What is the solution to the equation? 8 19–+X= 0 X=-6 x=-6 x X-20 O x-21

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

5 0

3 years ago

The base area of a triangular pyramid is 22 square yards and the height of the pyramid is 15 yards. What is the volume of the tr

galben [10]

Answer:

110 yards^3

Step-by-step explanation:

volume of a triangular pyramid= 1/3 area x height

1/3 x (22) x 15 = 110 yd^3

7 0

3 years ago

She has enough bricks to cover 60 square feet. She wants the length of the patio to be 4 feet longer than the width. What dimens

Natalija [7]

Answer:

10 feet length and 6 feet width.

Step-by-step explanation:

If the total area of the patio is going to be equal to 60 square feet and the length is going to be 4 feet longer than the width, the dimensions that she should use for the patio are 10 feet for the length and 6 feet for the width which will equal to 60 square feet in total.

I hope this answer helps.

3 0

3 years ago

What the slope of(7,3) (6,-2)

antoniya [11.8K]

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$slope = \frac{ - 2 - 3}{6 - 7} \\$

$slope = \frac{ - 5}{ - 1} \\$

$slope = 5$

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6 0

3 years ago

I need help please.....

maria [59]

Here, Function: h(t)= -16t² + 70t + 40

So, put the value of t, (time at which you want to calculate the height)

h(1) = -16(1)² + 70(1) + 40
h(1) = -16 + 110
h(1) = 94

Now, h(2) = -16(2)² + 70(2) + 40
h(2) = -64 + 180
h(2) = 116

h(3) = -16(3)² + 70(3) + 40
h(3) = -144 + 250
h(3) = 106

In short, Your height depends on time, and at each time it would be different, can be expressed by the coordinates on a Graph: (1, 94) (2, 116) (3, 106)

Hope this helps!

8 0

3 years ago

What is the solution to the equation? 8 19–+X= 0 X=-6 x=-6 x X-20 O x-21​

What is the solution to the equation? 8 19–+X= 0 X=-6 x=-6 x X-20 O x-21