Rebecca

Suppose each equation below is a utility function for the consumption of cookies, c. What restrictions on the parameters (for example, positive, negative, less than 1, and so forth) are required for the utility function to reflect that utility rises at a decreasing rate with the number of cookies consumed? (Assume that c > 0.)

U(c) = P + ae^(B * c), where the parameters are a, B, and P

Given the equation 15x2 + 18y2 = 1 Name the curve that is the graph of the equation. Find the foci, vertices, directrix, axis, and asymptotes, where applicable for this graph.

If someone could explain this step by step that would be amazing.

Given the equation x2 − 14x + 2y2 + 45 = 0

find the foci, vertices, directrix, axis, and asymptotes, where applicable.

Please, if anyone could go through how to get the right answer that would be awesome.

For an electron in the 2p state of an excited hydrogen atom, the probability function P for the electron to be located at a distance r from the atom's center is given by

P(r) = ((πr^4)/(6a^5))(e^(-r/a)

Find the most probable distance r of the electron from the center of the atom.

Write a function that models the distance D from a point on the line y = 3 x - 4 to the point (0,0) (as a function of x).

The point on the line that is closest to (0, 0) is:

A culture contains 2000 bacteria initially and doubles every 50 minutes. Assuming that the rate of growth is proportional to the number of bacteria, find a function that models the number P(t) of bacteria after t minutes.

A blue CU(II) cation salt was heated; the salt turned white and drops of a colorless liquid, thought to be water, were observed on the neck of the test tube. Addition of a few drops of water formed a blue solution; when it was heated to evaporate excess water, the blue salt came back.\

I'm leaning towards physical change, because it's a reversible process, but does anyone have a better explanation of it?

I need the chemical reaction formula for this and I have no idea how to get it.

Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long would you have to wait for 1/10 of it to disappear?

An explanation would be great, if anyone has the time.

What is f(x)? The question states that it has to be postive, and I keep getting f(x)= -1/2cos^2(x)+5.5

and I'm not sure how you could get a positive answer.

Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long would you have to wait for 1/10 of it to disappear?

You would have to wait ______ years for 1/10 of the radium to disappear.

Suppose an unknown radioactive substance produces 4000 counts per minute on a Geiger counter at a certain time, and only 500 counts per minute 13 days later. Assuming that the amount of radioactive substance is proportional to the number of counts per minute, determine the half-life of the radioactive substance.

It's a Calc question dealing with exponents and antiderivatives, I think. If someone could please explain..?

Let f (x) = 3x^(4/3).

Find all extreme values (if any) of f on the interval [-8, 8]. Determine at which numbers in the interval these values occur.

Maximum Value:

f ( _____ ) =______ = f ( ______ )

smaller

value of x larger

value of x

Minimum Value:

f ( ______ ) = _______

When the point is at (2, 7), its x coordinate is increasing at the rate of 12 units per second.

The point is moving in the clockwise or counterclockwise direction.

If someone could show me how to do this, that would be great.

The TA didn't go over this in class at all...

So what I though I was supposed to do was separate the problem out: x/sqrt(x)-1/sqrt(x)

then find the anti-derivative of that: 3/2(x)^(3/2)+1/2(x)^(1/2)

and then plug in 9 and 1 and have f'(1)-f'(9)

Unfortunately that did not give me the answer in the back of the book. I got 44, the book got 40/3. What am I missing here?

With steps if possible, I'm not very good at this..

help. please help me. I need this explained.

I've been getting y'=-9x/y, but after that I'm not sure what to do. The answer is y''=-81/y^3 and I cannot figure out how to get there.

Can someone please explain this to me?

I need to use implicit differentiation to find the equation of the tangent line to the curve at the point (0, .5)

x^2 + y^2 = (2x^2 + 2y^2 - x)^2