Can anyone help me set up a system of equations for these problems??

Mathematics

1 answer:

statuscvo [17]2 years ago

8 0

Answer:

L = the length of the field

W = the width of the field

The First Question:

The system is: L - 12 = w

2L + 2W = 76

Plug in L - 12 for W and you will get

2L + 2L - 24 = 76

4L -24 = 76

4L = 100

L = 25

To find W do L - 12 = w

25 - 12 = w

w = 13

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Arlecino [84]

I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set $y=1.25$ for this example.)

The length of each cross section (the side lying in the base) has length determined by the horizontal distance $x$ between the y-axis $x=0$ and the curve $y=\sqrt x$ . In terms of $y$ , this distance is $x=y^2$ . The height of each cross section is twice the value of $y$ , so the area of each rectangular cross section should be $2y^3$ .

This means the volume would be given by the integral

$\displaystyle\int_0^22y^3\,\mathrm dy$