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DochEvi [55]
3 years ago
10

Of all rectangles with a perimeter of 1313​, which one has the maximum​ area? (give the​ dimensions.) let a be the area of the r

ectangle. what is the objective function in terms of the width of the​ rectangle, w
Mathematics
1 answer:
saw5 [17]3 years ago
8 0

Let the length be l.

Formula of perimeter is P= 2(length +width )

1313 =2 (l+w)

l = \frac{1313}{2}-w

And the formula of area of rectangle = length times width .

A = l*w

A= (\frac{1313}{2}-w )*w

A = \frac{1313w}{2} -w^2

And that's the required objective function .

The equation represents parabola and a parabola is maximum at its vertex .

And the formula of vertex is

w = -\frac{b}{2a} =-\frac{1313}{4}

Substituting this value of w in the formula of area, we will get

A= \frac{1313*1313}{8} -(\frac{1313}{4})^2

Area= \frac{1723969}{16}=107748 \ square \ units .

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3 0
4 years ago
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5 0
4 years ago
Which fraction is close to, but less than 1/2?
qwelly [4]

Answer:

1/9, 2/9, 3/9, 4/9, 1/8, 2/8, 3/8, 1/7, 2/7, 3/7, 1/6, 2/6, 1/5, 2/5, 1/4, 1/3.

Step-by-step explanation:

hope this helps,

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3 years ago
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3 years ago
If it takes Charlie 45 minutes walking at 2.5 km/hr to get to the chocolate factory and it takes Willy Wonka 15 minutes walking
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Answer:

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Step-by-step explanation:

Given data

it takes Charlie 45 minutes walking at 2.5 km/hr

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distance= 52.5 km

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