Mathematics: Post your doubts here!

[palomafaith]

Is there any way that somebody could post the full solutions of p33 0ct/nov14 variant 32?? Need help so bad

 

[Sarosh Jameel]

PLZ tell me that why does the tension changes its direction in part (II) ??

 

[musiclover gurl]

e^x = 3^(x-2)
ln(e^x) = ln(3^(x-2)) .......taking ln on both sides...
x = (x-2)ln3 .......simplification, and dropping the power rule.
x = (ln3)x - 2ln3
2ln3 = (ln3 - 1)x
x = (2ln3) / (ln3 - 1) = 22.281

Thank you qwertypoiu !

 

[musiclover gurl]

To find exact values of trigonometric functions such as sin and cos, which triangles are used (isosceles, equilateral or both)? And how are they used?

 

[Sarosh Jameel]

To find exact values of trigonometric functions such as sin and cos, which triangles are used (isosceles, equilateral or both)? And how are they used?

generally right angle triangle is used ..

 

[musiclover gurl]

generally right angle triangle is used ..

Yeah but what about the lengths?

 

[Sarosh Jameel]

can u tell me the exact question ?

Yeah but what about the lengths?

 

[musiclover gurl]

can u tell me the exact question ?

It's not in a question. I just wanna know how to calculate the exact angles, e.g, sin 30, 60 and 45 using triangles. Hope you understood what I meant!

 

[Sarosh Jameel]

It's not in a question. I just wanna know how to calculate the exact angles, e.g, sin 30, 60 and 45 using triangles. Hope you understood what I meant!

exact angles can be calculated from any type of triangle if the required data is given to calculate the exact angles..

 

[musiclover gurl]

exact angles can be calculated from any type of triangle if the required data is given to calculate the exact angles..

Ok...so can you tell me whats the exact value of sin 30, with explanation? Sorry if am asking too many questions. It's just that trigo is a bit difficult!

 

[Sarosh Jameel]

u can take the help of calculator to get exact value of sin30 which is 1/2 ..

 

[musiclover gurl]

u can take the help of calculator to get exact value of sin30 which is 1/2 ..

Ok then. Thanks! This seems the only method.

 

[qwertypoiu]

PLZ tell me that why does the tension changes its direction in part (II) ??

There's something called Newton's Third Law.
It's famously known as "every action has an equal and opposite reaction"
The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.

When you are standing on the ground, on YOU, there are two forces. The earth pulls you down (weight), and the floor pushes you up (normal contact force). Note that these are NOT the two forces Newton talks about:
Action: earth pulls you. Reaction: You pull the earth.
Actions: ground pushes you up. Reaction: you push the ground down.

In simple words, when a string connects two objects A and B, there is tension in string acting on A towards B, and an opposite and equal tension acting on B towards A.

 

[Sarosh Jameel]

There's something called Newton's Third Law.
It's famously known as "every action has an equal and opposite reaction"
The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.

When you are standing on the ground, on YOU, there are two forces. The earth pulls you down (weight), and the floor pushes you up (normal contact force). Note that these are NOT the two forces Newton talks about:
Action: earth pulls you. Reaction: You pull the earth.
Actions: ground pushes you up. Reaction: you push the ground down.

In simple words, when a string connects two objects A and B, there is tension in string acting on A towards B, and an opposite and equal tension acting on B towards A.

Thanks !

 

[musiclover gurl]

Help please?

 

[Sarosh Jameel]

which year

Help please?
View attachment 57095

 

[sj0007]

Either my mind isnt working or the marking scheme is wrong................. can anyone tell me how the acceleration of P in the question below is gsin30? (I came to the conclusion that it is g/sin30)

 

[sj0007]

Help please?
View attachment 57095

(i) f(x) = 4, so: 6 - 4cos(0.5x) = 4
cos(0.5x) = 0.5
0.5x = π / 3 (since it says exact, no need for basic angles and stuff)
x = 2π / 3

(ii) Max = a + b = 6+4 = 10 and Min = a - b = 6 - 4 = 2
So, range: 2 <f(x)<10

(iii) The graph is going to be upside down since the cos is -ve.............. so it would be something like this: (sorry for the crappy drawing though)


(iv) The inverse is just like the normal one

Hope it helps...............

 

[Sarosh Jameel]

Either my mind isnt working or the marking scheme is wrong................. can anyone tell me how the acceleration of P in the question below is gsin30? (I came to the conclusion that it is g/sin30)
View attachment 57097

Resultant force down the slope is .... mgsina=ma
m and m cancel out ... remaining is ... a=gsina

 

[sj0007]

Resultant force down the slope is .... mgsina=ma
m and m cancel out ... remaining is ... a=gsina

Oooooooooh oki....... (Hadn't studied that part yet)..........thnx