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3 years ago

Please help Quickly!!

Mathematics

2 answers:

aksik [14]3 years ago

7 0

Answer:

D isthe correct anser i got a 100 on this so i wold know

Step-by-step explanation:

e-lub [12.9K]3 years ago

3 0

Answer:

Option D 3/16

Step-by-step explanation:

Carol is cross-country skiing.

With the help of the given table we have to calculate the rate of change.

If we draw a graph for distance traveled on y-axis and tins at x-axis we find two points, ( 2, 1/6) and (3, 17/48).

Then slope of the line connecting these points will be the rate of change.

Rate of change = Slope = $\frac{y-y'}{x-x'}$

= $\frac{\frac{17}{48}-\frac{1}{6}}{3-2}$

= $\frac{17-8}{48}$

= $\frac{9}{48}=\frac{3}{16}$

Option D 3/16 is the answer.

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

miss Akunina [59]

Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

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

Volume: $V=\pi r^2h$

Therefore, the height of a cylinder given its volume would be $h=\frac{V}{\pi r^2}$ , thus:

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

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:

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

$0=-\frac{800}{r^2}+4\pi r$

$0=800\pi+4\pi r^3$

$-800\pi=4\pi r^3$

$-200=r^3$

$r\approx5.848$

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

Therefore, the surface area is minimized when the radius is $r=5.848cm$ , making the minimum height $h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm$ .

In conclusion, the 2nd option is correct.

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2 years ago

Suppose the variable x is represented by a standard normal distribution. What is the probability of x > 0.3 ? Please specify

uysha [10]

Answer: 0.38

Step-by-step explanation:

Since the variable x is represented by a standard normal distribution, the probability of x > 0.3 will be calculated thus:

P(x > 0.3)

Then, we will use a standard normal table

P(z > 0.3)

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= 1 - 0.62

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The probability of x > 0.3 is 0.38.

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jek_recluse [69]

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