Solve the given initial-value problem. <br> (2y + 2t − 3) dt + (8y + 2t − 1) dy = 0, y(−1) = 2.

A snowmaking machine makes 3/4 inch of snow each minute. How many inches of snow can the machine make in 8 minutes?

Mnenie [13.5K]

Answer:

Step-by-step explanation:

8 minutes × (¾ inch)/minute = 8×¾ inches = 6 inches

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=4%20%5Cfrac%7B1%7D%7B2%7D%20x%20%5Cfrac%7B2%7D%7B3%7D%20" id="TexFormula1" title="4 \frac{1}{2

aleksley [76]

Answer:

Step-by-step explanation:

$4\frac{1}{2}* \frac{2}{3} =\frac{9}{2} *\frac{2}{3} =3$

8 0

3 years ago

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:

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

$3\cdot l^{2} = 30000$

$l = 100\,cm$

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.

4 0

3 years ago

a teacher plans a simulation to estimate the probability that a student will pick a vowel out of a bag of 26 tiles, each with a

Alex Ar [27]

Answer:

Yes

Step-by-step explanation:

Given that a teacher prepares 26 tiles with 5 vowels numbered 1 and 21 consonants numbered 2.

The probability for drawing vowel = $\frac{5}{26}$

Prob for consonant = $\frac{21}{26}$

If number of trials is atleast 30 we can expect reliable results.

Here the results are recorded for 120 times at random.

Since number of trials is large, we can expect a reliable and accurate results representing the actual probability.

This is because more the number of trials, the less would be the margin of error i.edeviationfrom the expected probability would be minimum

8 0

4 years ago

Read 2 more answers

A study claims that the combination of vitamin C with vitamin E is more effective for preventing the flu than vitamin C alone. I

victus00 [196]

1) In this study, the control group is the first group of 310 subjects that were instructed to take only 600 mg daily of vitamin C. (Option C; that is, group 1).

2) The study is not Blind (Option C).

In an experimental setup to test a theory, A control group is the set of experimental participants that the theory to be tested isn't applied upon.

In the case of testing a new treatment, the control group is the group that the new treatment isn't administered.

For this question, the experiment was set up to test the effectiveness of a combination of vitamin A and vitamin E in treating flu cases rather than using vitamin C alone. Group A is the only group that only the old treatment alone is applied to; group 1 participants received no dosage of the new combination of treatments to be tested involving vitamins A and E, unlike the two other groups.

It is obvious now why the experimental participants of group 1 are the control group.

2) A blind experiment/study is one in which the participants don't know which group they belong to, whether they are in the control group or the other experimental group. Like in this case, if this was a blind study, the participants wouldn't know which group they belonged to or which treatment is administered to them.

A double-blind experiment/study is one in which both the conductors of the experiment and the participants in the experiment wouldn't know which group any participant is in. The conductors wouldn't know which participants were in the control or treatment group and the participants too wouldn't have an idea whether they are in the control or treatment group.

To learn more about the vitamin visit: brainly.com/question/24324739

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3 0

1 year ago

Solve the given initial-value problem. (2y + 2t − 3) dt + (8y + 2t − 1) dy = 0, y(−1) = 2.