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Ahat [919]
2 years ago
10

Which set of ordered pairs has the same slope as the given set: (2,9) (1,12)?

Mathematics
1 answer:
Irina-Kira [14]2 years ago
6 0

The slope(m) of the given set is -3.

<h3>What is the slope of a pair of the ordered set?</h3>

The slope(m) of a pair of the given ordered set is the change in the rise over the run. The rise is the y-axis while the run is the x-axis.

Mathematically;

\mathbf{Slope(m) = \dfrac{\Delta y}{ \Delta x}}

\mathbf{Slope(m) = \dfrac{y_2-y_1}{x_2-x_1} }

Here:

  • x_1 = 2
  • y_1 = 9
  • x_2 = 1
  • y_2 = 12

\mathbf{Slope(m) = \dfrac{12-9}{1-2} }

\mathbf{Slope(m) = \dfrac{3}{-1} }

Slope (m) = -3

Therefore, we can conclude that the slope of the given set is -3. From the given option, kindly find out which of the slope is equivalent to -3.

Learn more about finding the slope of an ordered pair here:

brainly.com/question/1884491
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Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

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We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

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∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0
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