1/768)x-(1/3) but mymathlab says that it is wrong.

I also can't figure out this problem.
Suppose that x and y are both differential functions of t and are related by the given equation. Use implicit differentiation with respect to t to determine dy/dt  in terms of x, y and dx/dt

I got dy/dt = (-3x² dx/dt - 3y dx/dt) / (3x-7y^6) but I am not sure if that is right.

Find the x-coordinates of all points on the curve y=(-x²+10x-21)³ with a horizontal tangent line.

I got y'=3(-x²+10x-21)²(-2x+10) for the derivative but I am not sure if that is right. Once I have the right derivative I just set the derivative equal to 0 and solve for x right? When I solved I got x=3,7 but MyMathLab told me I was wrong.

Ecologists estimate that, when the population of a certain city is x thousand persons, the average level L of carbon monoxide in the air above the city will be L ppm (parts per million), where L=50+0.4x+0.0006x². The population of the city is estimated to be x=752+23t+0.5t² thousand persons t years from the present. Find the rate of change of carbon monoxide with respect to the population of the city, and the time rate of change of the population when t=2. How fast (with respect to time) is the carbon monoxide level changing at time t=2.

I don't even know where to begin. Can you explain what I need to do and how to set up the equation please?

Find the dimensions of a closed rectangular box with a square base and volume 125 in³ that can be constructed from the least amount of material.

What are the dimensions of the box?
The length of one side of the base is _____ in.
The height of the box is _____ in.

Let f(x) be the number (in thousands) of computers sold when the price is x hundred dollars per computer. Interpret the statements f(23)=30 and f'(23)=-6. Then estimate the number of computers sold if the price is set at $2325 per computer.

f(23)=30 implies that 30,000 computers are sold when the price is set at $2300.

f'(23)=-6 implies that when the price is $2300, for every $100 price increase, the sales decrease by 6,000 computers.

If computers are sold for $2325 per computer, how many computers will be sold?

I got 2850 computers, but MyMathLab says that isn't right.