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3 years ago

5

Which parabola has the graph shown?

1 answer:

ryzh [129]3 years ago

5 0

The vertex is (-1, 2).

The equation of parabola:

$x=(x-k)^2+h$ where (h, k) is the vertex

We have h = -1 and k = 2.

Substitute:

$x=(y-2)^2-1\ \ \ \ |+1\\\\(x+1)=(y-2)^2$

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Sketch the graph of the given equation. y = x2 + 8x +15

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2 years ago

A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s

Setler [38]

Answer:

$310\text{ feet and }210\text{ feet}$

Step-by-step explanation:

GIVEN: A farmer has $520 \text{ feet}$ of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is $310 \text{ feet}$ .

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be $x$ and $y$

perimeter of rectangular pen $=2(x+y)=520\text{ feet}$

$x+y=260$

$y=260-x$

area of rectangular pen $=\text{length}\times\text{width}$

$=xy$

putting value of $y$

$=x(260-x)$

$=260x-x^2$

to maximize $\frac{d \text{(area)}}{dx}=0$

$260-2x=0$

$x=130\text{ feet}$

$y=390\text{ feet}$

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen $=310\text{ feet}$

width of rectangular pen $=210\text{ feet}$

Maximum area of rectangular pen $=310\times210=65100\text{ feet}^2$

Hence maximum area of rectangular pen is $65100\text{ feet}^2$ and dimensions are $310\text{ feet and }210\text{ feet}$

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2 years ago

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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I hope this helps!

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Answer:

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Step-by-step explanation:

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2 years ago