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C2 - Radians help please
Hi i dont have answers to these questions but can someone please check and help me with the following - rep will be given + diagram attached
1) The diagram shows a minor sector OMN of a circle centre O and radius r cm. The perimeter of a sector is 100cm and the area of the sector is Acm^2.
a) show that A= 50r - r^2
I dont know how to do this one
b) Given that r varies, find :
i) The value of r for which A is a mximum and show that A is a maximum.
Rite here is my answer :
dA/dr = 50 - 2r
0 = 50 - 2r
2r = 50
r = 25cm
and its a maximum because d2A/dr2 = -2 which is >0 is this right?
ii) The value of <MON for this maximum area.
I dont know how to do this question - i tried doing P: 100 = 2r + r(theta)
But i get theta = 2?
And the third part i wil be able to do "find the maximum area of the sector OMN" if i have the answer to the second part.
Thanks for your time and effort,
Regards, Asad
1) The diagram shows a minor sector OMN of a circle centre O and radius r cm. The perimeter of a sector is 100cm and the area of the sector is Acm^2.
a) show that A= 50r - r^2
I dont know how to do this one
b) Given that r varies, find :
i) The value of r for which A is a mximum and show that A is a maximum.
Rite here is my answer :
dA/dr = 50 - 2r
0 = 50 - 2r
2r = 50
r = 25cm
and its a maximum because d2A/dr2 = -2 which is >0 is this right?
ii) The value of <MON for this maximum area.
I dont know how to do this question - i tried doing P: 100 = 2r + r(theta)
But i get theta = 2?
And the third part i wil be able to do "find the maximum area of the sector OMN" if i have the answer to the second part.
Thanks for your time and effort,
Regards, Asad
Reply 1
1)a)
The Perimeter = 2r + rx (where x is the angle of the minor sector in radians)
So 100 = 2r + rx
r(2+x) = 100
x = (100/r) - 2
The Area = 0.5r^2*x
= 0.5r^2*(100/r - 2)
= 50r - r^2
b) i) This is correct
The Perimeter = 2r + rx (where x is the angle of the minor sector in radians)
So 100 = 2r + rx
r(2+x) = 100
x = (100/r) - 2
The Area = 0.5r^2*x
= 0.5r^2*(100/r - 2)
= 50r - r^2
b) i) This is correct
Reply 2
Thanks a lot - do you know the answer to finding out the angle <MON
Using your formula for the first part it would be 2? What is 2 radians - in other words how do i express this
Using your formula for the first part it would be 2? What is 2 radians - in other words how do i express this
Reply 3
asadtamimi
Thanks a lot - do you know the answer to finding out the angle <MON
Using your formula for the first part it would be 2? What is 2 radians - in other words how do i express this
Using your formula for the first part it would be 2? What is 2 radians - in other words how do i express this
Yes, the answer is 2 radians (you can leave it at that unless you want to convert it into degrees)
Reply 4
Hi can someone please help me with this question as well - cos im clueless about this topic and can you explain to me how and why you have worked it out the way you have:
The diagram shows a circle, centre O, of radius 6 cm. The points A and B are on the circumference of the circle. The area of the shaded major sector is 80cm^2. Given that <AOB = (theta) radians, where 0<theta<pie. calculate:
a) The value, to 3 decimal places, of theta
b) the length in cm, to 2 decimal places, of the minor arc AB
The diagram shows a circle, centre O, of radius 6 cm. The points A and B are on the circumference of the circle. The area of the shaded major sector is 80cm^2. Given that <AOB = (theta) radians, where 0<theta<pie. calculate:
a) The value, to 3 decimal places, of theta
b) the length in cm, to 2 decimal places, of the minor arc AB
asadtamimi
Hi can someone please help me with this question as well - cos im clueless about this topic and can you explain to me how and why you have worked it out the way you have:
The diagram shows a circle, centre O, of radius 6 cm. The points A and B are on the circumference of the circle. The area of the shaded major sector is 80cm^2. Given that <AOB = (theta) radians, where 0<theta<pie. calculate:
a) The value, to 3 decimal places, of theta
b) the length in cm, to 2 decimal places, of the minor arc AB
The diagram shows a circle, centre O, of radius 6 cm. The points A and B are on the circumference of the circle. The area of the shaded major sector is 80cm^2. Given that <AOB = (theta) radians, where 0<theta<pie. calculate:
a) The value, to 3 decimal places, of theta
b) the length in cm, to 2 decimal places, of the minor arc AB
a) r²(2pi - x)/2 = 80
(x is the angle of the major sector)
theta = (2pi - 40/9) radians = 1.83874086... radians = 1.839 radians (3 d.p.)
b) rtheta = 6*1.83874086... = 11.0324...cm = 11.03cm (2 d.p.)
I think these are right.
Hope they help,
~~Simba
Reply 6
Yes they are right - thanks but why did you do r^2(2pi - theta)/2 = 80? is there a specific formula for these things?
Reply 7
oh wait i had the same formula but i had (theta - sintheta) in the brackets - when would that apply?
Reply 10
Oh ok thanks a lot - your better then my teachers 
But can i bother you just one last time please.
I have attached a diagram to the last question which i dont know how to do.
Triangle ABC has AB = 9cm, BC = 10cm and CA = 5cm. A circle, centre A and radius 3cm intersects AB and AC at P and Q respectively, as show in the diagram.
Show that, to 3 decimal places, <BAC = 1.504 radians.
But can i bother you just one last time please.I have attached a diagram to the last question which i dont know how to do.
Triangle ABC has AB = 9cm, BC = 10cm and CA = 5cm. A circle, centre A and radius 3cm intersects AB and AC at P and Q respectively, as show in the diagram.
Show that, to 3 decimal places, <BAC = 1.504 radians.
Reply 12
I know this thread is old, but can anyone explain how this answer of theta being 2 was worked out? Thanks
Original post by asadtamimi
Thanks a lot - do you know the answer to finding out the angle <MON
Using your formula for the first part it would be 2? What is 2 radians - in other words how do i express this
Using your formula for the first part it would be 2? What is 2 radians - in other words how do i express this
Reply 13
does anyone know what paper is this question on?
Reply 15
Original post by rejwana
I have a question about the question that started this thread, the second part asks how you can show that A is a maximum for that value of r. How do I do this?
Show that the second derivative for that value is less than 0.
Please don't post on old threads like these. Start a new one instead
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