A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 1500 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions

Step-by-step explanation:

Let x be the length and y be the width of the rectangular plot.

The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,

x+2y = 1500

x = 1500 - 2y ....(1)

We know that the area of a rectangular plot is given by :

A = xy ....(2)

Put the value of x from equation (1) in (2)

[tex]A=(1500-2y)y\\\\A=1500y-2y^2[/tex] .....(3)

For largest area, differentiate above area equation wrt y.

[tex]\dfrac{dA}{dy}=\dfrac{d}{dy}(1500y-2y^2)\\\\=1500-4y\\\\\text{Put}\ \dfrac{dA}{dy}=0\\\\1500-4y=0\\\\y=\dfrac{1500}{4}\\\\=375[/tex]

Put the value of y in equation (1).

x = 1500-2(375)

= 750 m

Put the value of y in equation (3).

[tex]A =1500(375)-2(375)^2\\A=281250\ m^2[/tex]

Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.

Find the values of the variables in each right triangle.​

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During the 1860s, the pony express delivered mail between San Francisco, California and Denver, Colorado. The riders where able
to cover about 245 miles per day before they would stop and rest. The trip between San Francisco and Denver takes 2.6 days.
Using this information, how many miles is it between San Francisco and Denver?

A)
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B)
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C)
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