Question: Sugar is dissolved in water in the ratio 1:3 to form sugar syrup. This sugar syrup is further diluted with the addition of water so that the ratio of the sugar syrup to the additional water is 5:7. FInd the ratio of sugar to water in the final mixture.
Hi can anyone explain the following?
Two identical coins are placed one inside and one outside a thin circular wire, which has twice the diameter of each coin. Each coin is rolled, without slipping, around the wire until it returns to its starting point. If the direction of rotation does not...
Hi,
1) Just wondering what happens when you reciprocate a vertical asymptote.
For example if you are given the graph y=1/x and asked to reciprocate it, will the origin be an open circle or closed circle.
2) If you are NOT given the equation of y=1/x but given something that looks similar...
Was stuck on a question:
Sketch the locus defined by arg(z^2+z)=pi/3, stating its equation.
Obviously this will turn into the hyperbola with the positive branch, but how do we find the equation?
Also, anyone know when the bored of studies trial will be held this year, of is it held already...
Hi,
A bit confused with the use of the notation y=f(x). If we have the circle x^2+y^2=1, we can obviously rearrange and make y the subject which gives y=+-(1-x^2)^0.5. Is it wrong to write f(x)=+-(1-x^2)^0.5 since this is not a function hence we can't use f(x)?
If so, does that also mean...
Consider the integral of sin(2x+1).
I note the normal method would be to let u=2x+1(if you are asked to use substitution).
But can someone explain the following method:
integral (sin(2x+1)dx)=integral(sin(2x+1) d(2x+1)/2)?
Was reading volumes by terry lee and it was a trapezoidal solid/frustum and we had to find the volume using similar solids. Mr Lee's answer claimed that the height (h) of the solid is linearly dependent to x which measures the length of the typical slice/cross-section. Is this valid? i mean we...
hi, is it safe to assume index laws and logarithmic laws only apply(apply without need to confirm other things...) for positive bases?
E.g. for equations like log(base x) 4=2, we only get the answer of 2 and not negative 2 right?
Ships A and B leave port P at the same time.
Ship A sails 4km on a bearing of 40 degrees , then a further 6km on a bearing of 155 degrees to reach destination D.
Ship B sails directly from P to the the destination D.
In which direction does Ship B sail?
I solved this in two ways (sine...
Hi guys, for those who sat the 2014 AMC, could someone please enlighten me on the last 2 questions. Especially the last question...i dont see any pattern for the primes...
I'm confused...MUST you use induction to prove De Moivre's theorem(by the way how do you prove De moivre's theorem for negative integers?)?
I mean, isnt zw=r_1 r_2 cis(theta_1+theta_2)? then isnt it obvious that z^n=(r^n)cis(n theta)? so why induction?
Given I_n=\int_{e^-1}^{1} (1+lnx)^n dx = 1-n(I_(n-1)) and J_n=\int_{e^-1}^{1} (lnx)(1+lnx)^n dx for n=0,1,2,3,...
show that J_n=1-(n+2)I_n for n=0,1,2,3,...
Sorry for my sloppy latex input
PS: is there a way to input latex on this forum?