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svlad2 [7]
3 years ago
5

What is the x intercept of the graph of the inequality 2x + 3y > 12

Mathematics
1 answer:
iogann1982 [59]3 years ago
8 0

Answer: x intercept = 6

This is the location (6,0)

===============================================================

Explanation:

I assume you're talking about the boundary line of the inequality. The boundary line equation is 2x + 3y = 12

To find the x intercept, plug in y = 0 and solve for x

2x + 3y = 12

2x + 3(0) = 12

2x = 12

x = 12/2

x = 6

The boundary line 2x+3y = 12 crosses the x axis at x = 6.

We can say the x intercept is x = 6. This is the location (6,0).

Side note: the y intercept is y = 4, which is found by plugging in x = 0 and solving for y.

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[25 POINTS] A cylinder has a volume of 400π cm3. Find the dimensions that minimize its surface area.
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Answer:

r = 5.848cm, h = 11.696cm

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Surface area: SA=2\pi rh+2\pi r^2

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SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r

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r\approx5.848

If 0If [tex]r>5.848, then the surface area of the cylinder increases

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