The greatest area for a rectangle on a track field.
$begingroup$
An athletic field with a perimeter of 0.25 miles consists of a rectangle with a semicircle at each end, as shown below. Find the dimensions that yield the greatest possible area for the rectangular region.
This is the work that I did below. I was wondering if this was the greatest possible area for the rectangle below.
quadratics
asked Dec 11 '18 at 1:35
mjjmjj
6118
$endgroup$
add a comment |
$begingroup$
An athletic field with a perimeter of 0.25 miles consists of a rectangle with a semicircle at each end, as shown below. Find the dimensions that yield the greatest possible area for the rectangular region.
This is the work that I did below. I was wondering if this was the greatest possible area for the rectangle below.
quadratics
asked Dec 11 '18 at 1:35
mjjmjj
6118
$endgroup$
add a comment |
$begingroup$
An athletic field with a perimeter of 0.25 miles consists of a rectangle with a semicircle at each end, as shown below. Find the dimensions that yield the greatest possible area for the rectangular region.
This is the work that I did below. I was wondering if this was the greatest possible area for the rectangle below.
quadratics
asked Dec 11 '18 at 1:35
mjjmjj
6118
$endgroup$
An athletic field with a perimeter of 0.25 miles consists of a rectangle with a semicircle at each end, as shown below. Find the dimensions that yield the greatest possible area for the rectangular region.
This is the work that I did below. I was wondering if this was the greatest possible area for the rectangle below.
quadratics
quadratics
asked Dec 11 '18 at 1:35
mjjmjj
6118
asked Dec 11 '18 at 1:35
mjjmjj
6118
asked Dec 11 '18 at 1:35
mjjmjj
6118
asked Dec 11 '18 at 1:35
mjjmjj
6118
asked Dec 11 '18 at 1:35
mjjmjj
6118
6118
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Near the end of page $1$, you wrote $r=frac{2}{16pi}$ when you meant to say $2r=frac{2}{16pi}$
Once we found out that $r=frac{1}{16pi}$, we can compute $$l=frac18 - pi r= frac18 -frac1{16}=frac1{16}$$ directly without finding $A$ explicitly.
answered Dec 11 '18 at 1:47
Siong Thye GohSiong Thye Goh
101k1466118
$endgroup$
$begingroup$
why would it be 2r?
$endgroup$
– mjj
Dec 11 '18 at 1:49
$begingroup$
you wrote $r=frac2{16pi}$ and then you wrote $w=frac{1}{8pi}$?
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:53
$begingroup$
I got r to equal 1/16pi. I then multiplied this by 2 because of 2r=w. I then got 1/8pi for w.
$endgroup$
– mjj
Dec 11 '18 at 1:55
$begingroup$
Great, do not write $r = frac1{16pi} times 2$, you can write $r times 2 = frac1{16pi} times 2$ or $2r = frac1{16pi} times 2$.
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:56
$begingroup$
so the 'l' and the 'w' are still correct?
$endgroup$
– mjj
Dec 11 '18 at 1:57
|
show 1 more comment
Your Answer
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1 Answer
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1 Answer
1
active
oldest
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active
oldest
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active
oldest
votes
$begingroup$
Near the end of page $1$, you wrote $r=frac{2}{16pi}$ when you meant to say $2r=frac{2}{16pi}$
Once we found out that $r=frac{1}{16pi}$, we can compute $$l=frac18 - pi r= frac18 -frac1{16}=frac1{16}$$ directly without finding $A$ explicitly.
answered Dec 11 '18 at 1:47
Siong Thye GohSiong Thye Goh
101k1466118
$endgroup$
$begingroup$
why would it be 2r?
$endgroup$
– mjj
Dec 11 '18 at 1:49
$begingroup$
you wrote $r=frac2{16pi}$ and then you wrote $w=frac{1}{8pi}$?
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:53
$begingroup$
I got r to equal 1/16pi. I then multiplied this by 2 because of 2r=w. I then got 1/8pi for w.
$endgroup$
– mjj
Dec 11 '18 at 1:55
$begingroup$
Great, do not write $r = frac1{16pi} times 2$, you can write $r times 2 = frac1{16pi} times 2$ or $2r = frac1{16pi} times 2$.
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:56
$begingroup$
so the 'l' and the 'w' are still correct?
$endgroup$
– mjj
Dec 11 '18 at 1:57
|
show 1 more comment
$begingroup$
Near the end of page $1$, you wrote $r=frac{2}{16pi}$ when you meant to say $2r=frac{2}{16pi}$
Once we found out that $r=frac{1}{16pi}$, we can compute $$l=frac18 - pi r= frac18 -frac1{16}=frac1{16}$$ directly without finding $A$ explicitly.
answered Dec 11 '18 at 1:47
Siong Thye GohSiong Thye Goh
101k1466118
$endgroup$
$begingroup$
why would it be 2r?
$endgroup$
– mjj
Dec 11 '18 at 1:49
$begingroup$
you wrote $r=frac2{16pi}$ and then you wrote $w=frac{1}{8pi}$?
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:53
$begingroup$
I got r to equal 1/16pi. I then multiplied this by 2 because of 2r=w. I then got 1/8pi for w.
$endgroup$
– mjj
Dec 11 '18 at 1:55
$begingroup$
Great, do not write $r = frac1{16pi} times 2$, you can write $r times 2 = frac1{16pi} times 2$ or $2r = frac1{16pi} times 2$.
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:56
$begingroup$
so the 'l' and the 'w' are still correct?
$endgroup$
– mjj
Dec 11 '18 at 1:57
|
show 1 more comment
$begingroup$
Near the end of page $1$, you wrote $r=frac{2}{16pi}$ when you meant to say $2r=frac{2}{16pi}$
Once we found out that $r=frac{1}{16pi}$, we can compute $$l=frac18 - pi r= frac18 -frac1{16}=frac1{16}$$ directly without finding $A$ explicitly.
answered Dec 11 '18 at 1:47
Siong Thye GohSiong Thye Goh
101k1466118
$endgroup$
Near the end of page $1$, you wrote $r=frac{2}{16pi}$ when you meant to say $2r=frac{2}{16pi}$
Once we found out that $r=frac{1}{16pi}$, we can compute $$l=frac18 - pi r= frac18 -frac1{16}=frac1{16}$$ directly without finding $A$ explicitly.
answered Dec 11 '18 at 1:47
Siong Thye GohSiong Thye Goh
101k1466118
answered Dec 11 '18 at 1:47
Siong Thye GohSiong Thye Goh
101k1466118
answered Dec 11 '18 at 1:47
Siong Thye GohSiong Thye Goh
101k1466118
answered Dec 11 '18 at 1:47
Siong Thye GohSiong Thye Goh
101k1466118
101k1466118
$begingroup$
why would it be 2r?
$endgroup$
– mjj
Dec 11 '18 at 1:49
$begingroup$
you wrote $r=frac2{16pi}$ and then you wrote $w=frac{1}{8pi}$?
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:53
$begingroup$
I got r to equal 1/16pi. I then multiplied this by 2 because of 2r=w. I then got 1/8pi for w.
$endgroup$
– mjj
Dec 11 '18 at 1:55
$begingroup$
Great, do not write $r = frac1{16pi} times 2$, you can write $r times 2 = frac1{16pi} times 2$ or $2r = frac1{16pi} times 2$.
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:56
$begingroup$
so the 'l' and the 'w' are still correct?
$endgroup$
– mjj
Dec 11 '18 at 1:57
|
show 1 more comment
$begingroup$
why would it be 2r?
$endgroup$
– mjj
Dec 11 '18 at 1:49
$begingroup$
you wrote $r=frac2{16pi}$ and then you wrote $w=frac{1}{8pi}$?
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:53
$begingroup$
I got r to equal 1/16pi. I then multiplied this by 2 because of 2r=w. I then got 1/8pi for w.
$endgroup$
– mjj
Dec 11 '18 at 1:55
$begingroup$
Great, do not write $r = frac1{16pi} times 2$, you can write $r times 2 = frac1{16pi} times 2$ or $2r = frac1{16pi} times 2$.
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:56
$begingroup$
so the 'l' and the 'w' are still correct?
$endgroup$
– mjj
Dec 11 '18 at 1:57
$begingroup$
why would it be 2r?
$endgroup$
– mjj
Dec 11 '18 at 1:49
$begingroup$
why would it be 2r?
$endgroup$
– mjj
Dec 11 '18 at 1:49
$begingroup$
you wrote $r=frac2{16pi}$ and then you wrote $w=frac{1}{8pi}$?
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:53
$begingroup$
you wrote $r=frac2{16pi}$ and then you wrote $w=frac{1}{8pi}$?
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:53
$begingroup$
I got r to equal 1/16pi. I then multiplied this by 2 because of 2r=w. I then got 1/8pi for w.
$endgroup$
– mjj
Dec 11 '18 at 1:55
$begingroup$
I got r to equal 1/16pi. I then multiplied this by 2 because of 2r=w. I then got 1/8pi for w.
$endgroup$
– mjj
Dec 11 '18 at 1:55
$begingroup$
Great, do not write $r = frac1{16pi} times 2$, you can write $r times 2 = frac1{16pi} times 2$ or $2r = frac1{16pi} times 2$.
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:56
$begingroup$
Great, do not write $r = frac1{16pi} times 2$, you can write $r times 2 = frac1{16pi} times 2$ or $2r = frac1{16pi} times 2$.
$endgroup$
– Siong Thye Goh
Dec 11 '18 at 1:56
$begingroup$
so the 'l' and the 'w' are still correct?
$endgroup$
– mjj
Dec 11 '18 at 1:57
$begingroup$
so the 'l' and the 'w' are still correct?
$endgroup$
– mjj
Dec 11 '18 at 1:57
|
show 1 more comment
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