Kirk and Montega mow the soccer playing fields. They must mow an area of 500 ft long and 400 feet wide. They agree that each will mow half the area. Kirk will mow around the edge in a path of equal width until half the area is left.
*What is the area each person will mow?
*write a quadratic wquation that could be used to find the width x that Kirk should mow. What width should Kirk mow?
*The mower ran a path 5 feet wide. to the nearest whole #, how many times should Kirk go around the field?
The area each person will mow is 100000 sq.ft.
how did u get it?
Area is l x w, so 400,000 x 500,000 is 200,000 and half of that is 100,000.
If Kirk mows half of the 400 ft. width, then 1/2(400) is 200.
If the mower mows a 5 ft. wide path, how many passes will Kirk need to make?
To find the area each person will mow, we need to divide the total area of the soccer field by 2 since they agree to divide it equally.
Area of the soccer field = length × width = 500 ft × 400 ft = 200,000 sq. ft
Area each person will mow = Total area / 2 = 200,000 sq. ft / 2 = 100,000 sq. ft
So each person will mow an area of 100,000 square feet.
To write a quadratic equation that could be used to find the width (x) that Kirk should mow, we know that the width of Kirk's mowing path plus the remaining area should equal the area each person will mow.
Let's denote the width of Kirk's mowing path as "w". The remaining area after Kirk mows around the edge will be (400 - 2w) ft wide and (500 - 2w) ft long.
Equation: w(400 - 2w) = 100,000
Simplifying the equation, we get:
-2w^2 + 400w = 100,000
Now, to find the width Kirk should mow, we can solve this quadratic equation. We can do this by factoring, completing the square, or using the quadratic formula.
Let's solve by factoring (if possible). Rearranging the equation:
-2w^2 + 400w - 100,000 = 0
Dividing the equation by -2, we get:
w^2 - 200w + 50,000 = 0
The quadratic equation is now in the form ax^2 + bx + c = 0.
Unfortunately, this equation does not factor into nice whole numbers.
Using the quadratic formula, we have:
w = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values, we get:
w = (-(-200) ± √((-200)^2 - 4(1)(50,000))) / (2(1))
w = (200 ± √(40,000 - 200,000)) / 2
w = (200 ± √(-160,000)) / 2
Since the square root of a negative number is not possible in real numbers, we cannot find a real solution for the width Kirk should mow using this quadratic equation. This means the problem might have been set up incorrectly, or a different approach is needed.
For the last question, if the mower ran a path 5 feet wide, we can determine how many times Kirk should go around the field by dividing the remaining area after subtracting Kirk's mowing path from the total area.
Remaining area after Kirk mows = (400 - 2w) ft wide × (500 - 2w) ft long
Number of times Kirk should go around = Remaining area / Kirk's mowing path width
Let's calculate the value, assuming a width of 5 ft for Kirk's mowing path:
Remaining area after Kirk mows = (400 - 2(5)) ft wide × (500 - 2(5)) ft long
Remaining area after Kirk mows = 390 ft × 490 ft = 191,100 sq. ft
Number of times Kirk should go around = 191,100 sq. ft / 5 ft = 38,220
Rounding to the nearest whole number, Kirk should go around the field approximately 38,220 times.