@RRITESH KAKKAR

In the interests of your edification I offer the following illustration of two methods of simultaneous solution...

@RRITESH KAKKAR --- Please read!

I am taking a good deal of time and effort to assist your study of mathematics -- What I require in return is earnest effort and attention to instruction on your part!
Meaning, among other things, that you carefully read this post and make an honest effort at comprehension of the techniques demonstrated herein -- That includes asking questions and practicing the techniques until you are comfortable with them!

We will return to the problem of post #972 following your demonstration of proficiency at simultaneous solution...K?

As an example, we'll use the problem you suggested yesterday -- To wit:

1) Make an algebraic 'statement of the case':

Eq1 ) 4M+6W=1/8 (i.e. 4 men and 6 women working for 1 day complete 1/8 of the job.)
Eq2 ) 3M+7W =1/10 (i.e. 3 men and 7 women working for 1 day complete 1/10 of the job.)

Where:
M = the fraction of the job completed by a single male worker per day.
W = the fraction of the job completed by a single female worker per day.

Clearly, to solve the problem we need only find the value of 'W'
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

Simultaneous solution via 'Cancellation':
Note that, for a number of reasons, this is the preferred method of simultaneous solution...

1) Rewrite one of the equations such that a term in an unknown is the additive inverse of the term in the same unknown in the other equation:

Example:
Given Eq1 and Eq2:
4M+6W=1/8
3M+7W =1/10

Rewrite Eq2 thus:
(-4/3)*(3M+7W=1/10) = -4M-(28/3)W=-2/15 --- NOTE: Owing to its linearity, the solution set of the equation is not altered!

2) Add the equations:
4M+6W=1/8
-4M-(28/3)W=-2/15

Resultant equation: 0M-(10/3)W=-1/120

3) Solve the resultant equation for the unknown:

-10/3W=-120 → w=1/400

Thus one woman completes 1/400 of the task per day hence the task completion time for ten women = 40 days...

/////////////////////////////////////////////////////////////////////////////////////////////////////////

Simultaneous solution via 'substitution':

1) Solve either equation for either of the unknowns:

Example:
Given eq1): 4M+6W=1/8
Solve for 'M'
M=(-48W+1)/32

3) Substitute the solution in the other equation

Given eq2): 3M+7W=1/10
Substitute 'M' in with "((-48W+1)/32)

Resulting equation: 3*((-48W+1)/32)+7W=1/10

4) Solve the resulting equation for the unknown:

3*((-48W+1)/32)+7W=1/10→W=1/400

Again the solution --- One woman completes 1/400 of the task per day hence task completion time for ten women = 40 days...

Note that the techniques illustrated above may be applied to any number of linear equations containing any number of unknowns --- and, with certain qualifications, to non-linear equations...

I expect you to have questions! -- Please ask them!!!!

Best regards
HP

PS --- Note that the productivity ratio of the men to the women is 11:1 --- Aye, aye! aye! --- More slackers for @Aleph(0) to dismiss!

Yes i have understand the method.
well explained .

 

Then would you argue that two people, picked at random, have equal ability to become star basketball players provided their training regime is a suitable match for their respective learning styles?

The analogy of mental ability to physical characteristics while, undeniably, useful at certain junctures - would seem tenuous at best

Very best regards
HP

 

The analogy of mental ability to physical characteristics while, undeniably, useful at certain junctures - would seem tenuous at best

Very best regards
HP

But it would also seem tenuous to acknowledge that people have different physical characteristics and yet deny that different mental characteristics exist.

 

Yes i have understand the method.
well explained .

Please be certain -- We'll expect you to use the skills in the exercises

 

But it would also seem tenuous to acknowledge that people have different physical characteristics and yet deny that different mental characteristics exist.

Well indeed mental differances do exist - hence the disparity in effective 'learning styles'... Then too handicaps exist (hence my 'clear mind' stipulation) - though we must be very cautious are we to eschew pathologizing 'non-standard' -- Which, embarrassingly, has, on more than one occasion, 'translated' to something akin to 'superior'

Best regards
HP

 

Do you mean as in being able to tell whether YOU are making progress in learning this stuff?

Yes..

 

@RRITESH KAKKAR

Ok then... Let's return the exercise of post #972

 

@RRITESH KAKKAR

As a matter of courtesy, please answer the question: Will you be studying here today! -- I am growing weary of refreshing my session every 30 minutes only to discover you larking about the site without the least thought to your math studies! -- A habit, I might add, which speaks very poorly of your commitment to said studies!

 

As a matter of courtesy, please answer the question: Will you be studying here today! -- I am growing weary of refreshing my session every 30 minutes only to discover you larking about the site without the least thought to your math studies! -- A habit, I might add, which speaks very poorly of your commitment to said studies!

Someone, was sitting nearby me thats why i was talking to him and forgot to respond.

 

Two cars are traveling at 60 mph and 45 mph respectively. If the faster car travels two hours longer and twice as far, then:
What are the distances traveled by each car?
What are the operation times of each car?

Hint 1: Although I am not insisting up on it, simultaneous solution of multiple equations will significantly simplify matters.
Hint 2: Having solved for any one of the unknowns, the solution of the remaining three is simple arithmetic --- Literally!

 

@RRITESH KAKKAR

Hey Ritesh! I must go for today -- I'll leave you with the small exercise (below) with which to practice your new skills:
Please solve this via the simultaneous approach, track your units and show your work!

A power handling resistor exhibits a resistance of 160Ω and a maximum dissipation of 113 watts...
What is the maximum applied 'voltage' that will not cause the resistor to overheat?

Hint 1: When solving non-linear equations, beware of extraneous solutions!

Hope to find you better prepared to study tomorrow! --- See you then!

Best regards
HP

 

A power handling resistor exhibits a resistance of 160Ω and a maximum dissipation of 113 watts...
What is the maximum applied 'voltage' that will not cause the resistor to overheat?

R=160Ω
P=133 Watts
V=?
P=V²/R
133Watts=V²/160
V²=21,280V
V=145.8V

 

A power handling resistor exhibits a resistance of 160Ω and a maximum dissipation of 113 watts...
What is the maximum applied 'voltage' that will not cause the resistor to overheat?

R=160Ω
P=133 Watts
V=?
P=V²/R
133Watts=V²/160
V²=21,280V
V=145.8V

First off -- what part of:
Please solve this via the simultaneous approach, track your units and show your work!
Didn't you understand?

 

Please solve this via the simultaneous approach, track your units and show your work!

How to solve this via simultaneous?
i have done this method only.

 

How to solve this via simultaneous?
i have done this method only.

Use what you said you learned in posts #1023 and #1024

Moreover, leave the solution in radical notation please!

What it comes down to is I'm asking you to think for yourself -- While I realize many schools tend to discourage that - we, nonetheless, insist upon it here!

Please study on it and I'll chat with you tomorrow!

 

A power handling resistor exhibits a resistance of 160Ω and a maximum dissipation of 113 watts...
What is the maximum applied 'voltage' that will not cause the resistor to overheat?

R1=160Ω
P1=113Watt
V1=X
P1(Watt)=V1²(Volt)/R1(Ω)

like this

 

Try to express the relationship via a set of 'simultaneous equations' -- then solve using either of the methods described in post #1203

This is not a test of your ability to manipulate basic electrical units, but, rather, a sample problem on which to practice your (hopefully) newly acquired skills with the added 'twist' of non-linearity

 

@RRITESH KAKKAR

If you'll pardon an observation -- you seem to have difficulty adhering to a single subject for any length of time -- you're making progress in mathematics! -- Please 'stay the course'!

Maybe he needs to up his Ritalin dosage?

 

Maybe he needs to up his Ritalin dosage?

At risk of reversing methylphenidate's 'therapeutic paradoxicality'?!?!

Saints preserve us!

Best regards
HP

 

Ooooh! I am enjoys this with peanuts.