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saul85 [17]
2 years ago
13

A line segment has end points R(-2, - 2) and S(4, 1). What are the coordinates of the point that is 2/3 of the way from R to S o

n this line segment?
​
Mathematics
1 answer:
Darya [45]2 years ago
3 0

Answer: (2, 0)

Step-by-step explanation:

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John wants to find the center of a wall so he can hang a picture. He measures the wall and determines it is 65.25" wide. 65.25"
antiseptic1488 [7]

Option B is correct.

John wants to find the center of a wall so he can hang a picture. He measures the wall and determines it is 65.25" wide.

Here, 65.25" is Quantitative, continuous

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As a general rule, counts are discrete and measurements are continuous. A continuous data can be recorded at many different points (length, size, width, time, temperature, etc.)

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3 years ago
A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the
Vinvika [58]

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

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

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

2744 cm^3 = L^3

∛(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

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2 years ago
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11 –2<br><br> · <br> 3 –4<br><br> · <br> 6 2<br><br> =
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Answer: negative 243

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