d py(b) For what value of x is the area largest?(c) What is the maximum area?R is44. Enclosing a Rectangular Field Beth has 3000 feet of fenc-ing available to enclose a rectangular field.revenue?(a) Express the area A of the rectangle as a function of xwhere x is the length of the rectangle.(b) For what value of x is the area largest?(c) What is the maximum area?sold of a45. Enclosing the Most Area with a Fence A farmer with 4000meters of fencing wants to enclose a rectangular plot thatborders on a river. If the farmer does not fence the side alongmember,the river, what is the largest area that can be enclosed? (Seethe figure.)he maxi-belaylonaximizele0.5VIpessold of adouA S2Xm4000-2xne maxi-mize rev-46. Enclosing the Most Area with a Fence A farmer with 2000meters of fencing wants to enclose a rectangular plot thatborders on a straight highway. If the farmer does not fencethe side along the highway, what is the largest area that cansold of abe enclosed?7 47. Analyzing the Motion of a Projectile A projectile is firedfrom a cliff 200 feet above the water at an inclination of 45°to the horizontal, with a muzzle velocity of 50 feet per sec-ond. The height h of the projectile above the water is given byhe maxi--32x2mize rev-+ x + 200h(x)(50)2ahere x is the horizontal distance of the projectile from thesold of abase of the cliff.(a) How far from the base of the cliff is the height of theprojectile a maximum?

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Asked Oct 27, 2019
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I need help with number 46

d py
(b) For what value of x is the area largest?
(c) What is the maximum area?
R is
44. Enclosing a Rectangular Field Beth has 3000 feet of fenc-
ing available to enclose a rectangular field.
revenue?
(a) Express the area A of the rectangle as a function of x
where x is the length of the rectangle.
(b) For what value of x is the area largest?
(c) What is the maximum area?
sold of a
45. Enclosing the Most Area with a Fence A farmer with 4000
meters of fencing wants to enclose a rectangular plot that
borders on a river. If the farmer does not fence the side along
member,
the river, what is the largest area that can be enclosed? (See
the figure.)
he maxi-
belay
lo
naximize
le
0.5
VIpes
sold of a
douA S2
X
m
4000-2x
ne maxi-
mize rev-
46. Enclosing the Most Area with a Fence A farmer with 2000
meters of fencing wants to enclose a rectangular plot that
borders on a straight highway. If the farmer does not fence
the side along the highway, what is the largest area that can
sold of a
be enclosed?
7 47. Analyzing the Motion of a Projectile A projectile is fired
from a cliff 200 feet above the water at an inclination of 45°
to the horizontal, with a muzzle velocity of 50 feet per sec-
ond. The height h of the projectile above the water is given by
he maxi-
-32x2
mize rev-
+ x + 200
h(x)
(50)2
ahere x is the horizontal distance of the projectile from the
sold of a
base of the cliff.
(a) How far from the base of the cliff is the height of the
projectile a maximum?
help_outline

Image Transcriptionclose

d py (b) For what value of x is the area largest? (c) What is the maximum area? R is 44. Enclosing a Rectangular Field Beth has 3000 feet of fenc- ing available to enclose a rectangular field. revenue? (a) Express the area A of the rectangle as a function of x where x is the length of the rectangle. (b) For what value of x is the area largest? (c) What is the maximum area? sold of a 45. Enclosing the Most Area with a Fence A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along member, the river, what is the largest area that can be enclosed? (See the figure.) he maxi- belay lo naximize le 0.5 VIpes sold of a douA S2 X m 4000-2x ne maxi- mize rev- 46. Enclosing the Most Area with a Fence A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can sold of a be enclosed? 7 47. Analyzing the Motion of a Projectile A projectile is fired from a cliff 200 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 50 feet per sec- ond. The height h of the projectile above the water is given by he maxi- -32x2 mize rev- + x + 200 h(x) (50)2 ahere x is the horizontal distance of the projectile from the sold of a base of the cliff. (a) How far from the base of the cliff is the height of the projectile a maximum?

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Expert Answer

Step 1

Let length = x and width=y

Total fence = x+2y=2000 so, x=2000-2y

Area= xy

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Step 2

Plug x=2000-2y and express area in terms of y. For maximum area dA/d...

Area=A=xy
A-(2000-2y)y
A-2000y-2y
dA
=2000-4y
dy
0-2000-4y
4y=2000
y 500
help_outline

Image Transcriptionclose

Area=A=xy A-(2000-2y)y A-2000y-2y dA =2000-4y dy 0-2000-4y 4y=2000 y 500

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