Math Is Fun Forum

Please look at image and help me solve all the problems.

I am preparing for an exam.

Thank you sooo much.

Let g(x) = f(x² + 1)    Find

a)  g'(x)

b)  g'(2)

c)  g'(x³)

d)  d/dx [g(x³)]

1) An average family of four uses roughly 1200 liters (about 300 gallons) of water per day. (One liter = 1000 cm^3.) How much depth would a lake lose per year if it uniformly covered an area of 50 square kilometers and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation and so on.

2) A heavy rainstorm dumps 1.0 cm of rain on a city 5 km wide and 8 km long in a 2-h period. How many metric tons (1 metric ton = 10^3 kg) of water fell on the city? [1 cm^3 of water has a mass of 1 gram = 10^-3 kg.] How many gallons of water was this?

3) Estimate how many days it would take to walk around the world, assuming 10 h walking per day at 4 km/h.

4) If you began walking along one of Earth’s lines of longitude and walked until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is called a “nautical mile.”

5) How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [Hint: Rock has mass per volume about 3 times that of water, which is 1 kg per liter (10^3 cm^3) or 62 lb per cubic foot.]

6) Noah’s ark was ordered to be 300 cubits long, 50 cubits wide, and 30 cubits high. The cubit was a unit of measure equal to the length of a human forearm, elbow to the tip of the longest finger. Express the dimensions of Noah’s ark in meters, and estimate its volume (m^3).

7) One liter (1000 cm^3) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of 2x10^-10m.

8) Jean camps beside a wide river and wonders how wide it is. She spots a large rock on the bank directly across from her. She then walks upstream until she judges that the angle between her and the rock, which she can still see clearly, is now at angle of 30° downstream. Jean measures her stride to be about one yard long. The distance back to her camp is 120 strides. About how far across, both in yards and in meters, is the river?

9) A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate is this watch, expressed as a percentage?

10)  The diameter of the Moon is 3480 km. What is the volume of the Moon? How many Moons would be needed to create a volume equal to that of Earth?

11) An angstrom is a unit of length, defined as 10^-10 m, which is on the order of the diameter of an atom.
(a)    How many nanometers are in 1.0 angstrom?
(b)    How many femtometers or fermis are in 1.0 angstrom?
(c)    How many angstrms are in 1.0 light year

12) How many angstroms are in 1.0 meter?

13) Determine the percent uncertainity in q, and in sin q, when
(a)    q = 15.0° +/- 0.5°

(b)    q = 75.0° +/- 0.5°

Thank you for helping. I figure this is a lot, but I appreciate your help.
This is a part of my Physics and I please need the answers.   
I know you will not let me down 

1.    [    2x/ (x^2  - 6x + 9)   -    1/(x+1)   - 8/ (x^2 - 2x - 3)  ]

2.  sq.rt x/ x

3.  ln e^7

4.  e ^(ln 3)

5.  3 (n +1) ! / (5n !)

6.     1/(3+x)  -  1/3 
    ---------------------------
                  x

7.   e ^ (1 + ln x)

8.  e^ (3 ln x)

Thank you for helping me.     

The average (arithmetic mean ) of four different positive integers is 9. If the first of these integers is 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?

        (A)  5
        (B)  4
        (C)  3
        (D)  2
        (E)  1

How many different teams of 2 people each can Joshua select from a group of 5 people?

Please see image