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I've actually just completed my first year of study in Visual Communications at UTS, and even though I really enjoy the course (despite the sleepless nights and stress) and believe I'm well suited for it, I still have doubts. My main question is regarding the reputation of the UTS VisComm...

I have to admit I've never really understood the difference between a cartesian and a parametric equation. From what I can gather, the difference is that a cartesian equation involves both the x and the y coordinates in the same equation (e.g. y = x2) while a parametric equation uses another...

I know the solution to this particular question, but I'm not too sure of the reasoning behind it. The question asks; Two curves, y = (sqrt3)cosx and y = sinx, are drawn on a graph. The first two intersections to the right of the y-axis are labelled A and B. a) Solve the equation (sqrt3)cosx =...

For some reason, when I enter the following information in to my calculator, I can't seem to get the correct answer. Could someone possibly explain why this is? The question asks; a) Show that there is a root to the equation sin x = x - 1/2 between x = 0.5 and x = 1.8. [This is the part I'm...

I'm not sure how to approach this question, can anyone help me? It asks; Simplify; a) n - 1Ck - 1 + n - 1Ck b) 10Ck ÷ 10Ck - 1

I'm not sure how to tackle this question, can anyone help me out? It asks; a) Show that (1 - cos2x)/(1 + cos2x) = tan2x. b) Hence find the value of tan 22.5o in simplest exact form.

I'm not quite sure how to tackle this question. It asks; a) Find the value of x such that sin-1x = cos-1x. b) On the same diagram, sketch the graphs of y = sin-1x, y = cos-1x and y = sin-1x + cos-1x. With this second part, I'm able to sketch the graphs of y = sin-1x and y = cos-1x, but I'm...

I'm having a lot of trouble with permutations and combinations, so I was hoping someone here could help me out with a few questions. Please make sure that you explain your working; I really want to understand this topic... The first question asks; A queue has 4 boys and 4 girls standing in...

I'm not sure how to tackle this question, can anyone help me out? It asks; The point P (x, y) is equidistant from the lines y = -2 and 3x - 4y - 12 = 0, and lies in the shaded region of the diagram. Find the equation of the locus of P.

Lets see if anyone can help me out of this one; ABC is a triange, in which AQ bisects angle CAB and angle PBA = angle BCA prove that PB = QB.

Can anyone help me out with this coordinate geometry question? It asks; The diagram shwos the points A (-2, 0), B (1, 4) and the point C which lies on the x-axis. D us the midpoint of the interval AC. F is a point on AB such that DF is parallel to BC. a) Find the gradient of AB. Easy, the...

I'm stuck on this trigonometry question, can anyone help me out? It asks; In the figure, ABCD is a rhombus in which AB = 60cm, and angle A = 60o. P is a point on AD and AP = AQ = 2cm. Angle PQC = xo. P is joined to C. a) Write down the length of PQ, gibing reasons. b) Show that PC = QC c)...

Having trouble with this question, can anyone show me the best way to tackle it? It asks; On a number plane, the points P, Q and R have coordinates of (3, 0), (0, 2) and (6, 4) respectively. Find the shortest distance from the point R to the line PQ. Do I simply find the equation of the line...

Can anyone give me a bit of help with this integration question? The first part I can figure out but I don't know how to do the second. It asks; The points A (3, 9) and B (-2, 4) lie on the parabola y = x2. The line y = x + 6 joins A and B. The point P (p, p2) is a variable point on the parbola...

I'm having a bit of trouble with the second half of this question... And open rectangular box has four sides and a base, but no lid. The box has a base of dimensions 3x cm and 2x cm, and a height of y cm. a) Write dow formulae for the outer surface area A cm2 of the box and the volume V cm3. =...

I'm stuck on this particular simple harmonic motion question. I can do the first half, but the second has me baffled. Here it is; a) If x = a sin nt + b cos nt, find the acceleration of the particle in terms of t and show that a = -n2x. = v = an cos nt - bn sin nt = a = -an2 sin nt - bn2 cos...

I've got a whole pile of questions I need help with, but I have restricted access to the internet at the moment, so I mightn't be able to check back here for a little while. Lets hope you guys can help me out. If a the displacement of a particle moving in simple harmonic motion is given by x =...

I'm not quite sure how to approach this question, could someone help me out here? It asks; A certaing brand of medicine tablet is in the shape of a sphere with diameter 5mm. Ther rate at which the pill dissolves is dr/dt = -k, where r is the radius of the sphere at time t hours, and k is a...

I'm having trouble with a particular parametric parabola question. Can someone go through them with me so I can understand? Here it is; Prove that SP = a(p2 + 1) units [where S = (0, a) or the focus, and P = (2ap, ap2)] and hence that SZ2 = OS x SP [where O is the origin].

I'm having some trouble with a few inverse trigonometry questions. Hopefully someone here can explain the process to me so I can figure out future questions for myself. Currently I'm stuck on; Find the exact value of sin[tan-1(3/7)] It can't simply be evaluated using a calculator since the...