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pav-90 [236]
3 years ago
15

A. Solve the differential equation

="y'=2x \sqrt{1-y^2} " alt="y'=2x \sqrt{1-y^2} " align="absmiddle" class="latex-formula">.
b. Explain why the initial value problem y'=2x \sqrt{1-y^2} with y(0) = 3 does not have a solution.
Mathematics
1 answer:
kirill [66]3 years ago
5 0
y' = \frac{dy}{dx}

seperable differential equations will have the form
\frac{dy}{dx} = F(x) G(y)

what you do from here is isolate all the y terms on one side and all the X terms on the other
\frac{dy}{G(y)} = F(x) dx
just divided G(y) to both sides and multiply dx to both sides

then integrate both sides
\int \frac{1}{G(y)} dy = \int F(x) dx



once you integrate, you will have a constant. use the initial value condition to solve for the constant, then try to isolate x or y if the question asks for it


In your problem,
G(y) = \sqrt{1-y^2}

F(x) = 2x

so all you need to integrate is
\int \frac{1}{\sqrt{1-y^2}} dy = \int 2x dx
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ValentinkaMS [17]

Answer:

0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 3 cm and a standard deviation of 0.04 cm.

This means that \mu = 3, \sigma = 0.04

What is the probability that a bolt has a length greater than 2.96 cm?

This is 1 subtracted by the p-value of Z when X = 2.96. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.96 - 3}{0.04}

Z = -1

Z = -1 has a p-value of 0.1587.

1 - 0.1587 = 0.8413

0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.

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What is 0.98435 rounded to one decimal place
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The answer would be 1.0
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What is 2.3 times 1.5 with the answer as a decimal
pshichka [43]

Answer: 3.45

Step-by-step explanation:

8 0
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\dfrac 5 6 \pi r^2 = \dfrac 5 6 \pi (10^2) = \dfrac{250 \pi}{3}


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Answer:

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Step-by-step explanation:

The amount you need will be the dose divided by the concentration.

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The dosage will be about 1.8 mL.

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