David Germany

John Locke has been spending the day building fences to keep varmints out. As he is tired, he goes to bed early. He wakes up at 4 AM with a new idea on fence-building. He would like to go to his workshop right away and put his idea into effect, but he knows that the noise will upset his landlady. So he decides to stay in bed and wait until the morning. He goes back to sleep, and when he wakes up again he has forgotten his great idea. He consoles himself by thinking that he made a free choice to stay in his room. What he doesn't realize is that the landlady had locked his door on the outside, so he couldn't have gone out if he had wanted to.

Was his staying inside still a free action?

What theory of freedom are you using for your answer? Would a different theory lead you to a different answer?

5.) On December 6, 2008, the world's population was estimated to be 6,741,727,032. If the growth rate is 1.167% per year, answer the following.

A.) When will the world's population reach 10 billion.

B.) by what year will the population double?

Im having a bunch of trouble with this model.

4.) The burial cloth of an Egyptian mummy is estimated to contain 59% of the carbon-14 it contained originally. The half -life of carbon-14 is 5730. How long ago was the mummy buried?

3.) A rectangle is inscribed in a semicircle (centered at the origin, above the x-axis) of radius 2. Let P=(x,y) be the point in quadrant 1 that is a vertex of the rectangle and is on the circle.

A.) Draw and accurately label a sketch of this situation.

B.) Express the area A of the rectangle as a function of x.

C.) Express the perimeter p of the rectangle as a function of x.

D.) use a graphing utility to graph A=A(x). For what value of x is A largest?

Round to the nearest tenth, if applicable. Provide a sketch of what you see in your grapher, including the window dimensions.

E.) Use a graphing utility to graph p=p(x). for what value of x is P largest?

Provide a sketch of what you see in your grapher, including the window dimensions.

Please help, I'm so lost on what to do for this.

2.) let P(x,y) be a point on the graph of y=x^2-4

A.) Draw an accurate sketch of this graph. Be sure to label your graph carefully and accurately.

B.) Mark and label the point (0,-1) on your graph. Express the distance d from P to the pint (0,-1) as a function of x.

C.) what is d if x=0

D.) what is d if x=-1

E._ use a graphing utility to graph d=d(x). Provide a sketch of what you see in your grapher, including the window dimensions.

F.) For what values of x is d the smallest? Round to the nearest tenth, if applicable.

Please help, I am extremely lost on this.

Beth has 2700 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing.

A.) Let x represent the length of the side parallel to the river. Draw a picture of this situation. Be sure to label each side of your rectangle carefully.

B.) Express the area A of the rectangle as a function of x.

C.) Graph A(x) using a graphing utility. For what value of x is the area the largest? Round to the nearest tenth , if applicable. Provide a sketch of what you seen in your grapher, including the window dimensions.

Please help, I'm so lost on this. I can do the graphing part but I'm unsure of how to arrive at the correct answers.

3.) The cooling turkey problem

A.) The temperature of your turkey, when it is removed from the oven, is 165 degrees. The temperature of the room in which it is placed immediately after its removal is 70 degrees.

B.) Let the turkey sit for about 15 minutes, and take its temperature again. The temperature of your turkey after 15 minutes is 175 degrees.

C.) Use the information from parts a and b to find a function that models the cooing process of your turkey.

D.) sketch an accurate graph of our function, being sure to label all important aspects of the graph.

E.) How long until the turkey reaches the temperature of 120 degrees?

F.) According to Roasting a Turkey for Dummies, the turkey should rest for 20 minutes after removal from the oven. What temperature would your turkey be at this time?

Please help, I haven't been able to solve this problem. I know I'm supposed to use Newton's Law of Cooling.

u(t)=T+(usub0-T)e^kt k<0

1.)

Archeologists working near a seasonal Native American encampment is People's Park along the Spokane River uncovered an ancient marmot den, containing the ancient remains of one of Spokane's unofficial mascots. It was determined that the bones contained 37.1% of the original amount of carbon 14. If the half-life of carbon 14 is 5730 years, how old are these remains.

Im just having a ton of trouble with these problems.

Okay so I'm having trouble with this decay problem in my precalculus class.

2. The half-life of radium-226 is 1600 years. Suppose we have a 22-mg sample.

A.) Find a function that models the mass remaining after t years.

B.) How much of the sample will remain after 4000 years?

C.) After how long will only 18mg of sample remain? Round your answer to the nearest year.

Im just having a ton of trouble with these. We have been working with uninhibited radioactive decay.

A(t)= Asub0e^kt k<0

One piece, of length x, is bet into the shape of a square. The other piece is bent into the shape of an equilateral triangle.Express the total area enclosed as a function of x. For what value of x is this total area a minimum?

a. What is the domain?

b. Does this function have any vertical asymptotes? If yes, state there equation. If no, state why not.

c.Does this function have any horizontal asymptotes? If yes, state there equation. If no, state why not.

d. Does this function have any oblique asymptotes? If yes, state there equation. If no, state why not.

e. Find the zeros and y intercept of the graph of this function.

f. List the equation you would use to sketch the graph.

Please help me, im so lost on this.

Please help me with this I am so lost.

Suppose some of the zeros of f(x)=0 are 2,-5 and 1/2, find the following.

Explain how you found the answers.

a. f(x-2)=0 b. f(x+6)=0 c. f(3x)=0 d.f(-1/4x)=0

It has to have three real zeros, one of multiplicity 2; y intercept 1;vertical asymptotes x=-2 and x=3; oblique asymptote y=2x+1. Is this rational function unique? Explain.

I understand how it deals damage in the for of -1/-1 counters, but for each counter on a creature for example, Say I attack with a 2/3 creature with infect. The blocking creature is also 2/3. What exactly do the two -1/-1 counters do? Do they now make his 2/3 creature pretty much a 0/1? or what? I am not sure how the counters actually play a role next turn or in terms of combat.What if the creature was a 2/2 and with the two -1/-1 counters I infect it with does that just destroy it because it would be a 0/0? does a creature get destroyed with a certain number of counters on it? I'm so confused with this whole ability. Please help!!!!!