Series Applications (1 Viewer)

[taggs-sasuke]

Hey (again). Can someone please help me with these questions? Thanks!!!

1.

A body is moving in a straight line. In the 1st second it travels 4.9m, in the 2nd second 7.35m, in the third second 9.8m, and so on.

(a) How far does it travel in the 7th second? Answer: 19.6m
(b) What is the total distance it would travel in 10 seconds? Answer: 159.25

Did you get that answer? If you did, can you please show me how you arrived at it? (Thank you) If you didn't, did you get 63.7 because that's what I got.

2.

A factory is expanding yearly and produces 250 vehicles in the 1st year. In each successive year it increases the output by 75 cars.

(a) How many cars are produced in the 12th year? Answer: 1075
(b) How many cars are produced altogether in the first 25 years? Answer: 28,750
(c) In which year is the 100 000th car produced? Answer: 49th

Again, did you get that answer? If you did, can you please show me how you arrived at it? (Thank you) If you didn't, did you get 1 331th because that's what I got.

3.

The cross section of a tree trunk shows growth rings. The innermost ring has a diameter 2.9cm, the next ring has diameter 3.23cm and each subsequent diameter is increased by the same amount. What is the diameter of the 12th ring? If each ring indicates a year's growth, what was the age of the tree if the total diameter was 19.4cm? <-- How do you do this?

Answers:
T(12) = 6.53cm
51 years

 

[kurt.physics]

Hey (again). Can someone please help me with these questions? Thanks!!!

1.

A body is moving in a straight line. In the 1st second it travels 4.9m, in the 2nd second 7.35m, in the third second 9.8m, and so on.

(a) How far does it travel in the 7th second? Answer: 19.6m
(b) What is the total distance it would travel in 10 seconds? Answer: 159.25

Did you get that answer? If you did, can you please show me how you arrived at it? (Thank you) If you didn't, did you get 63.7 because that's what I got.

I got 63.7 also.

edit: I think i made the same mistake as you (???). I put 10/5 instead of 10/2. Our brains must have done the 5 calculation with out thinking ;P

 

[~caramello~]

1b) S10 = n/2[2a + (n-1)d]
= 10/2 [2(4.9)+9(2.45)
= 5 (9.8 + 22.05)
= 159.25

 

[kurt.physics]

Hey (again). Can someone please help me with these questions? Thanks!!!

2.

A factory is expanding yearly and produces 250 vehicles in the 1st year. In each successive year it increases the output by 75 cars.

(a) How many cars are produced in the 12th year? Answer: 1075
(b) How many cars are produced altogether in the first 25 years? Answer: 28,750
(c) In which year is the 100 000th car produced? Answer: 49th

Again, did you get that answer? If you did, can you please show me how you arrived at it? (Thank you) If you didn't, did you get 1 331th because that's what I got.

I also got 1331 th

edit: OMG! yet again! My brain must be turned off :{

 

[kurt.physics]

Hey (again). Can someone please help me with these questions? Thanks!!!
3.

The cross section of a tree trunk shows growth rings. The innermost ring has a diameter 2.9cm, the next ring has diameter 3.23cm and each subsequent diameter is increased by the same amount. What is the diameter of the 12th ring? If each ring indicates a year's growth, what was the age of the tree if the total diameter was 19.4cm? <-- How do you do this?

Answers:
T(12) = 6.53cm
51 years

 

[~caramello~]

2.

A factory is expanding yearly and produces 250 vehicles in the 1st year. In each successive year it increases the output by 75 cars.

(a) How many cars are produced in the 12th year? Answer: 1075
(b) How many cars are produced altogether in the first 25 years? Answer: 28,750
(c) In which year is the 100 000th car produced? Answer: 49th

Again, did you get that answer? If you did, can you please show me how you arrived at it? (Thank you) If you didn't, did you get 1 331th because that's what I got.

Sn = n/2 [2a + (n-1)d ]
100000 = n/2 [2(250) + (n-1)75)
100000 = n/2 [500 + 75n - 75 ]
200000 = 425n + 75n^2
75(n^2+17/3) = 200000
n^2 + 17/3 = 2666 2/3
n^2 + 17/3 + 289/36 = 2674 25/36 (complete the square)
(n + 17/6)^2 = 2674 25/36
n + 17/6 = 51.717
n = 48.88
= 49

this might not be the quickest way to do it =/

 

[taggs-sasuke]

I got 63.7 also.

edit: I think i made the same mistake as you (???). I put 10/5 instead of 10/2. Our brains must have done the 5 calculation with out thinking ;P

Oh my goodness! Yes, I did do that! LOL! How funny. And I checked my work again. Haha.

 

[taggs-sasuke]

1b) S10 = n/2[2a + (n-1)d]
= 10/2 [2(4.9)+9(2.45)
= 5 (9.8 + 22.05)
= 159.25

Yeah, thanks...

 

[taggs-sasuke]

I also got 1331 th

edit: OMG! yet again! My brain must be turned off :{

Haha.

 

[taggs-sasuke]

2.

(c) In which year is the 100 000th car produced? Answer: 49th

Again, did you get that answer? If you did, can you please show me how you arrived at it? (Thank you) If you didn't, did you get 1 331th because that's what I got.

Sn = n/2 [2a + (n-1)d ]
100000 = n/2 [2(250) + (n-1)75)
100000 = n/2 [500 + 75n - 75 ]
200000 = 425n + 75n^2
75(n^2+17/3) = 200000
n^2 + 17/3 = 2666 2/3
n^2 + 17/3 + 289/36 = 2674 25/36 (complete the square)
(n + 17/6)^2 = 2674 25/36
n + 17/6 = 51.717
n = 48.88
= 49

Thank you

 

[taggs-sasuke]

I feel so stupid. Thank you