Nairaland Mathematics Clinic - Education (160)

Nairaland Mathematics Clinic - Education (160) - Nairaland

Nairaland Forum › Nairaland General › Education › Nairaland Mathematics Clinic (548289 Views)

1 2 3 ... 157 158 159 160 161 162 163 ... 284 Reply (Go Down)

Re: Nairaland Mathematics Clinic by donfourier(m): 9:08am On Jan 14, 2015

a matrix of 5x5 hmmmmmmmmmmmm......

Re: Nairaland Mathematics Clinic by donfourier(m): 9:24am On Jan 14, 2015

a positive integer is called tico if it is the product of three different prime number that add up to 74 . verify that 2014 is tico. which year will be the next tico year? which one will be the last tico year in the history?

Re: Nairaland Mathematics Clinic by donfourier(m): 11:47am On Jan 14, 2015

Laplacian:
recall, sec²y=1+tan²y.
From the LHS,
sec²x-1=1+2(sec²y-1) or
sec²x=2sec²y or
cos²y=2cos²x or
cos²y=(2cos²x-1)+1, does the expression in the bracket look familiar? *****

u can also use the condition given above to dissolve the question @ sir laplacian.....
- i used it ....

That's cos2x.
So, cos²y=cos2x+1
or
cos²y-1=cos2x
can u finish it from here? Hop it helps!

Re: Nairaland Mathematics Clinic by Nelsonesq(m): 2:47pm On Jan 14, 2015

Mathematicians in the house, Pls solve this
The transformation equations from ashy to cartesian coordinates are
X=e^u.secvcoshw
Y=e^u.tanvcoshw
Z=e^usinhw.
If f=f(x,y,z) is a differentaible function and H=y.df/dx+x.df/dy+df/dz, derive an appropriate expression for H in ashy coordinates.

Re: Nairaland Mathematics Clinic by jackpot(f): 7:04am On Jan 15, 2015

Laplacian:
Mr. A can complete a farm work in t₁ hours. Mr. B can finish the same work in t₂ hours. How would it take them if they worked together?

In an hour,
Mr A must have done (1/t_1) times the work
Mr B - (1/t_2) times the work
so, in an hour, both of them working together must have done (1/t_1+1/t_2) times the work
so, working together, they completes the work in 1 / (1/t_1 + 1/t_2) hours. This is the same as t₁t₂/(t₁+t₂) hours.

@Laplacian and others, please feel free to criticize.

Re: Nairaland Mathematics Clinic by Nobody: 7:37am On Jan 15, 2015

Laplacian:
Mr. A can complete a farm work in t₁ hours. Mr. B can finish the same work in t₂ hours. How would it take them if they worked together?

Let the farm work done be 1 farmwork. Hence the rate at which Mr. A works is 1/t₁ (Work/hrs). Similarly Mr. B's rate since the quantity of work is similar (1 farm work) is 1/t₂.

Hence both of them working together would accomplish 1/t₃ rate.

= 1/t₁ + 1/t₂ = 1/t₃

I'm sure you can take it from there.

Re: Nairaland Mathematics Clinic by Nelsonesq(m): 9:23am On Jan 15, 2015

Richiez:
We diagnose and solve math problems here
This thread is the meeting point for nairaland math gurus...I dare anyone to ask a question in mathematics without me having an answer to them, LETS START

Here is one for you to solve..... Abeg no fall my hand o
The transformation equations from ashy to cartesian coordinates are
X=e^u.secvcoshw
Y=e^u.tanvcoshw
Z=e^usinhw.
If f=f(x,y,z) is a differentaible function and H=y.df/dx+x.df/dy+df/dz, derive an appropriate expression for H in ashy coordinates.

Re: Nairaland Mathematics Clinic by Laplacian(m): 11:50am On Jan 15, 2015

jackpot:
In an hour,
Mr A must have done (1/t_1) times the work
Mr B - (1/t_2) times the work
so, in an hour, both of them working together must have done (1/t_1+1/t_2) times the work
so, working together, they completes the work in 1 / (1/t_1 + 1/t_2) hours. This is the same as t₁t₂/(t₁+t₂) hours.

@Laplacian and others, please feel free to criticize.

that's pretty!! (i didn't think of dis approach)

Scrypt:
Let the farm work done be 1 farmwork. Hence the rate at which Mr. A works is 1/t₁ (Work/hrs). Similarly Mr. B's rate since the quantity of work is similar (1 farm work) is 1/t₂.

Hence both of them working together would accomplish 1/t₃ rate.

= 1/t₁ + 1/t₂ = 1/t₃

I'm sure you can take it from there.

hahahaha...u pay me back in my coin? (nice work!!)

Re: Nairaland Mathematics Clinic by donfourier(m): 2:18pm On Jan 15, 2015

by using identity ie trigonometric identity

Re: Nairaland Mathematics Clinic by Kentnickole(m): 3:40pm On Jan 15, 2015*

Laplacian:
Mr. A can complete a farm work in t₁ hours. Mr. B can finish the same work in t₂ hours. How would it take them if they worked together?

Mr A's farm work per hr = 1/t1

Mr B's farm work per hr = 1/t2

A and B working together = 1/t1+ 1/t2
= t1t2/(t2 + t1)

Hope this helps.

Re: Nairaland Mathematics Clinic by Laplacian(m): 8:29pm On Jan 15, 2015

Show that; If 2ⁿ+1 is a prime, then, n is a power of 2

Re: Nairaland Mathematics Clinic by bigwig97(m): 9:03pm On Jan 15, 2015

can someone help to solve these questions in d pix..thankx

Re: Nairaland Mathematics Clinic by naturalwaves: 3:30pm On Jan 16, 2015*

agentofchange1:
hay guys...try this cheep 1 .

A box contains a 10-kobo piece ,a 5-kobo piece and a 1-kobo piece. Two coins are drawn , one at a time with replacement .
What is the probability that
i) the two coins are not of same value
ii )they are of same value .?

happy Sunday .

Let T, F, O represent the 10kobo,5kobo and 1kobo notes respectively.

The probability of picking anyone of them is. 1/3 and pr of not picking anyone is 2/3.

Pr ( they are not of the same colour)
Implies pr ( TF) or pr (TO)or pr(FO)
= (1/3 *1/3) + (1/3*1/3) + (1/3*1/3)
= 1/9 + 1/9 +1/9
=3/9
= 1/3.

Pr( same value)
Implies pr (TT) or pr (FF) or pr (OO)
= (1/3*1/3) + (1/3*1/3) + (1/3*1/3)
=1/9+1/9+1/9
=3/9
=1/3.

Re: Nairaland Mathematics Clinic by naturalwaves: 3:44pm On Jan 16, 2015

bigwig97:
can someone help to solve these questions in d pix..thankx

Hahahaha, go and study the bisection method very well and apply it to the question, you don't expect someone to start drawing all those lines and iterations for you.

Re: Nairaland Mathematics Clinic by Temieasy(m): 6:41pm On Jan 16, 2015

bigwig97:
can someone help to solve these questions in d pix..thankx

xup, guy I solved the bisection method, but when I got to the 10th iteration. but did not include the error tolerance in ur question. I think the answer should b 0.373046875 as d midpoint of the interval of [0, 1] I used.
shikena.. would try and upload d pic

Re: Nairaland Mathematics Clinic by bigwig97(m): 7:47pm On Jan 16, 2015

Temieasy:
xup, guy I solved the bisection method, but when I got to the 10th iteration. but did not include the error tolerance in ur question. I think the answer should b 0.373046875 as d midpoint of the interval of [0, 1] I used.
shikena.. would try and upload d pic

thanks man! dnt bother 2 upload pix av gotten t here also..bt the C++ part 4rm 2nd pix z nt stil clear

Re: Nairaland Mathematics Clinic by Nobody: 9:20pm On Jan 16, 2015

The solution to the question:
x+y=5 --------------(1)
x^x+y^y=31 --------------(2)
therefore by breaking down equation 2 we have x^x+y^y=2^2+3^3. By equating, we have x^x=2^2 and y^y=3^3. So x=2(twice) and y=3(twice)

Re: Nairaland Mathematics Clinic by Nobody: 9:25pm On Jan 16, 2015

Solve this:
x^2=2^x, find the value of x

Re: Nairaland Mathematics Clinic by Temieasy(m): 11:23pm On Jan 16, 2015

bigwig97:
thanks man! dnt bother 2 upload pix av gotten t here also..bt the C++ part 4rm 2nd pix z nt stil clear

did u get the same answer I got? as for the c++,am not too good at it just learning

Re: Nairaland Mathematics Clinic by ameer2: 6:56am On Jan 17, 2015

gurus in d house.pls help mee solve dis questions. Find the absolute and relative errors in Y given that the function y=2.0Sin x + 3 ln x to be evaluated for X=1.26.

Re: Nairaland Mathematics Clinic by bolkay47(m): 7:00am On Jan 17, 2015

jgenius:
Solve this:
x^2=2^x, find the value of x

use iteration method::
F(x)=x^2-2^x
F“(x)=2x-2^xln2
use x0=0 as starting point. You will get 2..

Re: Nairaland Mathematics Clinic by bigwig97(m): 7:14am On Jan 17, 2015

Temieasy:
did u get the same answer I got? as for the c++,am not too good at it just learning

i stopped at 4th iteration.. and my ans at dt point z 0.375...xo definately u would b correct. 4 d c++, i wil find how 2 do t sha.. thanks

Re: Nairaland Mathematics Clinic by mdee1(m): 8:23am On Jan 17, 2015

Pls guys help with this assignment
.

Find the equation of the line whose perpendicular from the origin is 3-units and is at an angle of 40 degree to the + y-axis
.
.
And the second picture, just show that the first answer PQ(up) equals is equal to the second answer PQ(down) equals. thanks in advance

Re: Nairaland Mathematics Clinic by Nobody: 10:01pm On Jan 17, 2015

Adol16:
Maths gurus pls help me solve the simultaneous equations

x + y =5
x^x + y^y=31

the simplest way of solving it is by breaking down eqn 2.i.e x^x+y^y=2^2+3^3,now by equating we have x^x=2^2 and y^y=3^3.Therefore x=2 and y=3.

Re: Nairaland Mathematics Clinic by 2nioshine(m): 4:06pm On Jan 18, 2015

badmus45:
1. The equation of motion of a forced oscillation is d2y/dt+2dy/dt
+5y=4sin5t solve the equation given that t=0 ,y=0 and dy/dt=0.
(2)determine the equation of the curve which satisfies the equation
xydy/dx=x^2-1 which passes. thru point (1,2)........abeg

check this out
Q1.
Hint: Obtain the auxiliary equation and solve the L.H.S
ie
m2 + 2m + 5=0
m=-1+2i or -1-2i
thus the first soln becomes
Y(t)=e^-t (Asin2t +B cos 2t)
since an expression in sine already appears in the soln the R.H.S is solved as thus.
Y=Ctsint +Dtsin
# Differentiate the above to the second power and order
# substitute values to the actual equation given in the Question

#compare coeficient and obtain a general equation in C and D
# combine the general solution of the LHS and RHS
#Input the given boundry condition

Hope it helps...................

Re: Nairaland Mathematics Clinic by efficiencie(m): 12:58am On Jan 21, 2015*

efficiencie: the partial derivative of (δx/δy) with respect to 'x' is equal to what?

Re: Nairaland Mathematics Clinic by rashywire: 6:43am On Jan 21, 2015

pls help me with dis question,
if (x-y)^3 = A(x+y), prove d@ (2x+y)dy/dx = x+2y
source: KA STROUD FURTHER PROBLEM 7

Re: Nairaland Mathematics Clinic by efficiencie(m): 9:51am On Jan 21, 2015

rashywire:
pls help me with dis question,
if (x-y)^3 = A(x+y), prove d@ (2x+y)dy/dx = x+2y
source: KA STROUD FURTHER PROBLEM 7

given that:
(x-y)^3 = A(x+y),
the derivative wrt x is:
3(x-y)^2 (1-dy/dx)=A(1+dy/dx)
And since
A=(x-y)^3/(x+y)
then
3(x-y)^2 (1-dy/dx)=((x-y)^3/(x+y))(1+dy/dx)
3(x+y)(1-dy/dx)=(x-y)(1+dy/dx)
3(x+y)-3(x+y)(dy/dx)=(x-y)+(x-y)(dy/dx)
((y-x)-3(x+y))(dy/dx)=(x-y)-3(x+y)
2(-y-2x)(dy/dx)=2(-x-2y)
(2x+y)(dy/dx)=x+2y which is the required relation.

1 Like

Re: Nairaland Mathematics Clinic by jaryeh(m): 3:51am On Jan 22, 2015

Chai! Long time........

I need help on this pls..

tag: jackpot, Alphamaximus, dejt4u, doubledx, Richie and other generals. I don forget una names finish o.

Re: Nairaland Mathematics Clinic by efficiencie(m): 2:10pm On Jan 22, 2015

jaryeh:
Chai! Long time........

I need help on this pls..

tag: jackpot, Alphamaximus, dejt4u, doubledx, Richie and other generals. I don forget una names finish o.

Given that:
arccosa+arccosb+arccosc=π

arccosa+arccosb=π-arccosc

Take sin of both sides

sin(arccosa+arccosb)=sin(π-arccosc)

sin(arccosa)cos(arccosb)+ cos(arccosa)sin(arccosb) =sinπ.cos(arccosc)- cosπ.sin(arccosc)

√(1-cos^2(arccosa)) cos(arccosb)+ cos(arccosa) √(1-cos^2(arccosb)) =sinπ.cos(arccosc)- cosπ. √(1-cos^2(arccosc))

b√(1-a^2)+a√(1-b^2)=√(1-c^2)

Similarly since we can rewrite the equation as:
arccosa+arccosc=π-arccosb

We have that:

c√(1-a^2)+a√(1-c^2)=√(1-b^2)

c√(1-a^2)-√(1-b^2)=-a√(1-c^2)

on solving for √(1-a^2) in the simultaneous equations below (using Crammer's rule):

b√(1-a^2)+a√(1-b^2)=√(1-c^2) ...1

c√(1-a^2)-√(1-b^2)=-a√(1-c^2) ...2

We have that:

√(1-a^2)=(-√(1-c^2)+a^2.√(1-c^2))/(-b-ac)

√(1-a^2)=(√(1-c^2)-a^2.√(1-c^2)/(b+ac)

(b+ac)√(1-a^2)=(1-a^2)√(1-c^2)

On squaring both sides:
(b+ac)^2.(1-a^2)=(1-a^2)^2.(1-c^2)

And dividing thru by (1-a^2)
(b+ac)^2=(1-a^2)(1-c^2)

b^2+2abc+a^2.c^2=1-a^2-c^2+a^2.c^2

b^2+2abc=1-a^2-c^2

a^2+b^2+c^2 +2abc=1

QED

Re: Nairaland Mathematics Clinic by bolkay47(m): 2:20pm On Jan 22, 2015

With each roll of a cutlass,a man cut 0.1% of grass in a field. if there were 20 square feet of grass to be cut. how much grass will remain after 60th stroke?

Please help me out...thanks

Re: Nairaland Mathematics Clinic by AlphaMaximus(m): 6:34pm On Jan 22, 2015*

1 2 3 ... 157 158 159 160 161 162 163 ... 284 Reply

Mathematics Clinic • 2015 Cowbell Mathematics Champion, Akinkuowo Honoured By School. • Lead City University Clinic Welcomes First Ever Baby Since 10 Years Of Opening • 2 • 3 • 4

Niger Delta University 2018/19 NDU POST UTME "Past Questions" • 2016/2017 University of Ibadan Admission Thread Guide. • Mastercard Foundation Scholarship, Enter Here

Viewing this topic: 1 guest(s)