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Ad libitum [116K]
3 years ago
10

You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer pe

r 1,000 square feet. The fertilizer comes in 50-pound bags. How many bags of fertilizer will you need to complete the job?
Mathematics
1 answer:
Assoli18 [71]3 years ago
6 0

Answer: 10 bags

Step-by-step explanation:

First we must calculate the field area. Assuming it is a rectangle then its area equals the product of its length times its width

A =360*160\\\\A = 57600 ft^2

You use 8 pounds of fertilizer per 1,000 square feet

So the amount of fertilizer you should use is:

57,600 ft^2 * \frac{8\ pounds}{1,000\ ft^2} = 460.8\ pounds

As the fertilizer comes in bags of 50 pound then you need

460.8\ pounds * \frac{1\ bag}{50\ pounds} = 9.2\ bags

Since you can not buy 9.2 bags then we round up to the next whole number.

Finally you need 10 bags of fertilizer

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Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis
stealth61 [152]

Complete question is;

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.) y = 6 - x²

Answer:

height = 4 and base = 2√2

Step-by-step explanation:

Area of a rectangle is given by;

A = base(b) × height(h)

To start off, we will first have to consider half of the rectangle.

Due to the fact that it is bounded by a parabola which is symmetric over the y-axis, it means that the rectangle will have the same area on the right and left hand sides.

So if we maximize the area of the first quadrant, it means that we are also maximizing the area of the entire rectangle.

Now, since we are dealing with the base and other 2 vertices on the x-axis, it means that the base(b) of this half rectangle will be x.

The height of this rectangle is the y coordinate of the corner that is directly above the x coordinate, which is also on the rectangle.

Therefore, the coordinates of the upper corner will be (x, y), or (x, 6 - x²). Thus our half base is x and full height is 6 - x². Area will be;

A = x(6 - x²)

A = 6x - x³

We will maximize this area by finding the derivative and equating to zero.

Thus;

A' = 6 - 3x²

At A' = 0,we have;

6 - 3x² = 0

3x² = 6

x² = 6/3

x² = 2

x = √2

Thus, from y = 6 - x², we have;

y = 6 - (√2)²

y = 6 - 2

y = 4

Since x is half base, it means our full width is 2x = 2 × √2 = 2√2

So, height = 4 and base = 2√2

8 0
3 years ago
Create and solve a linear equation that represents the model, where squares and triangles are shown evenly balanced on a balance
Rina8888 [55]

Let the weight of triangle be x units. You are given that the weight of square is 1 unit.

1) On the left side of the balanced beam you can see 3 triangles and 5 squares. The weight on left side is 3·x+5·1=3x+5 units.

2) On the right side of the balanced beam you can see 2 triangles and 7 squares. The weight on right side is 2·x+7·1=2x+7 units.

3) If the whole system is balanced, then the weights on left and right sides are equal:

3x+5=2x+7.

Solve this equation:

3x-2x=7-5,

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Answer:

One solution

Step-by-step explanation:

The only solution is x = 2/3

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2 years ago
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Blizzard [7]

Answer:

2.683281573

Step-by-step explanation:

Did it on a notebook and check if it was correct on my calculator. Please like and rate my answer.

7 0
4 years ago
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