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kaheart [24]
3 years ago
7

What is the equation in point−slope form of the line passing through (2, 2) and (4, 8)?

Mathematics
2 answers:
Vladimir [108]3 years ago
8 0
M = (8-2)/(4-2) = 6/2 = 3

equation <span>in point−slope form
</span>
y - 2 = 3(x - 2)
or
y - 8 = 3(x - 4)

hope it helps
prohojiy [21]3 years ago
3 0
Y-2=3(x-2)
y-2=3x-6
y=3x-4
hope this helps u out :D
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3 years ago
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If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in
Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume (V), in cubic centimeters, and surface area (A_{s}), in square centimeters, of the box with a square base are described below:

A_{s} = l^{2}+h\cdot l (1)

V = l^{2}\cdot h (2)

Where:

l - Side length of the base, in centimeters.

h - Height of the box, in centimeters.

By (2), we clear h within the formula:

h = \frac{V}{l^{2}}

And we apply in (1) and simplify the resulting expression:

A_{s} = l^{2}+ \frac{V}{l}

A_{s}\cdot l = l^{3}+V

V = A_{s}\cdot l -l^{3} (3)

Then, we find the first and second derivatives of this expression:

V' = A_{s}-3\cdot l^{2} (4)

V'' = -6\cdot l (5)

If V' = 0 and A_{s} = 30000\,cm^{2}, then we find the critical value of the side length of the base is:

30000-3\cdot l^{2} = 0

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Then, we evaluate this result in the expression of the second derivative:

V'' = -600

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

V = 30000\cdot l - l^{3}

V = 2000000\,cm^{3}

The largest possible volume of the box is 2000000 cubic meters.

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viktelen [127]

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Step-by-step explanation:

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