JF Mathematics clinic Special thread

sembo said:

Mkuu Qn 5 nimeshalijibu.

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Sorry ni 3 na 4

Ruttashobolwa said:

Sorry ni 3 na 4

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Poa Mkuu.

Gwangambo said:

Prove 1=2

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1=2
Hence proved!

Hesabu sijawahi kuzipenda...kwa kuwa uwongo ni mwingi sana. 2x+y=6 wapi na wapi?

CHAMVIGA said:

Wrong perception.

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Mkuu chamvinga mbona huoneshi jibu?

Mchawi wa calculus na trig niko hapa. Kama kuna mdau anahitaji msaada katika hizo topics asisite kunitonya

The Sum of the first ten term is -55 while the sum of next 7 term is -217. Find the sum of first 17th term and common difference

Ruttashobolwa said:

Mkuu chamvinga mbona huoneshi jibu?

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Nipo mkuu kitandani tangu nafungua thread hii so nikikaa fresh nitashuhulikia matatizo yote yalioshindikana.

Ruttashobolwa said:

The Sum of the first ten term is -55 while the sum of next 7 term is -217. Find the sum of first 17th term and common difference

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Soln:

From the formula S=0.5(2A1+d(n-1))n
where A1= the first term of the arithmetic progression
d= common differnce of the arithmetic progression
n= number of the terms of the progression and
S= Sum of the terms of the progression

Naomba mnifuate sasa taratiibu kabisa

The sum of the first ten term is -55, this means from the formula
-55=0.5(2A1+d(10-1))10
-55=0.5(2A1+9d)10.....then devide each side by 0.5X10
-11=2A1+9d..................................eqn (i)

The sum of the next 7 term is -217, this means that after the first 10 terms the next seven terms will start from A11
Then let A11 be the 11th term of the progression and the 1st term of the 7 next terms.

Then from the formula
-217=0.5(2A11+d(7-1))7
-217=0.5(2A11+6d)7..........then devide each side by 0.5X7
-62=2A11+6d..................................eqn (ii)

Then let the sum of the first 17 terms be S17
kwa akili ya kawaida sasa; the sum of the first 17 term= sum of the first 10 terms + sum of the next 7 terms
S17= -55+-217
S17=-272.....................eqn (iii)
Frm the eqn (iii) S17=-272 and the summation formula S=0.5(2A1+d(n-1))n
we have -272=0.5(2A1+d(17-1))17
-272=0.5(2A1+16d)17......then devide each side by 0.5X17
-32=2A1+16d.................................................eqn (iv)
Then
Solve eqn (i) and eqn (iv) together
We have -11=2A1+9d
-32=2A1+16d because we need d, we minus each side

21=-7d ...then d=-3

Conclusion, the common difference of the progression is -3, and the sum of the first 17 terms is -272.

teh teh enzi zangu hizi kule Uhuru secondary, Shinyanga huko.

Ruttashobolwa

Safi sana.

QN.1 Nahitaji clarification on the second sentence.

You have stated that "it takes pipe A and B 10 Minutes to fill tank and it takes pipe C 10Min to empty it." Kwa nilivyoelewa hapa if both pipes A and B are filling the tank at the same time then it will them take 10min to fill the tank.

If this is what it has been intended then to empty this tank it will take forever simply because the same rate filling the tank is the same rate empting the tank.

Take total volume of the tank being V. take R1 and t1 being the rate and time at which the tank is being filled by pipe A and B.Take R2 and t2 being the rate and time of empting the tank by pipe C.

Note when filling the tank by pipe A and B alone V=R1*t1----------------(i)

Also when empting the tank by pipe C alone V=R2*t2-------------(ii)

Now take the consideration when both three pipes are open The new net rate R at which tank will be filled or emptied at time t

V=R*t

R=R1-R2---if net action is filling and R=R2-R1 if net action is empting.

Now equate (i) and (ii)

R1t1=R2t2

R1/R2=t2/t1 recal t1=10 and t2=10

R1/R2=10/10

R1/R2=1 therefore R1=R2----------(*)

If R1=R2 then the net Rate R=R1-R2=0
Thus having a net Zero net Rate this means it will take forever to empty this tank.

Narejea ile sentensi ya pili kwenye swali kama ilikua imaanishe each pipe A and B takes 10minutes to fill the tank the hapo pangekua na solution inayoleta maana zaidi.

Mkuu franz hapo ina maanisha pipe A and B zinatumia dakika10 kujaza tank na Pipe C inachukua dakika 10 kumwaga let say mafuta yote yaliyo kwenye tank(to empty tank) Sasa kama pipe zote A,B,C zikufunguliwa kwa muda mmoja zitachukua dakika ngapi ku empty that tank?

Note that pipe C pekee inatumia dakika kumi kumaliza mafuta yote kwenye tank! Sijui kama umenipata hapo! Swali hili nimelitoa sehemu...nafikiri huu ni uwanja mpana wa kulichambua.
franz

Log (X+Y)=log 5 ni sawa na kusema Log X+Y=5?

How many different ways can the letters P,P,Q,Q,R,S,T to be arranged if..

a) The letter R must be to the left of the letter P ?
b) The letter Q must be the right of the letter T ?

Ruttashobolwa said:

Log (X+Y)=log 5 ni sawa na kusema Log X+Y=5?

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Si sawa kwasababu;

log(x + y) = log 5 is equal with
(x + y) = 5

log x + y = 5 is equal with
x = 10 power (5 + y)

sembo said:

Si sawa kwasababu;

log(x + y) = log 5 is equal with
(x + y) = 5

log x + y = 5 is equal with
x = 10 power (5 + y)

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Noted.....

Ruttashobolwa said:

Mkuu franz hapo ina maanisha pipe A and B zinatumia dakika10 kujaza tank na Pipe C inachukua dakika 10 kumwaga let say mafuta yote yaliyo kwenye tank(to empty tank) Sasa kama pipe zote A,B,C zikufunguliwa kwa muda mmoja zitachukua dakika ngapi ku empty that tank?

Note that pipe C pekee inatumia dakika kumi kumaliza mafuta yote kwenye tank! Sijui kama umenipata hapo! Swali hili nimelitoa sehemu...nafikiri huu ni uwanja mpana wa kulichambua.
franz

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kama swali la pipe umelitoa mahala ama limekosewa au umekopi vibaya, only 2 pipes are emptying the tank and not 3, this is maths, not a language test!

siyo siri hii thread imenipandishia malaria

na mimi naongezea math problems

1. (logx)square=log((x)square) find the value of x
2. underoot(logx)=log(x underroot) find the value of x

kamwamu said:

kama swali la pipe umelitoa mahala ama limekosewa au umekopi vibaya, only 2 pipes are emptying the tank and not 3, this is maths, not a language test!

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Ok..do as you think its correct