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I have a problem that I am a little stumped about.

There are 100 people with an inverse demand function P=10-1.0q, where q is number of miles preserved and P is per-mile price to pay for q miles of preserved river.

1) If MC is $500 per mile, how many miles would be preserved in an efficient allocation?

2) How large is the economic surplus?

I attempted it by doing, MR = 10 - 2.0q= MC=500 and solved from there, but it comes out to be a negative number. Please help!

Here is my homework problem.

Given P= 80-Q and MC of producing it is MC =1q, where P is the price of the product and q is the quantity demanded and/or supplied.

a. How much would be supplied by a competitive market?

b. Compute the consumer surplus and producer surplus.

I am very lost. I tried first to change MC to TC, but that doesn't do much. Please help!

A grapefruit is tossed straight up with an initial velocity of 50ft/sec. The grapefruit is 5 feet above ground when it is released. Its height at time t is given by:

y=-16t^2 + 50t + 5

How high does it go before returning to the ground?

I need help solving a profit, cost, revenue question for my calculus class.

The question is:

Total cost of producing q units of a product is given by c(q)=q^3-60q^2+1400q+1000 for 0<(eq.)q<(eq)50; The product sells for $788 per unit. What production level maximizes profit? Find the total cost, total revenue, and total profit at this production level. Where is profit maximized.

I am completely lost. I know MC=MR and profit=R(q)-C(q), but thats it. Please help. Thanks

I can't figure out this problem. I know its product rule

s=4tcos^2t

I have

4(cost)^2+(4t)(2)(-sint)

Is that right so far?

I need it simplified

I answered the problem for part a and b I seemed to have messed up on something.

suppose that f(T) is the cost to cool an apartment, in dollars per day, when the outside temperature is T fahrenheit. If f(23)=11.59 and f'(23)=-0.05

b. approximately what is the cost to cool my house when temp. is 20F?

c2-11.59/20-23=-0.25

do I add -0.25+11.59? what do I do?

here is the problem, two parts. I answered the first part.

7. The price in dollars of a house during a period of mild inflation is described by the formula P(t)=(120,000)e^0.05t, where t is in the number of years after 1990.

a. What is the derivative of p(t)?

Answer: P'(t)=6,000e^0.05t

b. How many years will it be before the house is increasing in value ata a rate of $11,000 per year?

Having some problems with these questions:

1. The price in dollars of a house during a period of mild inflation is in P(t)=(120,000)e^0.05t, where t is the number of years after 1990.

b) How many years will it be before the house is increasing in value at a rate of $11,000 per year?

2. s=4t(cos^2)t

I have

(4)(cost)^2 + (4t)(2)(-sint)

(4cost)^2 + (8t)(-sint)

Not sure if that is right when simplified

3.y=sin(x^3+7)

4.Y=5+sint/5-cost

I have a few problems that I have solved and thought were right, but the answer is different in my textbook. Am I doing anything wrong or is their answer just simplified

1. R=(q^2 + 1)^4

my answer:

4(q^2+1)^3(2q)

book answer:

8q(q^2 + 1)^3

2. 2=(t^3+1)^100

my answer:

100*(3t)^99

book answer:

300t^2(t^3+1)^99

I am having issues finding the derivatives of some hw problems. I am trying to use the product and quotient rule but they aren't working for a few of my questions.

1.f(x)=x/e^x

2.z= 1-t/1+t

3.w=(3y+y^2)/(5+y)

4. If f(x)=(3x+8)(2x-5) f ' (x) and f ' '(x)

5. if p is price in dollars and q is quantity, demand for a product is given by q=5000e^-0.08(p)

a)what quantity is sold at a price of $10?

b)find the derivative of demand with repect to the price when its 10.

I don't know how to find the derivatives of these problems

1.f(x)=-1/x^6.1

2.y=Sqrt(x)

3.y=z^2 + 1/2z

4. h(t)=3/t+4/t^2

5. f(t)=t^2-4t+5

I am looking for Humes belief of the advantages of being an accurat philosopher

I am wondering if bundle theory was mentioned in David Humes, An Enquiry Concerning Human Understanding. I feel like it is mentioned but I am unsure. I am working on an argument for HUme's 'existence of the self'. Help for either part of my problem would be great

I have a few calculus problems that I am stuck on.

1. Investing $1000 at an annual interest rate of r%, compounded continuously, for 10 years gives us a balance of $B, where B= g(r). Give a financial interpretations of the statements:

g(5) = 1649

g'(5)= 165. What are the units of g'(5)

2.Suppose that f(t) is a function with f(25)=3.6 and f ' (25)= -0.2. Estimate f(26) and f(30)

3. Annual net sales, in billions of dollars, for the Hershey company, is a function S=f(t) of time, t, in years since 2000.

a)Interpret the statements f(8)=5.1 and f ' (8)=0.22 in terms of Hershey sales.

b)Estimate f(12) and interpret it in terms of Hershey sales.

Given:

Y=C + I + G

C= c(sub)0 + c(sub)1Y(sub)D

Y(sub)D= Y - T

T= t(sub)0 +t(sub)1Y

Assume that the marginal; propensity to consume, c(sub)1, is between zero and one. Note that I and G are exogenous variables.

1. Solve the equilibrium output.

I get:

Y=((1/1-c(sub)1))(c(sub)0-c(sub)1T + I + G)

then

Y=((1/1-c(sub)1))(c(sub)0-c(sub)1(t(sub)0+t(sub)1Y) + I + G)

I'm not sure if that is right or what steps are after.

I have a few questions I am struggling with.

1.W, was 18,000 megawatts in 2000 and has been increasing at a continuous rate of approximately 27% per year. Assume this rate continues.

a) Give a formula for W, in megawatts, as a function of time, t, in years since 2000.

b)when is wind capacity predicted to pass 250,000 megawatts?

3. If you deposit 10,000 in an account earning interest at an 8% annual rate compounded continuously, how much money is in the account after five years?

5. If a bank pays 6% per year interest compounded continuously, how long does it take for the balance in an account to double?

If it takes 100 years for 80 grams of radioactive substance to decay to 60 grams, how long will it take for an amount of this substance to decay to 1/5 that amount?

Given the information, find the missing parts of ABC using law of sines and law of cosines

1. A=80(degrees), B=35 (degrees). a=12

2. A=138 (degrees), b=5, c=5

3. a=15, b=12, c=5

I need to solve for the inequality

1.2x/x^2-1<(equal to)0

I need to solve the given and leave in terms of natural logarithm

2. 2^2x-x=6^-x

According to Newton's law of cooling, the rate at which an object cools is directly proportional to the difference in temperature between the object and the surrounding environment. A metal rod whose initial temperature is 100*C cools as it is placed in air, which is kept at a temp of 15*C. Suppose the rods temp is =T. the rod will decrease exponentially to the equation T=15+85e^0.4m

Where m is the number of minutes the rod has been exposed. How long will to take the rod to cool down to a temp of 40*?