Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi,

The solution #2636 is perfect! Smart work, Monox D. I-Fly!

#2637. Solve:
(i) 3x + 2y = 11, 2x + 3y = 4.
(ii) 8x + 5y = 9, 3x + 2y = 4.

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi bobbym,

The solution #2637 (two parts) is perfect! Excellent!

#2638. If

, where

are acute angles, find the value of

.

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi bobbym,

#2639. If

, where 2A is an acute angle, find the value of A.

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi bobbym,

The solution #2639 is correct! Good work!

#2640. If

, where 5A is an acute angle, find the value of A.

---

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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Hi! When I graphed it, I found the answer, but couldn't remember how to solve it algebraically.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi Relentless,

The solution #2640 is correct! Neat work!

#2641. Given

, find the values of

.

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

I concur with bobbym, except technically sinθ and tanθ may also be negative (because cosθ=7/25 has two solutions).

Last edited by Relentless (2015-12-19 13:00:23)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi bobbym and Relentless,

The solution #2641 (three parts) are correct! Good work!

#2642. If

, evaluate

.

---

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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Yet again there are various solutions for this type of problem, yet clearly we are only expected to give the obvious one. That one is

Other solutions are (by substituting every combination of solutions): 1/5 and +/-4/5.

Last edited by Relentless (2015-12-19 18:00:02)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi Relentless,

The solution #2642 is correct! Excellent!

#2643. Evaluate:

.

---

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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi Relentless,

The solution #2643 is perfect! Excellent!

#2644. The following table shows the weights of 12 students:
Weight (in kilograms)      :     67      :     70      :     72     :     73     :     75
Number of students        :     4        :      3       :      2      :      2      :      1
Find the mean weight by using short-cut method.

---

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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Hi!

Although I never actually bothered to learn the short-cut method with frequencies ;s
Median is 70. Standard deviation is √(345/11) / 2 ~ 2.8002

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi Relentless,

The solution #2643 is perfect! Neat work!

#2644. Solve:

(Irrational roots)

---

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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

There seem to be a lot of questions toward the start of this thread that have never been answered.

Last edited by Relentless (2015-12-20 00:31:57)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi Relentless,

The solution#2644 is perfect! Brilliant!

#2645. Find the value of 'k' for which the given equation has equal roots. Also, find the roots.

.

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

I agree with bobbym

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi bobbym and Relentless,

The solutions in #2645 is correct! Neat work!

#2646. If -5 is a root of the quadratic equation

and the quadratic equation

has equal roots, find the value of 'k'.

---

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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Hi;

1/4 * (-√(p^2 + 120) - p) = -5
p = 7

k = 7/4

First equation has roots of -5 and 3/2, second has root of -1/2

Last edited by Relentless (2015-12-21 18:54:20)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,398

Re: Oral puzzles

Hi Relentless,

The solution #2646 is correct! Neat work!

#2647. Find the value of 'k' for which the given equation has equal roots. Also, find the roots.

---

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.