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#31 j87ibz 39th CTP (PAAS) Join Date: May 2010 Location: Wah Cantt + Charsadda. Posts: 71 Thanks: 60 Thanked 97 Times in 45 Posts  ||@sibgakhan :

Salam, but let me try to solve it, though i dont know much about pure maths. f(x)= x^2 -x-1
g(x)= 3/x

now fog(x)= f { g(x) } = f ( 3/x )
replace x by 3/x in f(x)

fog(x) = (3/x)^2 - (3/x) - 1

= (9/x^2) -3/x -1

The above expression can be simplified easily , taking LCM as x^2,

= 9 -3x - x^2
------------
x^2

Domain of f (x) = { all real numbers }
Domain of g (x) = { all real numbers except 0 }
Domain of fog(x) = { all real numbers except 0}

Lim x^3 -5x^2 + 6x / ( x^2 -9)
x--->3

Solution :

Applying limit to every factor, we get

Lim x^3 - Lim 5x^2 + Lim 6x / ( x^2 -9)
x-->3 x-->3 x-->3

The limit Lim 6x / ( x^2 -9) is in (c /0) form, so requires L hospital rule
x-->3

so taking d/dx to 6x / ( x^2 -9) in denominator and nominator separately, we get,

6/ (2x-9)

now putting value an applying limit, we get

Lim x^3 - Lim 5x^2 + Lim 6/ (2x-9)
x-->3 x-->3 x-->3

= 3^3 - 5(3)^2 + 6 /( 2*3 -9)

= 27 - 45 -2
= -20

03.

7< ( 1-2x) ≤ 10

can be broken to two in equalities

=> 7< 1-2x ||||||||| 1- 2x ≤ 10

=> 7-1 < -2x ||||||||| => -2x ≤ 10-1

=> 6< -2x ||||||||| => -2x ≤ 9

=> -6 > 2x ||||||||| => 2x > -9

=> -3 > x ||||||||| => x > -4.5
which means between -∞ , -3 ||||||||| which means between -4.5 , ∞

when plotted together.

__-9/2------4-------3_____-2_____-1_____0____ 1_____2_____3______4___
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 The Following 2 Users Say Thank You to j87ibz For This Useful Post: sahibakhushik89 (Sunday, May 29, 2016), sibgakhan (Saturday, October 30, 2010)
#32 tanolig Senior Member Join Date: Aug 2010 Posts: 105 Thanks: 33 Thanked 83 Times in 46 Posts  Q#01
Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10

Solution:
=> 7 < 1-2x ≤ 10
multiply through out by (-)
=> -10 ≤ 2x-1 <-7
=> -9 ≤ 2x < -7
Divide through out by 2
=> -9/2 ≤ x < -7/2
Hence the resultant solution is semi close semi open interval [-9/2 , -7/2) on real line.

Q#03
Simplify, then apply the rules of limit to evaluate
lim x->3 x3(power3)-5x2(power2)+6x/x2(power2)-9

Solution:
lim x->3 {x3(power3)-5x2(power2)+6x/x2(power2)-9} --------> {c/0 form}
(Applying Lop-ital)
Differentiating both denominator and nominator w.r.t 'x'
=> lim x->3 {3x2(power2)-10x+6/2x}
Now applying limt
=> {3*(3^2)-10*3+6}/2*3
=> {27-30+6}/6
=> 3/6
=> 1/2 Ans
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 The Following User Says Thank You to tanolig For This Useful Post: sibgakhan (Monday, November 01, 2010)
#33 tanolig Senior Member Join Date: Aug 2010 Posts: 105 Thanks: 33 Thanked 83 Times in 46 Posts  Maths!

@ Sibgakhan

Q#01
Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10

Solution:
=> 7 < 1-2x ≤ 10
multiply through out by (-)
=> -10 ≤ 2x-1 <-7
=> -9 ≤ 2x < -7
Divide through out by 2
=> -9/2 ≤ x < -7/2
Hence the resultant solution is semi close semi open interval [-9/2 , -7/2) on real line.

Q#03
Simplify, then apply the rules of limit to evaluate
lim x->3 x3(power3)-5x2(power2)+6x/x2(power2)-9

Solution:
lim x->3 {x3(power3)-5x2(power2)+6x/x2(power2)-9} -------->(A) {c/0 form}
L' Hospital Rule is applied only if function has the form either {0/0} or {∞/∞}.
Now we proceed as follows
=> lim {x->3 x^3-5x^2+6x}/x^2 - 9
Nominator can be expanded as
x^3-5x^2+6x = x^3-3x^2-2x^2+6x = x^2*(x-3)-2x*(x-3) = (x^2-2x)*(x-3) ---->(i)
Also
x^2 - 9 = (x+3)*(x-3) ------>(ii)
Now using (i) and (ii) in (A)
=> lim x->3 {(x^2-2x)*(x-3)}/(x+3)*(x-3)
=> lim x->3 {(x^2-2x)}/(x+3)
Applying limit
=> {3^2 -2*3}/3+3
=> {9-6}/6
=> 3/6
=> 1/2 Ans

Best Regards!
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#34
 sibgakhan SIBGA-TUL-JANAT Join Date: Jul 2005 Posts: 1,222 Thanks: 349 Thanked 427 Times in 261 Posts     how we can convert fraction part of a question into hours and min?
i mean 5 5/7 and 10 2/70 comtains how many hours and min and what the formula??

thanks
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#35 Ayesha Mahmood Senior Member Join Date: Jan 2010 Location: DGKhan & Isb Posts: 323 Thanks: 376 Thanked 264 Times in 178 Posts   Quote:
 Originally Posted by sibgakhan how we can convert fraction part of a question into hours and min? i mean 5 5/7 and 10 2/70 comtains how many hours and min and what the formula??
you can't convert fractions to minutes or hours. Only units are inter converted.

suppose you have to convert 5 5/7 seconds to minutes and hours then you may proceed as follows:

1 min = 60 sec
=>60 sec = 1 min
=>1 sec = 1/60 min
=>5 5/7 sec= 5 5/7 * 1/60 min = 40/7 *1/60 min = 2/21 min

1 hour = 60 min = 60 * 60 sec = 3600 sec
=>3600 sec = 1 hour
=>1 sec = 1/3600 hr
=>5 5/7 sec = 5 5/7 * 1/3600 hr = 40/7 * 1/3600 hr = 1/630 hr

and if 5 5/7 is not in sec but days then it will be converted to min and hours as follows:

1 day = 24 hrs
=>5 5/7 days = 5 5/7 * 24 hrs = 40/7 * 24 hrs = 137 1/7 hrs

also

1 day = 24 hrs = 24 * 60 min = 1440 min
=> 5 5/7 days = 40/7 * 1440 min = 8228 4/7 min.
 The Following User Says Thank You to Ayesha Mahmood For This Useful Post: sibgakhan (Sunday, November 07, 2010)
#36
 sibgakhan SIBGA-TUL-JANAT Join Date: Jul 2005 Posts: 1,222 Thanks: 349 Thanked 427 Times in 261 Posts     can anyone solve these questions...

1. If the area of rectangle increased by 69%, the length of arm of the rectangle should increase:

2. If the length of arms of rectangle increased by 5% and 7% respectively, then the area of rectangle should increase by:

3. Jack’s salary is 150% of Tom’s salary; Tom’s salary is 80% of Adam’s salary.
If Adam’s salary is S, then what is the ratio of Jack’s salary to Adam’s salary:

5. The cost price of a toy is \$50, but its offer price is 108%. After one week it is sold on 10% discount. What will be the cost of toy?

6. The cost of first 500 prints is \$10, while after it, cost for each is (10-x/50). What will be X, if the total cost is \$75

7. 45% of people of a town have brown hair, while 20% of people have brown eyes. Meanwhile 10% have both brown hair and brown eyes. How much people have neither brown hair nor brown eyes?

8. In a town an appeal for fund raising is made. People of the town respond to that in this way: 45% people contributed \$40, 30% contributed \$20 while rest contributes \$2. If the total amount of people who contribute \$2 is \$300, then what will be the total?

9. if the mean of 10 items is -10 and sum of 6 items is 100. what is the mean of remaining items?

10. In 2009, Ali read 10 English and 7 French books. In 2010, his ratio of English buks is 3times french buks and he read 60% of
french books in 2010 then how many books he read in 2010?

11. Ahmed buys a merchandise on commission of 25 paisa. if the cost price is Rs.20 what percentage of commission he received?

12. if the price of tea increases by 20%. suppose a consumer expenditure on tea is Rs.200. then by what percentage he should cut his consumption of tea so that 20% increase in price of tea does'nt effect on his original expenditure on tea?

13. The growth rate is increased by 25% from 2000 to 2010. if the growth in 2010 is "W". what was the growth on 2000?

14. A can do a piece of work in 20 days which A and B together can do in 12 days. B alone can do it in hw many days?

15. In an election one of the 2 candidates gets 40% of the total votes but he losses by 160 votes . what is the total number of votes?

16. Salma spent 1/10 of her income on clothes, 1/10 of the remaining on food, and 1/3 of the remaining on rental. if she left with Rs. 648 what is her total income?

17. The total no. of students in a class are 335250. if they are adjusted in a square class with equal rows and columns, only 9 are left behind. what is the no. of rows?
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Last edited by sibgakhan; Wednesday, February 16, 2011 at 12:51 AM.
#37
 sibgakhan SIBGA-TUL-JANAT Join Date: Jul 2005 Posts: 1,222 Thanks: 349 Thanked 427 Times in 261 Posts     1. If the area of rectangle increased by 69%, the length of arm of the rectangle should increase:

2. If the length of arms of rectangle increased by 5% and 7% respectively, then the area of rectangle should increase by:

plz solve these questions urgently.
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Hijr me lazt-e-talb, wasl main marg-e-arzoo...!!!
#38 bear Senior Member Join Date: Jun 2010 Location: لاہور Posts: 109 Thanks: 54 Thanked 93 Times in 50 Posts  question 1
area = 100 ( 50 x 2)
new area = 169 (increased by 69 percent )

169 = 84.2 x2

84.5 - 50 = 34.5
34.5 /50 = 69 %

this means arm length will also increase by same amount if other arm's length doesn't change .

question 2

area = a x b = ab
new area = 1.05a x 1.07b = 1.1235ab

new area - old area = 1.1235-1 = .1235 = 12.35 %
#39 Malik Asfand Yar Junior Member Join Date: Nov 2010 Location: Dera Ismail Khan Posts: 8 Thanks: 5 Thanked 0 Times in 0 Posts  Q9 100+X/10=-10
X=-200 and the average of remaining items is -50
#40 Aamish Bhatti Senior Member Join Date: Jan 2012 Location: Atlantis Posts: 268 Thanks: 609 Thanked 105 Times in 78 Posts  Quote:
 Originally Posted by ATIF FAUN 6) A shopkeeper sold an electric iron at 10% profit. Had he sold an iron at 20% profit, he would have gain rs.%) more. The cost price of the fan was: A)400 B)450 C)550 D)500

I think problem has been mis-typed. Please mention the amount.
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