Mathematics: Post your doubts here!

[sea_princess]

hi can anyone help me with this question

a curve is such that dy/dx= 5 - 8/x^2. the line 3y+x=17 is the normal to the curve at point P on the curve given that the x co-ordinate of P is positive , find

i) the coordinate of P
ii) the equation of the curve

to get to P i know that the normal line and the tangent which is dy/dx meet only once
so 5-8/x^2 = 17-x / 3
15- 24/x^2=17-x
2-x +24/x^2

but i know this sint right because after solving i get x^3 so i thought i have the integrate the dy/dx and then make it equal to the line

i dnt really know- can someone please help me out????

okay since it is a normal , it's gradient will be - 1/3
so dy/dx = 3
3 = 5 - 8/x^2
8/x^2 = 2 ( multiply by x^2)
2 x^2= 8 ( divide by 2)
x^2 =4
X= 2 this is the x-coordinate of P
ii) you integerate dy/dx
the equation of the curve = 5x - 8x^-1/-1 +c
= 5x + 8/x +c

 

[s1294]

okay since it is a normal , it's gradient will be - 1/3
so dy/dx = 3
3 = 5 - 8/x^2
8/x^2 = 2 ( multiply by x^2)
2 x^2= 8 ( divide by 2)
x^2 =4
X= 2 this is the x-coordinate of P
ii) you integerate dy/dx
the equation of the curve = 5x - 8x^-1/-1 +c
= 5x + 8/x +c

Thank you soooooo much! really helpful

 

[sea_princess]

Thank you soooooo much! really helpful

you're welcome

 

[s1294]

please help here

curve= (8x-x^2)^o.5
find an expression for dy/dx, and coordinates of the stationary points on the curve

i have 0.5* (8x-x^2)^-0.5 *(8-2x) = (4-x)*(8x-x^2)^-0.5
is this correct?
how do i get the stationary points?
please explain!

 

[umarashraf]

do you have the answer of it..???

 

[s1294]

do you have the answer of it..???

no i don't
can u just give me a guess?

 

[umarashraf]

put the derivative equal to zero.... i think its x=4...

 

[s1294]

put the derivative equal to zero.... i think its x=4...

okay thank you

 

[umarashraf]

where have you seen this question by the way...??? can you share the link of it...?? if possible...???

 

[s1294]

where have you seen this question by the way...??? can you share the link of it...?? if possible...???

this is from- 9709/12/0ct/nov/ 2011- there isnt a link available our teacher only gave us hard copy- on paper if i had the link i wld have checked the answer

 

[Zephyro]

Winter 2009 P31

http://www.xtremepapers.com/CIE/index.php?dir=International A And AS Level/9709 - Mathematics/&file=9709_w09_qp_31.pdf

Question 7 - Part 4 . I know the first inequality. Not sure about the Arg one.

Help, when you get some spare time please.

 

[umarashraf]

this is from- 9709/12/0ct/nov/ 2011- there isnt a link available our teacher only gave us hard copy- on paper if i had the link i wld have checked the answer

oh right ... yeah its x=4...

 

[s1294]

please help with this!!

 

[umarashraf]

please help with this!!

gradient of line AC is 0.5 and its equation is 2y-x=-1
gradient of line bd is -2 and its equation is y+2x=12
intersection of the two lines is the point M....

 

[passion hunter]

The complex number 2 + 2i is denoted by u.
(i) Find the modulus and argument of u. [2]
(ii) Sketch anArgand diagramshowing the points representing the complex numbers 1, i and u. Shade
the region whose points represent the complex numbers ß which satisfy both the inequalities
|ß − 1| ≤ |ß − i| and |ß − u| ≤ 1. [4]
(iii) Using your diagram, calculate the value of |ß| for the point in this region for which arg ß is least



can somebody explain me the last part of the question thanks....

 

[s1294]

please check if i have done this correctly
a college agrees a sponsorship deal in which grants will be received each year for sports equipment. this grant will be $4000 in 2012 and will increase by 5% each year. calculate

i) the value of grant in 2022
ii) the total amount the college will receive in the years 2012 to 2022 inclusive

10 years
4000*1.05^10=$6515.6

total amount of grant for 11 years
add all years grants together= $105027.15
is there an easier way to calculate part ii)?

 

[s1294]

please check if i have done this correctly
a college agrees a sponsorship deal in which grants will be received each year for sports equipment. this grant will be $4000 in 2012 and will increase by 5% each year. calculate

i) the value of grant in 2022
ii) the total amount the college will receive in the years 2012 to 2022 inclusive

10 years
4000*1.05^10=$6515.6

total amount of grant for 11 years
add all years grants together= $105027.15
is there an easier way to calculate part ii)?

please help- its the last one for the day

 

[DANGERBP]

guyz anyone can help with this its pretty easy just not to my brain r8 now .. here is it just part b ! =p
Two particles A and B are moving on a smooth horizontal plane. The mass of A is km,
where 2 <
k < 3 , and the mass of B is m. The particles are moving along the same straight
line, but in opposite directions, and they collide directly. Immediately before they collide
the speed of
A is 2u and the speed of B is 4u. As a result of the collision the speed of A is
halved and its direction of motion is reversed.
(a) Find, in terms of
k and u, the speed of B immediately after the collision.
(b) State whether the direction of motion of
B changes as a result of the collision,explaining your answer.

 

[johnsth]

i dont know how to solve p3 vector properly though i have some knowledge on it.like i dont know when to use common perpendicular and how to find position vector,etc.so guys can someone please help?

 

[smzimran]

please check if i have done this correctly
a college agrees a sponsorship deal in which grants will be received each year for sports equipment. this grant will be $4000 in 2012 and will increase by 5% each year. calculate

i) the value of grant in 2022
ii) the total amount the college will receive in the years 2012 to 2022 inclusive

10 years
4000*1.05^10=$6515.6

total amount of grant for 11 years
add all years grants together= $105027.15
is there an easier way to calculate part ii)?

Use geometric progression