Help ASAP Due Monday September 12, 12:00 p.m.

[tesha05]

I know the answers but we have to have the solutions. I need help with four problemd (1) An amoeba propagates by simple division; each split takes 3 minutes to complete. When such amoeba is put into a galss container with a nutrient fluid, the container is full of amoebas in one hour. How long would i take for the container to be filled if we start with not one amoeba, but two? I know the answer is 57 but how do you work it out????????????
(2) A woman start at point P on the earth's surface and walks 1 mi south, then 1mi east, then 1 mi north, and finds herself back at P, the starting point. Describe all points P for which this is possible (there are infinitely many).
(3)Suppose x + y = 1 and x squared + y squared = 4. Find x cubed + y cubed.

 

[stapel]

(1) An amoeba propagates by simple division; each split takes 3 minutes to complete. When such amoeba is put into a galss container with a nutrient fluid, the container is full of amoebas in one hour. How long would i take for the container to be filled if we start with not one amoeba, but two? I know the answer is 57 but how do you work it out?

If you have twice as many, how many fewer doublings ("splits") do you need to fill the container? How long is a doubling period?

(2) A woman start at point P on the earth's surface and walks 1 mi south, then 1mi east, then 1 mi north, and finds herself back at P, the starting point. Describe all points P for which this is possible (there are infinitely many).

Hint: Look at a globe. (And I don't see how there could be "infinitely many" such points.)

(3)Suppose x + y = 1 and x squared + y squared = 4. Find x cubed + y cubed.

Hint: Expand (x + y)². Solve for the value of xy. Then expand (x + y)³, and solve for the value of x³ + y³.

Eliz.

 

[TchrWill]

2) A woman start at point P on the earth's surface and walks 1 mi south, then 1mi east, then 1 mi north, and finds herself back at P, the starting point. Describe all points P for which this is possible (there are infinitely many).

There is a circle defined by the locus of all points 1/2Pi miles radius north of the south pole.

The radius of this circle being 1/2Pi, the circumference is C = 2(1/2Pi)Pi =1 mile.

Let P be any point on a circle defined by the locus of points 1 mile north of the previously defined circle.

Therefore, from any point P on the circle with radius 1/2Pi + 1, you can walk one mile south to the circle with circumference of 1 mile, walk one mile east and then one mile north and end up at the same point P that you started at.

Therefore, as you state, there are an infinite number of possible point P's.

 

[stapel]

Oooo, very clever! I'd missed that. Thanks!

Eliz.