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hi this is a concept thing i really dont get and cant find in the theory... can someone explain to me why tan β = y' = y(dot)/x(dot) because its in the solutions but i really dont understand where it came from by the way, β is any angle made by the tangent to the curve and the horizontal...

Don't know how to deal with this: find integral of (x+2)/x(x^2-1) dx * using partial fraction method.

how do i find: ∫ cosec(^3)x dx

someone help! i have no idea what to do when i look at these questions Dx 1. z^n - 1 =0 has roots 1, z1, z2, ... , zn-1. Show that (1 - z1)(1 - z2) ... (1 - zn-1) =n. 2. The equation x^3+3px^2+3qx+r=0, where p^2 (doesnot =) q, has a double root. Show that (pq-r)^2 =4(p^2-q)(q^2-pr).

A cone is made by joining together the radii of the sector of a circle of radius 16cm. The radius of the base of the cone is 4cm. Find the angle at the centre of the sector and the curved surface area of the cone. Thanks ahead for any help; :)

Water is poured into a cone vessel at a constant rate of 24cm^3 per second. The depth of water is h cm at any time t seconds. What is the rate of increase of the area of the surface S of the liquid when the depth is 16cm... Thanks ahead for any help.

The equation of the tangent of p(x1,y1) on the ellipse E: x^2/a^2 + y^2/b^2=1 is xx1/a^2 + yy1/b^2 =1 It meets the major axis in T and a directrix in Q, PN is the ordinate of P, S is the focus corresponding to this directrix. Show that: a) ON.OT=a^2 (done) b) SQ is perpendicular to SP...

PQ is a diameter of the ellipse x^2+4y^2=9. If the eccentric angle of P is pie/3, find the coordinate of P. What is the eccentric angle of Q? Find the coordinates of the corresponding point on the auxiliary circle. Show that the tangents at P and Q are parallel? Thanks ahead for any help.

hi; i feel very noob at conics.. can someone help me with these questions? 1. The chord joining the poitn alpha and beta on the ellipse with the equation x^2/a^2+y^2/b^2=1 subtends a right angle at the point (a,0). Show that tan(alpha/2)tan(beta/2)=-b^2/a^2 2. Show that the line 2y+x+5=0 is a...

hi could someone help me with this question pls? i kno how to do it but i cant quite get the radius in terms of the height.. Sand is poured into a heap in the shape of a right circular cone whose semi-vertex angle is alpha, where tan alpha=3/4. When the height of the cone is 16cm, the height is...

If alpha and beta are roots of the equation x^2 +mx +n=0, find the roots of nx^2+(2n-m^2)x+n=0 in terms of alpha and beta. [darn this is probably real simple but i havent got the hang of how to do these ones] ok here are a few more that i ended up not being able to do... 18. If the roots of...

hey i looked at this question and went blank; can someone help? Q2. Let x = alpha be a root oft the quadratic polynomial P(x)=x^4+Ax^3+Bx^2+Ax+1 where (2+B)^2 does NOT = 4A^2 a) Show that alpha can not be 0 or 1 or -1 b) Show that x=1/alpha is a root c) Deduce that if alpha is a multiple...

hi i'd like to ask for any help available for the last part of this question.. i've tried everything but i still cant show the answer 1. the normal at a point p(x1,y1) on the ellipse x^2/16 + y^2/9 = 1 cuts the x-axis and y-axis at two points A and B respectively a) SHow the equation of the...

hi thanks in advance for any help :) using the substitution u = x - 1 using the substitution u = y + 1 [when a question doesnt contain the derivative but the sole pronumeral (as above) then what am i supposed to do?! ]

hi i have quite a few complex questions which i have absolutely no idea what to do: 1) if z1= 24+7i and |z2|=6. Find the greatest and smallest values of |z1+z2| 2) On an Argand diagram the points A and B represent the numbers z1 and z2 respectively. I is the point (1,0). D is the point...

this sucks we still hav a year ahead of us :(