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#1 Re: Help Me ! » domain of a function » 2012-05-11 08:28:33
Hi anonimnystefy
Thank you for replying.
you are right for f(x) i have missed the negative sign.
what about he f(g(x)) is it right?
#2 Help Me ! » domain of a function » 2012-05-11 07:50:18
- siyanor
- Replies: 3
hello there,
Lets say we have F(x) = (x-2)÷(x+3)and G(x) = 1÷√(x^2-5x+6) now we have to find domain of each function and domain of f(g(x)), i will not write the calculation but
domain for f(x) = R-{3)
domain for g(x) = (-∞,2)U(3,∞)
domain for f(g(x)) = (-∞,2)U(3,∞)
is the last domain correct?question is also asking to find out if these function are one to one on their domain or not?
i know that f(x) is one to one and already got the answer i also know that g(x) is not one to one , but how we can find inverse of g(x) if its possible ?
#3 Re: Help Me ! » Circumference and Area » 2012-05-10 10:48:00
Finally I'm thinking properly (I hope)
The equal area and perimeter will never happen!
ignore for a moment the semicircles.
area of rectangle = 60 x 40 = 2400
perimeter of rectangle = (60 + 40) x 2 = 200
So the values are way, way apart!
Now chop off the triangles and add bigger semicircles. The area goes up. (maybe the perimeter does too but not by thousands)
So .....
(i) Is this diagram correct?
(ii) Is the wording correct?
(iii) Is the question setter having a laugh?
Bob
What the question is asking for what value of x so the Area and circumference of field A(polygon) will be equal to field B(it will be like Area(A)=Area(b) , and Circum(A)=Circum(B))
#4 Re: Help Me ! » Circumference and Area » 2012-05-10 10:42:58
hi siyanor,
dont you think we are counting the diameter area in two places?!.
Based on your area formula (which I agree with) and my perimeter, I've tried to make them equal.
I get a quadratic with no real roots. (?)
Bob
Hi Bob,
sorry i didnt see this part of your reply.i have resolved the quadratic equation for Area and the answer was x=-21.608 and x=21.608,and for sure we will be using the positive one.
#5 Re: Help Me ! » Circumference and Area » 2012-05-09 22:46:22
Hi Bob
I think you are absolutely right. thank you for making it so easy to understand
i guess the second part of the question that says "without counting the diameter ", is trying to say the same thing that you just said.
Thank you again
#6 Re: Help Me ! » Circumference and Area » 2012-05-09 21:36:32
Hi Bob Bundy,
Thank you for replying.
regarding the "without counting the diameter" part is asking us to find the value of x when areas and circumferences of A and B are equal. ( like we have to to write Area A=Area B , and then we can find the value of x.)
Regarding the trees, it will be only around the field ( exactly the area you have shown in red)
regarding your solution for perimeter :
= (perimeter of rectangle) - (8 straight line segments) + (4 x circumference divide by 2)
dont you think we are counting the diameter area in two places?!. i mean its been included in semicircle perimeter and in polygon perimeter (please correct me if I'm wrong).
#7 Re: Help Me ! » Circumference and Area » 2012-05-09 16:43:11
Hi,
we want to plant trees around the field for x= 5 and the minimum distance between each tree should be 2 meters ,the question is asking for quantity of trees that could be planted around the field.
we have to find the length of sides and arcs (we will not use diameters in this situation ).
#8 Re: Help Me ! » Circumference and Area » 2012-05-09 09:30:39
Thank you for replying .
I think i finally got what you are trying to say 
but one more thing , lets say we want to find the length of around of the field(here we have to calculate the arc size ) how we are suppose to do that ?we can not use the Perimeter of the field ,thats for sure .
#9 Re: Help Me ! » Circumference and Area » 2012-05-09 09:19:21
we say that circumference of a circle is (Pi*Diameter) or (Pi *r²), here because we have semicircular we have to multiply it by 1/2 ,what you mean by do not add Diameter ( im really not getting this )
#10 Re: Help Me ! » Circumference and Area » 2012-05-09 08:54:39
so i have to substract it's length from the circumference ,right?
#11 Re: Help Me ! » Circumference and Area » 2012-05-09 08:44:07
But how am i suppose to do that ?considering we need diameter to calculate the area and perimeter of the circle ?
Im really confused ?
#12 Re: Help Me ! » Circumference and Area » 2012-05-09 08:25:48
what do you mean by OP ?original Post ?
#13 Re: Help Me ! » Circumference and Area » 2012-05-09 07:46:31
Hello there,
No thats the complete draw .
Regarding the second part of question (we are on the same side).well the question is saying for what value of x perimeter and Area of each filed will be equal (meaning we have to put Area=Perimeter)
i didnt get the part that is saying without counting the diameter!
#14 Help Me ! » Circumference and Area » 2012-05-09 07:04:59
- siyanor
- Replies: 23
Hello there ,
we have the below picture which contain two parts,part A(the 8 sided polygon) and Part B (four semicircles).first we have to calculate the whole field Area and Circumference in X expression second we have to find out for what values of x, areas and the circumferences of A and B equal (not counting the diameters in B)?
My answer is :
Area (A)=2400-2x² Area(B)=Pi(x)²
Area(field)=Area (A)+Area(B)=2400-2x² +Pi(x)²
Circum(A) =200+(4√2 - 8)x Circum(B)=2√2(Pi+2)x
Circum(field)=Circum(A)+circum(B)=(200+(4√2 - 8)x)+(2√2(Pi+2)x)
second part of the question , i was thinking to equal the Area of each part with its circumference (but i didnt understand who im suppose to do that in semicircular without counting the diameters?
Would you please do me a favor and see if my calculation is correct?
Thank you
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