C1 Qs-need help!!!

Could someone please help me with these:

1) a) Show that (3x-4)^2 may be written as P + Q/x + R/x^2, where P, Q and ZR are constants to be found.
b) The curve C has equation y=(3x-4)^2 /x^2(the whole (3x-4)^2 is /x^2) x not=0. Find the gradient of the tangent to C at the point on C where x=-2.
c) Find the equation of the normal to C at the point on C where x=-2, giving your answer in the form ax+by+c=0, where a, b and c are integers.

Reply 1

Gaz031

15

*girlie*

Could someone please help me with these:

1) a) Show that (3x-4)^2 may be written as P + Q/x + R/x^2, where P, Q and ZR are constants to be found.
b) The curve C has equation y=(3x-4)^2 /x^2(the whole (3x-4)^2 is /x^2) x not=0. Find the gradient of the tangent to C at the point on C where x=-2.
c) Find the equation of the normal to C at the point on C where x=-2, giving your answer in the form ax+by+c=0, where a, b and c are integers.

For part (a) did you mean (3x-4)^2/(x^2) ?

Reply 2

*girlie*

OP

5

Gaz031

For part (a) did you mean (3x-4)^2/(x^2) ?

yes, I did...sorry, (3x-4)^2 / x^2

Reply 3

john !!

14

(3x-4)^2 = 9x^2 - 24x + 16
are you sure you've typed 1.(a) out right?

(b) y= [(3x-4)^2]/x^2 = 9 - 24x^-1 + 16x^-2
dy/dx = 24/x^2 - 32/x^3
dy/dx (when x=-2) = 24/(-2)^2 - 32/(-2)^3 = 24/4 - 32/-8 = 6 + 4 = 10

(c) gradient of normal = -1/10. when x=-2, y = 9 - 24/-2 + 16/(-2)^2 = 9 + 12 + 4 = 25, so the line passes through the coordinates (-2,25)
y - 25 = -(x + 2)/10
10y - 250 = - x - 2
x + 10y - 248 = 0

which looks completely wrong... argh I hate C1.. too easy ... to make mistakes!

Reply 4

Gaz031

15

Nono, above is right.
Seems like i need a faster scanner o_o. I dislike writing math over the internet sometimes though. It can get confusing, it's easy to make a mistake and look stupid.
I'll post anyway.
http://img104.exs.cx/img104/2537/SWScan00065.jpg

Reply 5

*girlie*

OP

5

So could someone pls help me with the second question??? And this one too!:

3) a) Given that x^2+4x+c=(x+a)^2+b, where a, b and c are constants:
i) find the value of a.
ii) find b in terms of c.
iii) Given also that the equation x^2+4x+c=0 has unequal real roots, find the range of possible values of c.
b) Find the set of values of x for which:
i) 3x<20-x
ii) x^2+4x-21>0
iii) both 3x<20-x and x^2+4x-21>0.

Reply 6

*girlie*

OP

5

oh wait, here's the 2nd Q:

2) In the year 2001, a car dealer sold 400 new cars. A model for future sales assumes that sales will increase by x per year for the next 10 years, so that (400+x) cars are sold in 2002, (400+2x) cars are sold in 2003, and so on. Using this model with x=30, calculate:
a) The number of cars sold in the year 2010.
b) The total number of cars sold over the 10 years from 2001 to 2010.
The dealer wants to sell at least 6000 cars over the 10 year period. Using the same model:
c) Find the least value of x required to achieve this target.

Reply 7

ThugzMansion7

9

*girlie*

oh wait, here's the 2nd Q:

2) In the year 2001, a car dealer sold 400 new cars. A model for future sales assumes that sales will increase by x per year for the next 10 years, so that (400+x) cars are sold in 2002, (400+2x) cars are sold in 2003, and so on. Using this model with x=30, calculate:
a) The number of cars sold in the year 2010.
b) The total number of cars sold over the 10 years from 2001 to 2010.
The dealer wants to sell at least 6000 cars over the 10 year period. Using the same model:
c) Find the least value of x required to achieve this target.

gaz if ur on let me do one of these..lol :biggrin:

Reply 8

evariste_3086

1

*girlie*

So could someone pls help me with the second question??? And this one too!:

3) a) Given that x^2+4x+c=(x+a)^2+b, where a, b and c are constants:
i) find the value of a.
ii) find b in terms of c.
iii) Given also that the equation x^2+4x+c=0 has unequal real roots, find the range of possible values of c.
b) Find the set of values of x for which:
i) 3x<20-x
ii) x^2+4x-21>0
iii) both 3x<20-x and x^2+4x-21>0.

(x+2)^2+c-4=x^2+4x+c
so a=2
b=c-4
unequal real if 16-4c>0 so c<4
3x<20-x implies 4x<20 hence x<5
x^2+4x-21>0
(x+7)(x-3)>0
either x+7>0 and x-3>0 (1)
or x+7<0 and x-3<0 (2)
(1) gives x>-7 and x>3 implies x>3
(2) gives x<-7 and x<3 implies x<-7
so x<-7 or x>3
iii) both 3x<20-x and x^2+4x-21>0
need x<5 and x<-7 or x>3 so x<-7 or 3>x<5