What is the quotient of -32/8?

Answer:

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Step-by-step explanation:

Answer:

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Final answer:

The given expression -8 ÷ 343 can situationaly be written in power notation as -8 ÷ 7^3. This transformation changes '343' to '7^3' since 343 is 7 cubed.

Explanation:

The expression -8 ÷ 343 cannot be directly written in 'power notation', as the concept of'power notation' commonly refers to writing an expression in the form of a base value raised to an exponent.

Power notation is typically represented as a^n, where 'a' is the base and 'n' is the exponent. However, '343' can be written in power notation since it is 7 cubed (7^3).

So, while we should clarify the details, one way to write the expression could be -8 ÷ 7^3.

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Answer:?

Step-by-step explanation:?

Let x be the shorter side, and y be the longer side

There would be 4 fences along the shorter side, and 2 fences along the longer side

4x + 2y = 800

Rewrite in terms of y:

y = 400 − 2x

The area of the rectangular field is

A = x*y

Replace Y with the equation above:

  A = x(400 − 2x)

  A = − 2x^2 + 400x

The area is a parabola that opens downward, the maximum area would occur at the parabola vertex.

At the vertex

x = −b/2a

  = −400/[2(−2)]

  = 100

y = 400 −2x

y = 400 -2(100)

y = 400-200

y = 200

The dimension of the rectangular field that maximize the enclosed area is 100 ft x 200 ft.

The dimension of the rectangular field that maximize the enclosed area is 100 ft by 200 ft.

Application of the vertex of a quadratic equation

The formula for calculating the vertex of  a quadratic equation is given as:

x = -b/2a

From the given question

Let the shorter side be x

Let the longer side of the field be y

If there are 4 fences along the shorter side, and 2 fences along the longer side, hence;

4x + 2y = 800

Write the resultinq equation in slope-intecept form

2y = -4x + 800

y = -2x + 400

y = 400 − 2x

Determine the area of the field

Area = x*y

Substitute the expression above into the area to have:

A = x(400 − 2x)

A = − 2x^2 + 400x

Since the parabola opens downward, the maximum area would occur at the parabola vertex as shown;

x = −b/2a

x = −400/2(-2)

x = 400/4

x = 100

Determine the value of y

y = 400 −2x

y = 400 -2(100)

y = 400-200

y = 200

Hence the dimension of the rectangular field that maximize the enclosed area is 100 ft by 200 ft.

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