does anyone have answers for this paper or you know what paper this is? ty (1 Viewer)

[yashbb]

 

[yashbb]

also does anyone know how to do 1 part b

 

[ExtremelyBoredUser]

also does anyone know how to do 1 part b

Yep. This is how I did it because it was most apparent to me, I'm sure there's a faster way but this is the first thing that came to my mind.

Since we are trying to find the coordinates of contact;

x^3 -3x^2+2x=2x-4
x^3 -3x^2 + 4 = 0

Now you already have a root to this equation, x=2, since the intercepts of the cubic and tangent are now roots since we made them equal to each other. You can choose to do sums roots if you want but if you look closely, you can substitute -1 into the equation and it would produce 0 meaning it is an intercept.

x = -1, y = ?

Substitute back into the equation;
y = 2(-1)-4
y= -2-4 = -6

Hence other point of contact is (-1,-6)

Edit: Checked with Desmos:

 

[yashbb]

Yep. This is how I did it because it was most apparent to me, I'm sure there's a faster way but this is the first thing that came to my mind.

Since we are trying to find the coordinates of contact;

x^3 -3x^2+2x=2x-4
x^3 -3x^2 + 4 = 0

Now you already have a root to this equation, x=2, since the intercepts of the cubic and tangent are now roots since we made them equal to each other. You can choose to do sums roots if you want but if you look closely, you can substitute -1 into the equation and it would produce 0 meaning it is an intercept.

x = -1, y = ?

Substitute back into the equation;
y = 2(-1)-4
y= -2-4 = -6

Hence other point of contact is (-1,-6)

yep just wanted to know if i did it correct and i did, thank you so much.

 

[jimmysmith560]

@yashbb the answers to Question 5 are as follows:

(a)

(b)

(c)

I hope this helps!

 

[yashbb]

@yashbb the answers to Question 5 are as follows:

(a)

(b)

(c)

I hope this helps!

tyyyy

 

[CM_Tutor]

Yep. This is how I did it because it was most apparent to me, I'm sure there's a faster way but this is the first thing that came to my mind.

Since we are trying to find the coordinates of contact;

x^3 -3x^2+2x=2x-4
x^3 -3x^2 + 4 = 0

Now you already have a root to this equation, x=2, since the intercepts of the cubic and tangent are now roots since we made them equal to each other. You can choose to do sums roots if you want but if you look closely, you can substitute -1 into the equation and it would produce 0 meaning it is an intercept.

For anyone who didn't realise, is not just a root, it's a double root. So, sum of roots gives , the other root.