s17

Solve the equation z^5=-1 giving the solutions in polar form I've got z^5 =1 but just not sure as its a negative

9 years ago

Taylor series: f(x)=(1/16 +x)^(-1/4) =2-8x+80x^2 -960x^3..... and through differentiation g(x) = (1/16 +x)^(-5/4) =32-640x+11520x^2 but i then need to integrate about 0, h(x)=(1/16 +x)^(3/4) not really sure where to start out the integration one

9 years ago

Find a parametrisation of the hyperbola that is obtained by translating the hyperbola with equation 9x^2 - (y^2)/16 =1 by -2 unit(s) right and 4 unit(s) up x=? y=?

8 years ago

Two ships pursue straight-line courses at steady speeds. At each time t (in hours, where 0 less-than-or-equal t less-than-or-equal 14), the positions of the two ships are given by: Ship A (10t+35, 20t+25) Ship B (11t+15, 22t+15) These coordinates are with...

8 years ago

The equation 4x^2 +9y^2 -36 = 0 represents an ellipse in standard position. Find the coordinates of the foci and the equations of the directrices. The Foci are (+-f, 0) where f>0 I have worked out f=sqrt(5) not sure how to work out the directrices (d)

8 years ago

Show that -3 is a multiplicative inverse of 17 modulo 26 Started with 17 * -3 = -51 but doesn't seem right? help

8 years ago

the position of a car in time t (in hours) is (-10+45t,40+70t) and a truck (40-40t,20+75t) find the distance between the car and the truck at time t=0 in km) i have 53.9km to 1dp find an expression for d^2 in terms of t) I have 7250t^2 -8700t+290 Complete...

8 years ago

A basket of flowers weighing 2kg is placed on a flat grassy slope. The coefficient of static friction between the basket and the slope is 0.4, and the basket is on the point of slipping down the slope. Draw a force diagram to indicate forces (including fr...

8 years ago

A particle, which remains at rest, is acted on by three forces F, G, and H. The force F has magnitude 6N and is directed to the right and up, making an angle of 20' with the vertical. The force G has magnitude 15N and is directed to the right and down, ma...

8 years ago

A bucket hangs from two wires. The left-hand wire makes an angle of 60 with the vertical, and the magnitude of the tension in the wire is 326N. The right-hand wire makes an angle of 45 with the vertical. Calculate the mass of the bucket, in kilograms, to...

8 years ago

A carton of mass 35kg is at rest on a rough plane inclined at an angle of 40 degrees to the horizontal. Calculate the magnitude of the friction force in newtons.

8 years ago

Let f be the linear transformation represented by the matrix A=(-2 3 4 -4) a=-2, b=3, c=4, d=-4 Find the point (x,y) such that f(x,y)=(4,4)

8 years ago

Find the equation of the line that is the image set of the flattening, f(x,y)=(3x-3y, x-y)

8 years ago

With the matrix A = (0 6 4 12) I have calculated the inverse of (-1/2 1/4 1/6 0) I'm then asked to find the equation of the image f(C) in the unit circle C, in the form of ax^2 +bxy+cy^2=d, where a, b, c and d are integers. I have currently got; (40x^2 -3...

8 years ago

dy/dt = -t^3y^2-ty^2 dx/dt=(sin t)/(cos t+10) dy/dx -3y/x =x^3cosx Which differential method should be used for each equation?

8 years ago

Which of the following equivalences is true? P(n), n is a multiple of 3 Q(n), n is even -P(4) and Q(3) -P(3) and Q(3) -P(3) or Q(3) -P(4) or Q(3) -P(4) and Q(4)

8 years ago

A particle of mass 40 40kg moves in a straight line such that the force (in newtons) acting on it at time,t (in seconds) is given by, 160t^4-320t^2-360 at time t=0, v is given by v(0)=10, and its position x is given by x(0)=14. What is the position of the...

8 years ago

Let A1 = { 1 , 2 , 3 , 4 , 5 , 6 }, A2 = { 7 , 8 , 9 , 10 , 11 , 12 , 13 } and A3 = { 14 , 15 , 16 , 17 , 18 , 19 }. How many non-empty sets are there which are a subset of A1 OR a subset of A2 Or a subset of A3?

8 years ago

How many positive integers less than 1000 are there which contain at least one 4 or at least one 9 (or both)?

8 years ago

In the local boating pond there are 11 plain wooden boats, each with a different number. The owner decides that some of these boats will be painted: one in blue, one in green, one in red, and one in orange and the remaining are left unpainted. How many wa...

8 years ago

Ash, Kim and Josh meet every Wednesday to go for a run. If they all agree, they go for a long run rather than a short run. Based on previous experience, the probability that Ash is up for a long run is 0.4, Kim 0.3 and Josh 0.7. What is the probability th...

7 years ago

In a study, info about 224 amphora was gathered. The locations where the amphora were found were recorded as, north, south or elsewhere. Also the positions in which the amphora were found was recorded as layer, pit or other. I need to state the null and a...

7 years ago

Consider the following subsets of R^2: A={(x,y)∈R^2 : x2 +y2 ≤9}, B={(x,y)∈R^2 : y≥2x+1}, C = {(x, y) ∈ R^2 : y ≥ (x + 1)2}. Prove that C is a proper subset of B.

6 years ago

Determine the vector equation of the line l in R^3 through the points P and Q with position vectors p = (2, −1, 6) and q = (1, 0, 11). Determine the equation of the plane perpendicular to the line PQ which passes through the origin.

6 years ago

(i) Express the complex number z = 4i/(1-i√3)in Cartesian form. (ii) Determine the modulus and argument of z, and hence express z in polar form. (b) Solve the equation z4 − z = 0, expressing your solutions in Cartesian form.

6 years ago