[CIE] All Pure Mathematics (P1, P2 and P3) doubts here !

[Most UniQue™]

Done step by tiny step in attachment. Am in a slow mood.

Thank you!

[silvercameron]

this is a Diffrentiation question and i have got no idea how to solve it:

A rectangular box is to be made with a square base, and its capacity is to be 4000 cm^3. Find the length of the side of the base when the amount of material used to make the box is as small as possible.

[astarmathsandphysics]

An optimization question. Find expression for area and volume, sub the expression for area into thhat for volume then find turning point bydifferentiation.

[silvercameron]

thanks to you, sir.
I got the correct answer.

[astarmathsandphysics]

I wrote that on my phone cos I was out. It was a note to myself to do the question, but if you did it yourself that's great.

[White Eagle]

chan any one explain how a vector equestion is found from a cartesian equestion

I AM stuck with
Find vector equestion of cartesian equestion
x+3y=7

[astarmathsandphysics]

Do you mean for lines?
http://astarmathsandphysics.com/a_level_maths_notes/C4/a_level_maths_notes_c4_changing_between_cartesian_and_vector_forms_of_equations_of_lines.html

[donhassan]

hello everyone please help me out in this question please


The planes p1 and p2 have equations X+Y-Z=0 AND 2X-4Y+Z+12=0 respectively.
1.) find the numbers p,q,r such that vector (p,q,r) is parallel to both p1 and p2
2.)hence find the equation of the plane through the point (3,8,2) which is perpendicular  to both p1 and p2


answer:1.)p=1 q=1 r=2
           2.)X+y+2z=15
guys pls explain me in lucid way

thanks
donhassan

[astarmathsandphysics]

1. The normals are n_1=(1,1,-1) and n_2=(2,-4,1)
find n_1 x n_2 =(-1,-1,-6)
2.-3x-3y-6z=d
Put x=3,y=8, z=2 to find d=-45 so -3x-3y-6z=-45
and dividing by -3 gives x+y+2z=15

[donhassan]

1. The normals are n_1=(1,1,-1) and n_2=(2,-4,1)
find n_1 x n_2 =(-1,-1,-6)
2.-3x-3y-6z=d
Put x=3,y=8, z=2 to find d=-45 so -3x-3y-6z=-45
and dividing by -3 gives x+y+2z=15

sir i didn't understood first part

[astarmathsandphysics]

The components of the normal are the coefficients of the equation of the plane.
A plane with equation 3x+4y+6z=2423 has normal (3,4,6)

[HUSH1994]

P3 MJ 2008 Q3 part 1 and Q6 please 

[sabbath_92]

P3 MJ 2008 Q3 part 1 and Q6 please 

a=rsin x

and the next is just implicit differentiation, equate dy/dx = 0

[LekhB]

Stuck with those two:

[haris94]

Stuck with those two:

Looks like your in luck. I just finished doing the first question and then saw your post....so here you go  

Hope you're able to read my handwriting  

First question continues on the second attachment