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strojnjashka [21]
3 years ago
6

suppose a farmer encloses a rectangular region of a land next to a river. fencing will be used on 3 sieds, and none is needed al

ong the river. tje farmer ha 180 feet of fencing available to use. using x and y for the dimensions of the rectangle. the equation for the amount of fencing used on each side is 2x u
Mathematics
1 answer:
nexus9112 [7]3 years ago
4 0

Answer:

Dimensions :

x (the longer side, only one side with fence )   =  90  ft

y ( the shorter side two sides with fence )        =  45  ft

Total fence used   45 * 2  +  90    =  180 ft

A(max)  =  

Step-by-step explanation: If a farmer has 180 ft of fencing to encloses a rectangular area with fence in three sides and the river on one side, the farmer surely wants to have a maximum enclosed area.

Lets call "x" one the longer side  ( only one of the longer side of the rectangle will have fence, the other will be along the river and won´t need fence. "y" will be the shorter side

Then we have:

P = perimeter  =  180  =  2y  +  x        ⇒   y  =  ( 180 - x )  / 2        (1)

And   A (r)   =  x * y

A(x)   =  x  *  ( 180 - x ) /2       ⇒   A(x)   = (180/2) *x   -  x² / 2

Taking derivatives on both sides of the equation :

A´(x)   =  90   -  x    

Then if    A´(x)   =  0   ⇒        90   -  x    =  0     ⇒   x  =  90 ft

and from :       y  =  ( 180 - x )  / 2     ⇒     y  =  90/2

y  =  45  ft

And

A(max)  =  90 * 45    =  4050  ft²

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3 years ago
Help! asap!
grigory [225]

The measure of angle 3 from the figure is 110 degrees

<h3>Lines and angles</h3>

An angle is the intersection between two lines. From the given figure, we have the following parameters

m∠1= 40°,

m∠2= 70°.

Required

Measure of angle 3

The sum of the interior angles of the triangle is equal to the exterior

Sum of interior = <1 + <2

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Hence the measure of angle 3 from the figure is 110 degrees

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Gerardo works at an ice cream shop each flavor of ice cream is stored in a right cylindrical tub that measures approximately 9 i
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Answer:

Volume left = 404.32 cubic inches

Step-by-step explanation:

volume of a cylinder = \pir^{2}h

volume of ice cream in the cylindrical tub = \frac{22}{7} x 5^{2} x 9

                                           = \frac{22}{7} x 25 x 9

                                           = 707.1429

Volume of ice cream in the cylindrical tub is 707.14 cubic inches.

The ice cream scoop has a spherical volume, so that;

volume of a sphere = \frac{4}{3}\pir^{3}

r = \frac{2.5}{2}

 = \frac{5}{4} inches

volume of the scoop = \frac{4}{3} x \frac{22}{7} x (\frac{5}{4} )^{3}

                                  = \frac{4}{3} x \frac{22}{7} x \frac{125}{64}

                                  = 8.1845

volume of the scoop is 8.19 cubic inches.

If he scoops 37 scoops,

volume of the 37 scoops = 37 x 8.1845

                                          = 302.8265

volume of 37 scoops is 302.83 cubic inches.

Volume of ice cream left in the tub = 707.1429 - 302.8265

                                                           = 404.3164

Volume of ice cream left in the tub is 404.32 cubic inches.

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3 years ago
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