solomon111: The fifth equation follows the principle/laws of logarithm.
E.g
1)logx +logy =logxy
2)alogx +blogy=ablogxy.
3)logx-logy=logx/logy

benbuks: someone here should define d CARTESIAN PRODUCTS of two sets X and Y?
hence prove rigorously that AX(B-C)=(AXB)-(AXC)?

benbuks:

let y=5^-3x

using say d (a^x ) /dx = a^x Ina ........( from standard derivative )

now put -3x= u

=> -3=du/dx

=> y=5^u

dy/du =5^u In5

dy/dx = du/dx * dy/du

=> (-3)(5^u.In5 )

since u=-3x

we thus have

-3(5^-3x.In5) …

hope you get...?

benbuks:

ok.

from trig. identities

tan² x + 1 = sec² x

=> put v= secx & replacing in our question above we have

=> v² +2v -6=0

now use quadratic formula to obtain v & make your deductions


then cos2x = 1-2sin²x

put v= sinx then finish up from there ... hope it helps

or.....?

Elliotwiz1: sorry you didn't get a reply after you posted. i did solve and get this answer but the material i saw the question on had a different answer and i was beginning to get confused. they got 5^3x.3ln5. but since you got what everyone else is getting i guess they made a mistake. try out the integral of cos(wt+teta).dt

ugonna1054: Pls guys another.
A + C = 1.........1
10A + 15B=9.....2.
15B - 10C = -1.....3
Find A.B and c..

dejt4u:
a=9/10, b=0, c=1/10

tuwayz: Please guys who can brief me on binary operations am lost

ugonna1054: Pls guys, help me out wit these...
Suppose we av 2 bags in wch fst one contains 3 white and 7 blue bulbs and d second contains 7 White and 3 blue bulbs..a bag is presented to a student and he draws a bulb and finds it to be white.. From wch bag did he draw from??

benbuks: some1 try this abeg.


integral of √( 1 + sinx) dx


asap.

akpos4uall:
Use the substitution u = sin x
du = cos x dx
du = √(1 - sin² x) dx
du = √(1 - u²) dx
The integral becomes
∫[√( 1 + u)]du/√(1 - u²)
∫√[( 1 + u)/(1 - u²)] du
∫√[( 1 + u)/{(1 + u)(1 - u)}] du
∫√[1/(1 - u)] du
∫(1 - u)^-0.5 du
-1 * 2(1 - u)^0.5 + k
-2√(1 - u) + k
-2√(1 - sin x) + k

Soneh:
sorry for replying this late,my phone had a problem.
pls I dont get the part where you introduced v to the equation representing both tan and sec
PLEASE explain.

benbuks:

ok bro , let's do a check.

obtaining back the integrand by computing the differential coefficient of '-2√(1-sinx) + k '

=> (-2) * (1/2) * (-cosx) * (1- sinx) ^-1/2

=> cosx/√(1-sinx) ..

can we go further to obtain √(1+sinx) ?

akpos4uall:
Yes we can
cos x = √(1 - sin² x)
Using s = sin x
cosx/√(1-sinx) = [√(1 - s²)]/√(1-s)
= √[(1 - s)(1 + s)/(1 - s)]
= √(1 + s)
= √(1 + sin x)

benbuks: evaluate d value of x for which 2^x >2x

asap.

ayibawanemi: what course are you studying in school?

benbuks: evaluate d value of x for which 2^x >2x

asap.

jackpot: Dear Math Generals, Lieutenants, Colonels, and friends of Maths, please help out:

Derive the condition on the constants a, b, c, u, v, w, such that the two circles
C₁: x²+y²+ax+by+c=0
and C₂: x²+y²+ux+vy+w=0
intersect each other.



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thankyouJesus: Please house, in terms of intra/extra competition(s), rigorous tranning and "prospects", which university is the best to study pure and applied mathematics with reason(s)?

actYourDreams: In Nigeria or abroad?