Math Is Fun Forum

SEQUENCE AND SERIES

Geometric series

A ball takes 1 second to hit the ground when dropped. It then takes 90% of this time to rebound to its new height and this continues unil the ball comes to rest.

a) Show that the total time of motion is given by 1 + 2(0.9) + 2(0.0)^2 + 2(0.9)^3 + .....

b) Find Sn for the series in a.

c) How long does it take for the ball to come to rest.

Please show how you came to the conclusions....ty.

Right...so I have a test tomorrow that might have questions like these in it....could some of youse help me with two questions and show me how youse came to this conclusion?

Q1.  A rectangular swimming pool is 12m long by 6m wide. It is surroudned by a pavement of uniform width, the area of the pavement being 7/8 of the area of the pool.

a) If the pavement is Xm wide, show that the area of the pavement is 4x^2 + 36x m^2.
b) Hence, show that 4x^2 +36x -63 = 0
c) How wide is the pavement?

Q2.  A circular magnet has an inner radius x cm and an outer radius 2cm larger and its depth is the same as the inner radius. If the total volume of the magnet is 120pii cm^3. Find X.

Danke!

Hello again....I owned those math problems well in the last few months...from probablity to quadratic functions but now it's problem solving.....

So please help me with a few...THANKS!

(1) Mouldy Oldy claims that if the digits in his age are multiplied, the result would be  equal to his age 40years ago. How old is MOuldy Oldy?

(2) To pick all the oranges in an orchard it would take 14 people a total of 10 days. If 3 of the workers are sick and cannot work and 2 others can work at half the usual rate, how long will it take to pick all of the oranges?

(3) When positive integer N is divided by 2 the remainder is 1. When N is divided by 3 the remainder is 2 and when N is divided by 4 the remainder is 3. Show that N is any integer of the form 12a - 1 where a = 1,2,3,4...

I tried my hardest but I can't figure anything >.<...

I'm back at this forum...not to have a chat but to ask for help!

Here are the problems.

(1) Solve the system where a, b and c are positive integers.
     ab + bc = 44
     ac + bc = 23

(2) A rocket is fired vertically above the North Pole. How high must the rocket rise if the horizon to be seen from it is
     a) The latitudinal circle of 30o
     b) The latitudinal circle of ao        o=degrees

(3) In triangle ABC, if angle A has size $ and angle B has size 2$, and the sides BC, CA and AB have lengths a, b and c respectively, show that b^2 = a(a+c).

Solutions would gladly be welcomed !

Kisses for the girls and beers for the guys!

I know, I know, I know, mods, this is like the nth time I posted for help with math....and no, n doesn't equal to blablabla infinity to the power of infinity !

Just that I am a bit slow and need help to find the answers. Trust me, i won't be sleeping when you people are working hard !

So please help me: !

Q1 Two circles of radii 4cm and 2cm touch a straight line at A and B as shown. Find the distance between A and B.

A_________________________B with circles on the line.

Q2 A rope is stretched tightly over an plane hangar from A to B. The shape of the hangar is semi-cylindrical. Find the length of the rope. 
Shape is sorta like that with A at one end and B on the other.

      (I have no clue on this one >.<, stupid weird roof!)

Q3 Solve the problem, "Two numbers have a sum of 1 and a sum of cubes of 31. Find their product!"

I gotta use the (x + y)^3 in it though I think.

Q4  Find a and b given that a^b x b^a = 800, where a and b are integers.

Thanks for your help peoples....One day...ONE DAY, I will help those who need help !