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3 years ago

I'm giving brainliest to best answer

Mathematics

1 answer:

Natali5045456 [20]3 years ago

3 0

Answer:

2) 62.5 wpm

3) 12.7 miles per gallon

4)18 commercials per hour

5) 22.9 ounces per dollar

Step-by-step explanation:

2) 500 words / 8 minutes = 62.5 words per 1 minute

3) 216 miles / 17 gallons = 12.7 miles per gallon

4) 36 commercials / 2 hours = 18 commercials per hour

5) 64 oz / $2.79 = 22.9 oz per $1

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A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down t

frosja888 [35]

The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y

since the rectangle has four sides and opposite sides are equal

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

$\mathbf{L = 3x - 2( \dfrac{1000000}{x})}$

$\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}$

$\mathbf{ x^2= \dfrac{2000000}{3} }$

$\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }$

$\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}$

Now, if we replace the value with equation (1), then y will be:

$\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\ \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}$

$\mathbf{x =500\sqrt{6}}$

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

$\mathbf{L = 3( \dfrac{1000 \sqrt{6}}{3}) + 2(500 \sqrt{6})}$

$\mathbf{L =1000 \sqrt{6} + 1000 \sqrt{6}}$

$\mathbf{L =2000 \sqrt{6} }$

$\mathbf{L \simeq 4899 \ ft}$

Learn more about the area of a rectangle here:

brainly.com/question/25292087

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2 years ago

The force F of attraction between two bodies varies jointly as the weights of the two bodies and inversely as the square of the

Maksim231197 [3]

Since we are to express the given conditions as a joint variation, we employ the use of k as our constant proportionality which we will denote in this item as k.
From the sentence,
F = kM₁M₂/d²
as we can see those in the denominator as those that vary inversely to the given parameter.

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3 years ago

What is the solution to the system of equations graphed below?

wariber [46]

Answer:

a) (2,4)

Step-by-step explanation:

it's where the points meet

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Sarah drank 75% of a one pint carton of milk at lunchtime. How many ounces of milk were left in the carton? PLZZ help! Will mark

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There's 4oz left
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Answer:

A !

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