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allsm [11]
2 years ago
15

This is a Differential Equations problem, I only need help on part 1 from question five. I need steps as well, thank you.

Mathematics
1 answer:
jolli1 [7]2 years ago
6 0

Answer:

a) y(t) =  \sqrt{2t + 1 }

b) 1.5 hours after thickness will be 2 inches.

Step-by-step explanation:

\frac{dy}{dt}  =  \frac{1}{y}   \\   \\ ydy = dt  \\ \\ integrating \: both \: sides \\   \\  \int y \: dy =  \int 1 \: dt \\  \\  \frac{ {y}^{2} }{2}  = t + c \\  \\  {y}^{2}  = 2t + 2c \\  \\ y (t)=  \sqrt{2t + 2c} ...(1) \\  \\ a)  \:  \: \: plug \: t = 0 \: in \: (1) \\  \\  y (0)=  \sqrt{2(0) +2 c} \\  \\ y (0)=  \sqrt{0 +2 c} \\  \\ 1 =  \sqrt{2c}  \:  \: ( \because \: y (0)=1) \\  \\  2c = 1   \:  \implies \: c =  \frac{1}{2} \\  \\ plug \: c = \frac{1}{2} \: in \: (1) \\  \\ y(t) =  \sqrt{2t + 2 \times  \frac{1}{2} } \\  \\  \huge \:  \red {y(t) =  \sqrt{2t + 1 } } \\  \\b) \:  \:  plug \: y(t) = 2 \: in \: above \: equation \\  \\ 2 =  \sqrt{2t + 1}  \\  \\ 4 = 2t + 1 \: \\  (squaring \: both \: sides) \\  \\ 4 - 1 = 2t \\  \\ 2t = 3 \\  \\ t =  \frac{3}{2}  \\  \\ t = 1.5 \: hours \\

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djverab [1.8K]

The weights are within 2 standard deviations of the mean are 8.9 lbs, 9.5 lbs and 10.4 lbs

<h3>How to determine the weights?</h3>

The given parameters are:

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The weights within 2 standard deviation is represented as:

μ - 2σ ≤ x ≤ μ + 2σ

Substitute known values

9.5 - 2(0.5) ≤ x ≤ 9.5 + 2(0.5)

Evaluate the product

9.5 - 1 ≤ x ≤ 9.5 + 1

Evaluate the sum

8.5 ≤ x ≤ 10.5

This means that the weights are between 8.5 and 10.5 (inclusive)

Hence, the weights are within 2 standard deviations of the mean are 8.9 lbs, 9.5 lbs and 10.4 lbs

Read more about standard deviation at:

brainly.com/question/11743583

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2 years ago
A company with a fleet of 150 cars found that the emissions systems of only 4 out of the 32 they tested failed to meet pollution
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Answer:

Yes

Step-by-step explanation:

First, we need to find how many cars out of the entire fleet fail the test

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32x/32 = 600/32

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Step-by-step explanation:

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2 years ago
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Dmitry [639]

Answer:c

Step-by-step explanation:

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4 0
2 years ago
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Mrac [35]

Answer:

<h2>Amount of ounces of candy left = 22ounces</h2>

Step-by-step explanation:

Amount of halloween candy bought by Jack = 5pounds

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Before we can determine the amount of halloween candy that Jack has left, we need to convert the pounds to ounces in order to make the units consistent.

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