# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #2701 2023-07-25 15:05:58

Jai Ganesh
Registered: 2005-06-28
Posts: 47,158

### 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.

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## #2702 2023-07-26 14:53:34

Jai Ganesh
Registered: 2005-06-28
Posts: 47,158

### 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.

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## #2703 2023-07-27 00:06:05

Jai Ganesh
Registered: 2005-06-28
Posts: 47,158

### 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.

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## #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.

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## #2705 2023-07-27 13:11:32

Jai Ganesh
Registered: 2005-06-28
Posts: 47,158

### 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.

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## #2706 2023-07-27 15:08:14

Jai Ganesh
Registered: 2005-06-28
Posts: 47,158

### 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.

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## #2707 2023-07-28 14:20:37

Jai Ganesh
Registered: 2005-06-28
Posts: 47,158

### 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.

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## #2708 2023-07-28 17:09:36

SHANTAMURTHY HIREMATH
Novice
Registered: 2023-07-28
Posts: 1

### Re: Compute the solution:

Jai Ganesh wrote:

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..

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## #2709 2023-07-28 18:02:39

Jai Ganesh
Registered: 2005-06-28
Posts: 47,158

### 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.

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## #2710 2023-07-29 00:09:30

Jai Ganesh
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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
Registered: 2005-06-28
Posts: 47,158

### 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