rashywire: pls help with these questions

1. if x and y are real, solve d equation;
jx / 1+jy = 3x+j4/ x+3y



2. if z = a+jb / c+jd , where a,b,c and d are real quantities, show d@
(a) if z is real then a/b = c/d and
(b) if z is entirely imaginary then a/b = -d/c
3. if (R1 + jwL) / R3 = R2 / ( R4 - j 1/wC ) , where R1, R2, R3, R4 , w, L, C are real, show d@
L = ( C R2 R3) / w^2 C^2 R4 ^2 + 1

NO 3 HAS NO SOLUTION CAUSE R1 WHICH IS IN D QUES IS NOT IN D VALUE 4 L

plz i need solutions@my generals:
.
(1).if x=Intan(¥/2) and y=tan¥-¥,prove dat d^2y/dx^2=tan^2¥sin¥(cos¥+2sec¥).
(2).if y=[x+root(1+x^2)]^(3/2),
show dat 4(1+x^2)d^2y/dx^2+4xdy/dx-9y=0.
answers will b really appreciated

Mr Calculus: NO 3 HAS NO SOLUTION CAUSE R1 WHICH IS IN D QUES IS NOT IN D VALUE 4 L

boss, pls if u have K.A STROUD, Help check page 465 number 19 n 20. pls @ all gurus, help luk @ those questions.
Topic: Complex numbers 1
Textbook: K.A Stroud
nb: not advance oo
thanks in anticipation

Mr Calculus:
solution(a)::
if z is real,lets take z as 1.
then by cross multiplying::
c+jd=a+jb.
by comparison
=>c=a and d=b.
=>c/a=d/b or a/b=c/d.
.
solution(b)::
if z is imaginary.den lets take z as j.
by cross multiplying:
=>jc+j^2d=a+jb.
=>jc-d=a+jb.
by comparison:
c=b and -d=a.
=>c/b=-d/a or a/b=-d/c

tanks 4 dis

Mr Calculus: NO 3 HAS NO SOLUTION CAUSE R1 WHICH IS IN D QUES IS NOT IN D VALUE 4 L

permit me 2 use i for j
(R₁+iwL)/R₃=R₂/(R₄-i/wC)
or
(R₁+iwL)/R₃=R₂*(R₄+i/wC)/((R₄)²+(1/wC)²)
or
(R₁+iwL)=R₃*R₂*(R₄+i/wC)/((R₄)²+(1/wC)²)
but Mr. Calculus had already shown that if z, a, b, c, and d are Real and z=(a+ib)/(c+id), then a/b=c/d
now set a=R₁, b=wL, c=R₄, d=1/wC and z=R₃*R₂/((R₄)^2 + (1/wC)²)
then all the conditions of questn 1 are satisfied.
Hence, R₁/wL=R₄*wC, so L=R₁/(R₄*w²C).
IF U DOUBT THE RESULT, SUBSTITUTE REAL NUMBERS TO VERIFY

Laplacian:
permit me 2 use i for j
(R₁+iwL)/R₃=R₂/(R₄-i/wC)
or
(R₁+iwL)/R₃=R₂*(R₄+i/wC)/((R₄)²+(1/wC)²)
or
(R₁+iwL)=R₃*R₂*(R₄+i/wC)/((R₄)²+(1/wC)²)
but Mr. Calculus had already shown that if z, a, b, c, and d are Real and z=(a+ib)/(c+id), then a/b=c/d
now set a=R₁, b=wL, c=R₄, d=1/wC and z=R₃*R₂/((R₄)^2 + (1/wC)²)
then all the conditions of questn 1 are satisfied.
Hence, R₁/wL=R₄*wC, so L=R₁/(R₄*w²C).
IF U DOUBT THE RESULT, SUBSTITUTE REAL NUMBERS TO VERIFY

pls help check d question again in d textbook.
tanks in anticipation

.

Richiez: @kaxmytex, thank alot and happy new year too, do u av any new yr maths question 4 me?

a.

Satellite information has revealed that the average albedo of the Earth’s surface is 0.32. Briefly describe what is conveyed by this measurement of albedo, and how albedo might affect the temperature experienced on Earth’s surface.

(5 marks)
b.

Imagine a situation where Earth’s atmosphere begins to trap more of the incoming solar radiation (e.g. this could occur through an increase of ‘greenhouse’ gases such as CO2). Explain what effect this would have on the temperatures experienced at Earth’s surface, then, with reference to the different types of surfaces listed in Table 1, complete the eight blank entries.

(9 marks)

Table 1
Surface type Albedo Nature of the change Effect on total area of surface Effect on Earth’s albedo

Ocean surface 3% less sea ice covering increase
Conifer forests (summer) 9% longer growing season increase
Grassy fields 25% decrease
Sea ice 40% decrease decrease
Desert sand 40% expanding desert increase
Fresh snow 85% decrease

c.

Briefly outline how the Earth’s overall (i.e. average) albedo might respond to such a rise in CO2 (e.g. over a period greater than 100 years) and, with the aid of a simple diagram, state whether this response would represent a positive or a negative feedback loop.

djkay1000:

a.

Satellite information has revealed that the average albedo of the Earth’s surface is 0.32. Briefly describe what is conveyed by this measurement of albedo, and how albedo might affect the temperature experienced on Earth’s surface.

(5 marks)
b.

Imagine a situation where Earth’s atmosphere begins to trap more of the incoming solar radiation (e.g. this could occur through an increase of ‘greenhouse’ gases such as CO2). Explain what effect this would have on the temperatures experienced at Earth’s surface, then, with reference to the different types of surfaces listed in Table 1, complete the eight blank entries.

(9 marks)

Table 1
Surface type Albedo Nature of the change Effect on total area of surface Effect on Earth’s albedo

Ocean surface 3% less sea ice covering increase
Conifer forests (summer) 9% longer growing season increase
Grassy fields 25% decrease
Sea ice 40% decrease decrease
Desert sand 40% expanding desert increase
Fresh snow 85% decrease

c.

Briefly outline how the Earth’s overall (i.e. average) albedo might respond to such a rise in CO2 (e.g. over a period greater than 100 years) and, with the aid of a simple diagram, state whether this response would represent a positive or a negative feedback loop.

bros dis one na 4 astrophysicists ooo...*hands on chin, sighin, waitn patiently 4 som1 2 unravel d mystery*

...can the product of two distinct, non-zero integers when increased by one, divide the sum of their squares?...solutions&suggestions 're welkom....

Mr Calculus: plz i need solutions@my generals:
.
(1).if x=Intan(¥/2) and y=tan¥-¥,prove dat d^2y/dx^2=tan^2¥sin¥(cos¥+2sec¥).
(2).if y=[x+root(1+x^2)]^(3/2),
show dat 4(1+x^2)d^2y/dx^2+4xdy/dx-9y=0.
answers will b really appreciated

.dude the proof is kinda long oo..guess that‘s why no1 has paste it yet....btw. check. Q1,,‘y=tan¥-¥‘....dont get u ...for d 2nd question i“ll try n post solution later....

benbuks:
.dude the proof is kinda long oo..guess that‘s why no1 has paste it yet....btw. check. Q1,,‘y=tan¥-¥‘....dont get u ...for d 2nd question i“ll try n post solution later....

yes boss....its tan¥-¥.
[like saying tan@-@].
[tan(teta)-teta]

[color=#000099][/color].y=(x^2lnx)/sinx...find dy/dx

HOLIDAY ASSIGNMENT
SUBJECT: ENGLISH LANGUAGE
QUESTION 1
Title of the novel: Dairy of a Wimpy Kid
The Author Information: Jeff Kinney is an online game developer and designer,and the author of the number one New York times best seller Dairy of a Wimpy kid. He sent his childhood in the Washington, D.C.,area and moved to New England in 1995. Jeff lives in southern Massachusetts with his wife Julie , and thier two sons,will and Grant.
Theme(s) of the novel:
a. Boy’s experience
Themes: Awkwardness, Change, Gender Roles, Growing Up, Outward Appearance, Teen Issues
b. Middle-school experience
Themes: Acceptance, Comparison, Judging, Pleasing Others, Self Worth, Status, Teen Issues
c. Teens rejection
Themes: Abandonment, Acceptance, Isolation, Loneliness, Rejection, Teen Issues

Most Favourite(s) characters in the novel and why?
My most favourite character in the novel is Greg.
"So if you want to find somebody to blame for the way I am, I'd guess you'd have to start with the public education system."
--Greg Heffley
Greg explains throughout the series that he has no strong talents, other than video games and comics. As such, he spends most of his time on them, which deters him away from schoolwork and chores. For a time, he harbored a hope of drawing for the school newspaper, but his comic was bowdlerized by the editor and Rowley’s comic, which was also Greg's idea, was better liked by the people at his school. He hardly shows any other talents. However, Greg is probably good at singing, due to the fact that when he was auditioning for the school play, the drama teacher told him he had a "nice soprano voice", and is also good at sewing, but he complains that these talents do not make him stand out.
Greg almost always tries to find a scapegoat to put the blame on for his behavior, but he is oblivious to the fact that nobody forced or influenced him, other than probably his elder brother, Rodrick, to act in this manner. Very few times has Greg actually admitted to being "wrong" in a decision he made and took responsibility for it. It should also be noted that while Greg is arguably a watered down version of Rodrick, he does not have any productive interests and could actually be considered more hurtful than Rodrick psychologically.
Greg's best friend throughout the series has been Rowley most of the time, but their relationship is quite strained. He almost always takes advantage of Rowley, and uses him as a decoy for his own schemes and desires. Because of this, Rowley's parents see Greg as a bad influence to their son. Not only does he force Rowley to become a person that he wasn't meant to be, he also sets a bad example- he gets poor grades, doesn't try at all in school, and sets his expectations exceedingly high.
Greg is usually depicted with black shorts, or black pants (sometimes black jeans) and a white shirt. He is very skinny and does not seem to eat nor work out much. His father has tried to get him to work out and exercise, but he prefers playing video games. His nose is a simple oval while his ears are circled.

Setting of the Novel
At his school and home mostly.
Plot of the Novel
To Greg Heffley, middle school is the dumbest idea ever invented. It's a place rigged with hundreds of social landmines, not the least of which are morons, wedgies, swirlies, bullies, lunchtime banishment to the cafeteria floor - and a festering piece of cheese with nuclear cooties. To survive the never-ending ordeal and attain the recognition and status he feels he so richly deserves, Greg devises an endless series of can't-miss schemes, all of which, of course, go awry. And he's getting it all down on paper, via a diary - "it's NOT a diary, it's a journal!" Greg insists, preferring the less-sissyfied designation - filled with his opinions, thoughts, tales of family trials and tribulations, and (would-be) schoolyard triumphs. "One day when I'm famous," writes Greg, "I'll have better things to do than answer people's stupid questions all day." So was born the Wimpy Kid's diary.

Synopsis of the Novel
September
Greg starts his new journal by briefly explaining how his summer went which included a swim team and an embarrassing secret only he and Rodrick know about. With the school year starting, Greg is reminded he has the Cheese Touch from last year, but passes it on to Jeremy Pindle. Greg states how his best friend, Rowley, went to South America for the summer, and how Rowley gets caught up in whatever fad is going on, an example being Joshie.
October
Greg notices the arrival of his old friend, Chirag Gupta, and is thrilled to see him back, but decides to pay a pratical joke he got from his mom, the Invisible Chirag. The whole class gets in on the joke, but Chirag manages to find their weakness.
November
Greg starts the month being bugged by Rodrick until Dad notices that there is no lock on the bathroom door, but doesn't connect the evidence to Rodrick's relief. Greg then decides to let his parents know about Rodrick's party without him finding out. He then gets another letter from Mamadou, but finds it dumb they have to write letters instead of e-mails. A few nights later, Greg heads to Rowley's house and meets Leland. The two friends are soon addicted to Magick and Monsters, but Susan becomes suspicous of their activities so she observes a game.
December
Susan sends Frank to pick up pictures from Thanksgiving, but he comes back with a picture from Rodrick's party. They severely punish Rodrick. Because Greg didn't say anything about it, they suspect that he was hiding it from them and gives him a video game ban. Knowing the brothers can't be trusted, Susan and Frank drop the two at the Leisure towers where Grandpa lives.
QUESTION 2
S/NO CONSONANT EXAMPLE 1 EXAMPLE 2
1. /b/ ball Tube
2. / ʧ/` torch Chin
3. /d/ dish Bird
4. /f/ fish Enough
5. /g/ goat Stag
6. /h/ horse Head
7. /j/ you Unity
8. /k/ king Kick
9. /s/ shirt Shelves
10. /l/ live Leaf
11. /m/ mouse Mama
12. /n/ net Nine
13. /ᴐ/ going Honk
14. /p/ power Pet
15. /r/ rashes Rest
16 /s/ stop Speed
17 /t/ tall Take
18 /Ɵ/ thief Thin
19 /∂/ the Width
20 /v/ violin Velvel
21 /w/ wash Watch
22 /z/ zebra Cosy/cozy
23 /ᶚ/ measure Vision

QUESTION 3
Subject Of A Sentence
The subject of a sentence is the person, place, thing, or idea that is doing or being something. You can find the subject of a sentence if you can find the verb. A. The computers in the learning centre must be replaced.
The subject is “computer’’
B. The Johnsons added a double garage to their house.
C. The Jury returned a verdict of mans laughter.
D. The deans report was reviewed by the faculty senate.
3b Predicate Of A Sentence
The predicate of a sentence tells something about the subject
Examples.
1. Michael runs.
2. Michael and his dog run on the beach every morning.
3. The audience littered the theatre floor with tom wrapping and spilled pop-corn.

Object of a sentence is the entity that is acted upon by the subject .
1. Tom studies grammer .
2. A book was given to me.
3. The girl ate fruit.
A phrase is a collection of words that may have nouns or verbals,but it does not have
a subject doing a verb.
Examples : Leaving behind the dog.
Smashing into a tree.
Before the first test.
A clause is a collection of words that has a subject that has a subject that is actively doing a verb.
– since she laughs at different men. - I despise individuals of low character.
- When the saints go marching on.

Ayomide002: [color=#000099][/color].y=(x^2lnx)/sinx...find dy/dx

y ‘ = (vu‘ -uv‘)/v^2

put u=x^2 lnx. & v= sinx

=> u‘ = dx^2 /dx (lnx) + dlnx /dx (x^2)= 2xlnx +x (product rule.)

aslo v‘= cosx..
, ‘ , y ‘=dy/dx=[ (sinx)(2xlnx +x) - (x^2 lnx)(cosx) ]/ sin^2 x

..u cn simplify.. further..

Mr Calculus: yes boss....its tan¥-¥.
[like saying tan@-@].
[tan(teta)-teta]

ok....leme c...

greetinz n hailinz to ma boss @ dx....i respect oo

benbuks: greetinz n hailinz to ma boss @ dx....i respect oo

Hailings bruv, happy new year to you man!

I've always believe in numbers,in equations and
logics that leads to reasoning , but after a
lifetime of such persuit, i ask what truely is
logic? And who decides to reason..my question
has taken me to physical , to metaphysical ,to
illusional and back..and i'v made the most
important discovery of my career , the most
important discovery of my life: It is only in the
mysterious equations of love that logical reason
can be found,only it is because you,you are the
reason i am...you are all my reasons....thank
you.for integrating all my differentiated
mistakes...your love always tends to
infinity..irrespective of my infinitesimal
faithfulness..

#teamdontacceptfactsswithoutproofs#

doubleDx:

Hailings bruv, happy new year to you man!

reciprocated. sir..
.thanks..

Mr Calculus: plz i need solutions@my generals:
.
(1).if x=Intan(¥/2) and y=tan¥-¥,prove dat d^2y/dx^2=tan^2¥sin¥(cos¥+2sec¥).
(2).if y=[x+root(1+x^2)]^(3/2),
show dat 4(1+x^2)d^2y/dx^2+4xdy/dx-9y=0.
answers will b really appreciated

for those interested .
d no 2::>dy/dx=(3/2[root(1+x^2])*[x+root(1+x^2)]^(3/2).
and
d^2y/dx^2=-3x[x+root(1+x^2)]^(3/2)/2[1+x^2]^(3/2) +9[x+root(1+x^2)]^(3/2)/4[1+x^2].
STILL EXPECTING D NO 1 FROM MY GENERALS

Sorry...i have not been typing on this thread since all this while...it's just that i have been at the hospital since last year and i'm still there now...i follow the thread always and commend my generals works.i'm typing now coz of a question posted by mr calculus which has not been solved.i have waited so long for the generals to attempt it coz it's not convenient for me to type...but.since no one has attempted it.i think i have no alternative but to type...
SOLUTION LOADING

X=ln.tan(¥/2)...y=tan¥-¥...dx/d¥=1/2.1/tan(¥/2).sec^2(¥/2)....dy/d¥=sec^2¥-1(from trig.identity...1+tan^2¥=sec^2¥...tan^2¥=sec^2¥-1)..dy/d¥=tan^2¥....dy/dx=dy/d¥.d¥/dx...dy/dx=(tan^2¥)*{2tan(¥/2)}/{sec^2(¥/2)}....when we simplify.d¥/dx=..{2tan(¥/2)}/{sec^2(¥/2)}.we will get sin¥...
PROOF...
{2tan(¥/2)}/{sec^2(¥/2)}...tan(¥/2)=sin(¥/2)/cos(¥/2)...sec^2(¥/2)=1/cos^2(¥/2)...{2tan(¥/2)}.1/sec^2(¥/2)... 2.sin(¥/2)/cos(¥/2).cos^2(¥/2)...then 2sin(¥/2)cos(¥/2)..d¥/dx=sin¥...back to where we stopped...dy/dx=sin¥tan^2¥...to find...d^2y/dx^2...find d/dx of both sides...d/dx.dy/dx=d/dx.sin¥tan^2¥...d^2y/dx^2=d/d¥.d¥/dx.sin¥tan^2¥...d^2y/dx^2=d/d¥.sin¥tan^2¥.d¥/dx...d^2y/dx^2=(2sin¥tan¥sec^2¥+cos¥tan^2¥).d¥/dx...d^2y/dx^2=(2sec¥tan^2¥+cos¥tan^2¥).d¥/dx...don't forget what we got at the top for d¥/dx...we got it as sin¥...then d^2y/dx^2=(2tan^2¥sec¥+cos¥tan^2¥).sin¥...simplify to get sin¥tan^2¥(2sec¥+cos¥)...d^2y/dx^2=tan^2¥sin¥(cos¥+2sec¥)......Q.E.D

Ayomide002: [color=#000099][/color].y=(x^2lnx)/sinx...find dy/dx

...y=x^2lnx/sinx...take naparean log of both sides...lny=ln of x^2lnx/sinx...lny=lnx^2+ln(lnx)-lnsinx...take d/dx of both sides...d/dx.lny=d/dx{lnx^2+ln(lnx)-lnsinx}...d/dy.dy/dx.lny=d/dx.ln.x^2+d/dx.ln(lnx)-d/dx.lnsinx....d/dy.lny.dy/dx=2x/x^2+1/(xlnx)-cosx/sinx...1/y.dy/dx=2/x+1/(xlnx)-cotx...dy/dx=y{2/x+1/(xlnx)-cotx}...don't forget y=x^2lnx/sinx...then dy/dx=x^2lnx/sinx.{2/x+1/(xlnx)-cotx}

gurus.. welldone

@f(x).
thanks 4 d calculations i now know my flaws

I've got mixed feelings for the data loss cos of some vital points lost her and the fact that we might need to organise another math quiz

hmmmmm.m. feel like crying ....



more than 50 pages containing vital mathematical info lost . .?? owing to some cyber issues .. its well sha..

thank God NAIRALAND IS BACK & BETTER ..


#team...math..continues .