1. find the orthogonal trajectory of the curve y^3+3x^2y=c1.

Pls mathematicians I urgently need d solution to dis problem av solved it buh couldn't got it d question reads thus "the cost of painting a room is two parts 1 part is directly proportional to the area and d other to the square of d length of d room. D cost of painting a room measures 20m by 30m is #200 and d cost of painting anoda room measure 15m by 40m is #256. What is d cost of painting a table in metre square

Try dis pls.

Mikebis: Pls ma oga at d top help me wt dis little questn..(2y+3)^-5.its a binomial questn

..simple bt kinda long....dia diff. Ways of doin dis...(2y +3)^-5 =3^-5(1+2/3 y)^-5...using (1+y)^n=ny+n(n-1)/2! Y^2 +n(n-1)(n-2)/3! Y^3 + ...
....3^-5[-10y/3 +60y^3/9 -280y^3/27+...]. Finish up frm dia..

Mikebis: Pls ma oga at d top help me wt dis little questn..(2y+3)^-5.its a binomial questn

(a+b)^-n = a^-n + (-5)(b)(a)^-n-1 +[ (-n)(-n-1)/2](b^2) (a)^-n-2 + [(-n)(-n-1)/6](b^3)(a^-n-3)......endless
where a=2y and b=3
therefor,(2y + 3)^-5 =-32(y^-5) -5/64(y^-6) + 135/128(y^-7)-945/256(y^-.........endless

PLZ SIRS I NEED D ANS TO DIS::
if z=x+jy,where x and y are real,show that d locus|(z-2)/(z+2)|=2 is a circle and determine its centre and radius.
NOTE: | | means modulus

benbuks: Try dis pls.

writing the question down §e^-1/x/(x²[1-e^-1/x])²......... subtitute (1-e^-1/x) for u..... then du/dx(e^-1/x)/x²..making dx= du(x²/e^-1/x) ...... replacing this in the integral, we have §1/u².du.... finally integrating, we have 1/u, which equals 1/(1-e^-1/x).... replacing it with 1 and -1 respectively, we have (e+1)/(e-1)

Mbahchiboy: PLZ SIRS I NEED D ANS TO DIS::
if z=x+jy,where x and y are real,show that d locus|(z-2)/(z+2)|=2 is a circle and determine its centre and radius.
NOTE: | | means modulus

replacing the complex number in the locus we will have...... z-2= (x-2)+jy...... and z+2= (x+2)+jy..... remembering that |(z-2)/(z+2)|= |z₁|/|z₂|...... having said , we replace the values, giving us sqrt((x-2)²+y²)/sqrt((x+2)²+y²) =2....... squaring both sides and cross multiplying, the locus becomes.. 3x²+3y²+20x+12=0.... the equation is the equation of a circle..... the equation can be rewritten as (x+10/3)²+(y+0)²= 64/9....... the coordinates of the center of the circle is (10/3, 0) and the radius is (8/3)units

ADEWALE7777: Pls mathematicians I urgently need d solution to dis problem av solved it buh couldn't got it d question reads thus "the cost of painting a room is two parts 1 part is directly proportional to the area and d other to the square of d length of d room. D cost of painting a room measures 20m by 30m is #200 and d cost of painting anoda room measure 15m by 40m is #256. What is d cost of painting a table in metre square

How did table come into the question...pls check and type again

TNX@honey

if z=-16,express z in d form a+jb and find its fourth root

Mr Calculus: if z=-16,express z in d form a+jb and find its fourth root

the complex number can be expressed in the polar form p(cos¤+jsin¤)...........p= 16 and ¤=180,...... it now becomes 16(cos180+jsin180)........ following the rule that z^1/n=p^1/n([cos(¤+2pi.k/n)]+j[sin(¤+2pi.k/n)]), replacing the values, we have.......the fourth root= 2(cos[45+(pi.k/2)]+ j.sin[45+(pi.k/2)])...... where k= 1, 2, 3, 4, 5........ i hope i am correct

honey: the complex number can be expressed in the polar form p(cos¤+jsin¤)...........p= 16 and ¤=180,...... it now becomes 16(cos180+jsin180)........ following the rule that z^1/n=p^1/n([cos(¤+2pi.k/n)]+j[sin(¤+2pi.k/n)]), replacing the values, we have.......the fourth root= 2(cos[45+(pi.k/2)]+ j.sin[45+(pi.k/2)])...... where k= 1, 2, 3, 4, 5........ i hope i am correct

hmm.......
tnx 4 attemptin
u tried sir but dats not it.
and also rememba i dint ask 4 d polar form

Solve dis exponetial equation:3^x + 4^x = 5^x.

Solve d equation: 4^x = 8x

Prove that 2=1

I am going to teach you some tricks in muiltipying numbers without the use of calculator. Here we go

Multiplying 11 with other numbers

For example,

Case1:11 x 13

Step 1: write down the unit digit which is 3
Step2: add 3 to 1 and u will have 4
Step 3: write down 1 and u will have 1.

Therefore, the answer is 143.

Case2: 11 x 14423

Step1: write down 3 as the unit digit n u have 3
Step2: add 3 to 2 and u will have 5
Step 3: add 2 to 4 and u will have 6
Step 4: add 4 to 4 and u will have 8
Step 5: add 4 to 1 and u will have 5
Step 6: write down 1 and u will have 1
Therefore, the answer is 158653.

d citizen:
I am going to teach you some tricks in muiltipying numbers without the use of calculator. Here we go

Multiplying 11 with other numbers

For example,

Case1:11 x 13

Step 1: write down the unit digit which is 3
Step2: add 3 to 1 and u will have 4
Step 3: write down 1 and u will have 1.

Therefore, the answer is 143.

Case2: 11 x 14423

Step1: write down 3 as the unit digit n u have 3
Step2: add 3 to 2 and u will have 5
Step 3: add 2 to 4 and u will have 6
Step 4: add 4 to 4 and u will have 8
Step 5: add 4 to 1 and u will have 5
Step 6: write down 1 and u will have 1
Therefore, the answer is 158653.

Nice job citizen...they call this vedic maths...there are many other vedic maths tricks

d citizen:
Solve dis exponetial equation:3^x + 4^x = 5^x.

..x=2...use (FLT)

Proof dat 1 = 2,

You know dat a^2- a^2= 0

Then a^2 - a^2=a (a - a) ( by factorising)

But a^2 - a^2 = (a - a) (a + a) (difference of two square)

Therefore, a(a - a) = (a- a) (a +a)
a= (a+a)
a=2a
1=2
NEED ANSWER TO MY PREVIOUS EQUATIONS

d citizen:
Prove that 2=1

,.let p=q.
Multiplying both sides with p we have p^2=pq
p^2-q^2=pq-q^2 (subtracting q^2 frm both side)
(p+q)(p-q)=q(p-q)
=>p+q=q
recall that p=q
2q=q
hence 2=1 (dividing through a non-zero integer).
.proved.

Gud dey my gud peopl, pls can smone help me with this Qa1. Differentiate f(x)= 3/x3 using first principle method
b. First the first derivative when y= -1/3x 1/2

let me give you some tricks on how 9 with other numbers without the use of calculator

Here we go

Case1= 9 x 2

Step1: subtract 1from 2 and u get 1. Write it down as the tenth digit

Step 2: think of a number dat u will add to 1 to get 9 and the result is 8. Write it down as the unit digit

Therefore, the answer for 9x 2 = 18

Case 2: 9 x 3

Step 1: subtract 1 from 3 and u get 2. Write it down as the tenth digit.

Step 2: think of a number dat will be added to 2 to get 9 n the result will be 7 . Write it down as the unit digit.

Therefore, the answer for 9 x 3 = 27

U like the tricks . Try and do the following practice drills

1.9 x 5=

2. 9 x 8=

@benbuk, i need u to solve the problem not just giving me the answer to the problem. I need the working of the problem.

Q2. Find the maxima and minima value of y=2X3 -5X2 +4x-1
Q2b. If y =X4 +2X2-3X2-4X+6 when d3y/dx3=0

Limx------->-1{x3-6x+2/-x2+x+9}

Qa. A polytechnic emloys 79 staff, 52 of whom are men, 38 people including all the women are lecturers. Find the number of men that are lecturers.
B. the daily profit, q, of a supermarket is give as q(x)=8x-0.04x2, when x is the number of good sold. Hw many goods will yield maximum profit and what is the maximum profit?

Q2(a),

Y= 2x^3 -5x^2 + 4x -1

dy/dx=6x^2-10x + 4

At the stationary point, dy/dx =0

6x^2- 10x + 4= 0

6x^2 -6x -4x + 4=0

6x (x-1) -4(x-1)=0
(6x-4)(x-1)=0
x=1 or x=4/6=2/3

But, d^2y/dx^2 = 12x-10

Wen x=1, d^2y/dx^2= 12(1)-10=2 (minimum becos d^2y/dx^2 >0

Ymin= 2(1)^3 -5(1)^2 +4(1)-1=0

Ymax=2(2/3)^3 -5(2/3)^2 + 4(2/3)-1
. Calculate it

y=x^4+2x^3- 3x^2 -4x 6.

dy/dx=4x^3+6x^2-6x-4.

d^2y/dx^2= 12x^2 +12x-6.

d^3y/dx3= 24x- 12

Since d^3y/dx^3=0,

24x-12=0
X=-12/24=-1/2. right on board, the math doctor

@worldlife,

Limit x3 -6x + 2/ -x2+x +9
X=-1

Put x=-1, (-1)^3 -6(-1) +2 / - (-1)^2 + (-1) + 9

Answer is 7/7=1

Q(a) the number of men dat re lecturer is 11. U are going to use a lattice diagram to solve the problem

The number of women dat are lecturer =79-52= 27

Since the sume of women lecturer and men lecturer = 38, the number of men lecturer = 38-27=11. Simple.

@worldlife

Q(x)= 8x-0:04x^2

dq(x)/dx= 8-0.08x

At the turning point, dq(x)/dx=0

8-0.08x=0, x=8/0.08=100
The number of item sold for max profit = 100,
The max profit = 8(100)- 0:04 (100)^2=400