Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#2701 2023-07-25 15:05:58
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1850.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2702 2023-07-26 14:53:34
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1851.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2703 2023-07-27 00:06:05
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1852.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2704 2023-07-27 05:02:11
- cheetahflycello
- Novice
- Registered: 2023-04-19
- Posts: 6
Re: Compute the solution:
For the arithmetic progression problem, let's call the three terms a-d, a, and a+d (where 'd' is the common difference). We know their sum is -6, so we have: (a-d) + a + (a+d) = -6. Simplifying gives us 3a = -6, and therefore, a = -2. Now, let's find the common difference 'd': (-2) + a + (-2+d) = -6. Solving this gives us d = -2. Now we can find the three terms: -2-(-2) = -4, -2, -2+(-2) = -4. So the three terms are -4, -2, and -4.
For the cylindrical jar and leadshots problem, first, let's find the volume of the jar when it's half-full of water. The volume of a cylinder is V = π * r^2 * h, where 'r' is the radius and 'h' is the depth. The radius is half of the diameter, so r = 14 cm / 2 = 7 cm. When half-full, the water level is 20 cm / 2 = 10 cm. So, the volume of water in the jar is V_water = π * 7^2 * 10 = 490π cm³.
After dropping the 300 leadshots, the water level rises by 2.8 cm, so the new depth is 20 cm + 2.8 cm = 22.8 cm. Let's call the diameter of each leadshot 'd'. The volume of one leadshot is V_leadshot = (π * d^3) / 6. The total volume added by the 300 leadshots is 300 * V_leadshot. Since the total volume added equals the increase in water volume (490π cm³), we can set up the equation: 300 * (π * d^3) / 6 = 490π.
Now, we can solve for 'd': 300 * d^3 = 2940. Dividing both sides by 300 gives d^3 = 9.8. Finally, taking the cube root of both sides, we get d ≈ 2.15 cm (rounded to two decimal places).
So, the diameter of each leadshot is approximately 2.15 centimeters.
Offline
#2705 2023-07-27 13:11:32
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi cheetahflycello,
Where are the problems?
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2706 2023-07-27 15:08:14
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1843.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2707 2023-07-28 14:20:37
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1844.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2708 2023-07-28 17:09:36
- SHANTAMURTHY HIREMATH
- Novice
- Registered: 2023-07-28
- Posts: 1
Re: Compute the solution:
1. The sum of three terms of an Arithmetic Progression is -6 and their product is 90. Find the three terms.
2. A cylindrical jar of diameter 14 centimeters and depth 20 centimeters is half-full of water. 300 leadshots of same size are dropped into the jar and the water level raises by 2.8 centimeters. Find the diameter of each leadshot.
Solution: let the terms of an ap be a-d, a and a+d
sum of these will be 3a=-6, then we get the value of a as -2.
as per the second statement. -8+2 dsquare = 90
then we will have d squared= 49
then value of d is 7
hence the terms are -9, -2, 5
thank you for posting this question..
Offline
#2709 2023-07-28 18:02:39
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
Now go to compute 1844 and solve!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2710 2023-07-29 00:09:30
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1845.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2711 2023-07-30 00:31:06
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1846.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2712 2023-07-31 00:03:34
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1847.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2713 2023-07-31 20:10:01
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1848.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2714 2023-08-01 21:19:36
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1849.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2715 2023-08-02 19:44:57
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1850.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2716 2023-08-03 20:58:34
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1851.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2717 2023-08-04 18:24:51
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1852.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2718 2023-08-05 18:32:41
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1853.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2719 2023-08-06 14:28:39
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1854.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2720 2023-08-07 15:08:11
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1855.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2721 2023-08-08 15:16:47
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1856.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2722 2023-08-09 00:32:35
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1857.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2723 2023-08-10 00:05:20
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1858.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2724 2023-08-10 19:51:09
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1859.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2725 2023-08-11 14:52:38
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,351
Re: Compute the solution:
Hi,
1860.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline