Mathematics: 1 1/2 mile field divided into fields 1/4 mile long and 1/4 mile wide - how many fields would we have

1 1/2 mile field divided into fields 1/4 mile, №14718640, 09.07.2020 21:58

Biology

Farmer brown tests the hypothesis that the more alfalfa sprouts cattle eat, the more milk they produce. he divides his pasture into four fields and puts twenty cattle in each field. field 1 cows get no alfalfa sprouts, field 2 cows get ten pounds of sprouts per day, field 3 cows get twenty pounds of sprouts, and field 4 cows get thirty pounds. he feeds all groups fifty pounds of regular hay per day, uses the same breed of cattle, and gives them the same amount of water. he measures gallons of milk produced per cow every day. what is the independent

Step-by-step answer

P Answered by Master

40

The amount of alfalfa sprouts the cattle are fed.

Biology

Farmer brown tests the hypothesis that the more alfalfa sprouts cattle eat, the more milk they produce. he divides his pasture into four fields and puts twenty cattle in each field. field 1 cows get no alfalfa sprouts, field 2 cows get ten pounds of sprouts per day, field 3 cows get twenty pounds of sprouts, and field 4 cows get thirty pounds. he feeds all groups fifty pounds of regular hay per day, uses the same breed of cattle, and gives them the same amount of water. he measures gallons of milk produced per cow every day. what is the independent

Step-by-step answer

P Answered by Specialist

40

The amount of alfalfa sprouts the cattle are fed.

Mathematics

Suppose a farmer buys another 1/2 square mile of land and divides all his land into square field 1/4 mile long and 1/4 mile wide. how many fields will he have?

Step-by-step answer

P Answered by Specialist

Hello,

We have the area of the total land, so we want to find the area of each smaller square field so we can divide the large area by the small area to obtain the number of fields.

To find the area of a square, the formula $s^{2}$ is used, where s is the length of one side of the square.

In this case, s = 1/4, so the area is = $(1/4)^{2} = 1/16$ square miles

If we have 1/2 square miles of land divided into 1/16 square mile fields, then we have (1/2) / (1/16) = (1/2) * (16/1) = (16/2) = 8 fields.

He will have 8 fields.

Hope this helps!

Mathematics

field book of agricultural land .it is divided into 4 plots. plot 1 is a right angle triangle , plot 2 is an equilateral triangle, plot 3 is a rectangle, plot 4 is a trapezium . find the area of each plot and total the area of field(use√3=1.73)

Step-by-step answer

P Answered by Master

1

Plot 1 area= 32.5cm²

Plot 2 area = 73.0925cm²

Plot 3 area = 35cm²

Plot 4 area = 54cm²

Total the area of field = 194.5925cm²

Step-by-step explanation:

To find the area of each plot, we need to find the area of the shape of each plot.

A diagram related to the question found at (question ID: 18861101)

has been attached.

Plot 1 is a right angle triangle:

Area = ½ × base × height

AE = 19cm, CF = DE = 7cm

Ad = AE - DE

base =AD = 19-7 = 12cm

Using Pythagoras theorem

height = CD = √(AC² - AD)²

AC = 13cm

CD = √(13² - 12²) = √(169-144)

height = CD = √25 = 5

Area = ½ × 13×5 = 65/2

Area = 32.5cm²

Plot 2 is an equilateral triangle

Area = ½ × base × height

Area of the equilateral triangle = s²/4 ×(√3)

Where s = side = 13cm

√3=1.73

Area of the equilateral triangle = (13)²/4 ×(√3) = 169/4 × 1.73

= 42.25 × 1.73 = 73.0925cm²

Plot 3 is a rectangle

Area of the rectangle = length × width

length = FC = 7cm

width = CD = 5cm

Area of the rectangle = 7×5 = 35cm²

Plot 4 is a trapezium

Area of trapezium = ½(a+b) × height

a = FE = CD = 5cm

b = GH = 17cm

Height = ?

To get night let's break the trapezium diagram. We would have two triangles and 1 rectangle.

FE = CD= 5cm

From the 2nd diagram of the triangle,

Using Pythagoras theorem to find h in both triangles:

9² = h²+x²

h² = 81-x² ...(1)

15² = h²+(12-x)²

225 = h² +144-24x+x²

81 = h²-24x+x² ...(2)

Substitute 1 in 2

81 = 81-x² + x²-24x

24x = 0

x = 0

h² = 81-0² = 81

h = √81 = 9cm

base of the triangle = GH-FE = 17-5 = 12cm

Area of trapezium = ½(5+7) × 9

= 12/2 × 9 = 54cm²

Total the area of field = area of right angled triangle + area of equilateral triangle + area of rectangle +area of trapezium

= 32.5cm² + 73.0925cm² + 35cm² + 54cm²

Total the area of field = 194.5925cm²

field book of agricultural land .it is divided into 4 plots. plot 1 is a right angle triangle , plot

Mathematics

field book of agricultural land .it is divided into 4 plots. plot 1 is a right angle triangle , plot 2 is an equilateral triangle, plot 3 is a rectangle, plot 4 is a trapezium . find the area of each plot and total the area of field(use√3=1.73)

Step-by-step answer

P Answered by Specialist

1

Plot 1 area= 32.5cm²

Plot 2 area = 73.0925cm²

Plot 3 area = 35cm²

Plot 4 area = 54cm²

Total the area of field = 194.5925cm²

Step-by-step explanation:

To find the area of each plot, we need to find the area of the shape of each plot.

A diagram related to the question found at (question ID: 18861101)

has been attached.

Plot 1 is a right angle triangle:

Area = ½ × base × height

AE = 19cm, CF = DE = 7cm

Ad = AE - DE

base =AD = 19-7 = 12cm

Using Pythagoras theorem

height = CD = √(AC² - AD)²

AC = 13cm

CD = √(13² - 12²) = √(169-144)

height = CD = √25 = 5

Area = ½ × 13×5 = 65/2

Area = 32.5cm²

Plot 2 is an equilateral triangle

Area = ½ × base × height

Area of the equilateral triangle = s²/4 ×(√3)

Where s = side = 13cm

√3=1.73

Area of the equilateral triangle = (13)²/4 ×(√3) = 169/4 × 1.73

= 42.25 × 1.73 = 73.0925cm²

Plot 3 is a rectangle

Area of the rectangle = length × width

length = FC = 7cm

width = CD = 5cm

Area of the rectangle = 7×5 = 35cm²

Plot 4 is a trapezium

Area of trapezium = ½(a+b) × height

a = FE = CD = 5cm

b = GH = 17cm

Height = ?

To get night let's break the trapezium diagram. We would have two triangles and 1 rectangle.

FE = CD= 5cm

From the 2nd diagram of the triangle,

Using Pythagoras theorem to find h in both triangles:

9² = h²+x²

h² = 81-x² ...(1)

15² = h²+(12-x)²

225 = h² +144-24x+x²

81 = h²-24x+x² ...(2)

Substitute 1 in 2

81 = 81-x² + x²-24x

24x = 0

x = 0

h² = 81-0² = 81

h = √81 = 9cm

base of the triangle = GH-FE = 17-5 = 12cm

Area of trapezium = ½(5+7) × 9

= 12/2 × 9 = 54cm²

Total the area of field = area of right angled triangle + area of equilateral triangle + area of rectangle +area of trapezium

= 32.5cm² + 73.0925cm² + 35cm² + 54cm²

Total the area of field = 194.5925cm²

Mathematics

Suppose the farmer buys another 1/2 square mile of land and divides all his land into square fields 1/4 mile long and 1/4 mile wide. how many fields will he have

Step-by-step answer

P Answered by PhD

18

To answer this question, you need to find the area of the divided land that the farmer want. Since it was a square with 1/4 mile length then the area would be:
1/4 mile * 1/4 mile= 1/16 miles square.

Then you can divide the total area of land the farmer buys, with the area of divided land. The calculation would be: (1/2 square miles) / (1/16 square miles)= 16/2=8 pieces of field

Mathematics

Afarmer has one square mile of land. suppose the farmer buys another 1/2 square mile of land and divides all his land into square fields 1/4 mile long and 1/4 mile wide. how many fields will he have? what is the total area of his land in square miles?

Step-by-step answer

P Answered by PhD

2

Total area of land = 1 + 1/2 = 3/2 square miles

Area of square fields = 1/4 x 1/4 = 1/16 square miles

Number of fields = (3/2) / (1/16) = 24 fields.

Mathematics

Suppose the farmer buys another 1/2 square mile of land and divides all his land into square fields 1/4 mile long and 1/4 mile wide. how many fields will he have

Step-by-step answer

P Answered by PhD

3

Total area of land = 1 + 1/2 = 3/2 square miles

Area of square fields = 1/4 x 1/4 = 1/16 square miles

Number of fields = (3/2) / (1/16) = 24 fields.

Mathematics

Suppose the farmer buys another 1/2 square mile of land and divides all his land into square fields 1/4 mile long and 1/4 mile wide. how many fields will he have

Step-by-step answer

P Answered by PhD

18

To answer this question, you need to find the area of the divided land that the farmer want. Since it was a square with 1/4 mile length then the area would be:
1/4 mile * 1/4 mile= 1/16 miles square.

Then you can divide the total area of land the farmer buys, with the area of divided land. The calculation would be: (1/2 square miles) / (1/16 square miles)= 16/2=8 pieces of field

Mathematics

Suppose the farmer buys another 1/2 square mile of land and divides all his land into square fields 1/4 mile long and 1/4 mile wide. how many fields will he have and the total area of his land square miles? need to know how to work problem to get answser.

Step-by-step answer

P Answered by Specialist

He will have 8 fields in the total area of his land.

Explanation

Both length and width of each square field are $\frac{1}{4}$ mile

So, the area of each square field $= (\frac{1}{4}*\frac{1}{4})=\frac{1}{16}$ square mile.

Total area of the land bought by the farmer is $\frac{1}{2}$ square mile.

For finding the number of fields, we need to divide the total area of land by the area of each field.

So, the number of fields = $\frac{1}{2}$ ÷ $\frac{1}{16}$ = $\frac{1}{2}$ × $\frac{16}{1}$ = $\frac{16}{2}$ = 8

1 1/2 mile field divided into fields 1/4 mile long and 1/4 mile wide - how many fields would we have

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