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2 years ago

The back of Tom's property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing

Mathematics

1 answer:

Anna71 [15]2 years ago

8 0

9514 1404 393

Answer:

1250 square feet

Step-by-step explanation:

If x is the length of the side perpendicular to the creek, then the third side is (100 -2x) = 2(50 -x). The area is the product of length and width:

A = x(2)(50-x)

We observe that this is a quadratic function with zeros at x=0 and x=50. The vertex (maximum) of a quadratic function is on the line of symmetry, halfway between the zeros. The value of x there is (0 +50)/2 = 25.

Then the maximum area is ...

A = (25)(2)(50 -25) = 1250 . . . . square feet

_____

Additional comment

Note that half the length of the fence is used in one direction (parallel to the creek), and half is used in the other direction (perpendicular to the creek). This 50/50 split is the generic solution to all sorts of rectangular corral problems, with or without a creek, with or without internal partitions.

Half the fence is perpendicular to the other half. (If the costs are different in different directions, then the cost is what is split 50/50.)

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Aleksandr-060686 [28]

Step-by-step explanation:

Given function is y = –x.

Substitute the values of x in the function and find the values of y.

y = –x

At x = –2,

y = –(–2) = 2

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y = –(–1) = 1

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y = –(0) = 0

At x = 1,

y = –1(1) = –1

At x = 2,

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The image of the table is attached below.

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On a coordinate plane, quadrilateral Q R S T has points (0, 2), (negative 4, 0), (0, negative 3), and (4, 0).

Afina-wow [57]

By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).

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Herein we must apply a rigid transformation into a given point to determine an image. Rigid transformations are transformations applied on a geometric locus such that Euclidean distance is conserved. Dilations are a kind of rigid transformations such that:

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If we know that Q(x, y) = (0, 2) and k = 0.5, then the coordinates of Q' are:

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By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).

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The given function is

$f(x)=4\cos \text{(}\pi x)+1$

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2pi/b is the period

c is the phase shift

d is the vertical shift

By comparing the two functions

a = 4

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c = 0

d = 1

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$\begin{gathered} \text{Period}=\frac{2\pi}{\pi} \\ \text{Period}=2 \end{gathered}$

The equation of the midline is

$y_{ml}=\frac{y_{\max }+y_{\min }}{2}$

Since the maximum is at the greatest value of cos, which is 1, then

$\begin{gathered} y_{\max }=4(1)+1 \\ y_{\max }=5 \end{gathered}$

Since the minimum is at the smallest value of cos, which is -1, then

$\begin{gathered} y_{\min }=4(-1)+1 \\ y_{\min }=-4+1 \\ y_{\min }=-3 \end{gathered}$

Then substitute them in the equation of the midline

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The answers are:

Period = 2

Equation of the midline is y = 1

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