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4> Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o

Answers

Answer 1

Answer:

Answer:

$y=3e^(-4t)$

Step-by-step explanation:

$y''+5y'+4y=0$

Applying the Laplace transform:

$\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0$

With the formulas:

$\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)$

$\mathcal{L}[y']=s\mathcal{L}[y]-y(0)$

$\mathcal{L}[x]=L$

$s^2L-3s+5sL-3+4L=0$

Solving for $L$

$L(s^2+5s+4)=3s+3$

$L=(3s+3)/(s^2+5s+4)$

$L=(3(s+1))/((s+1)(s+4))$

$L=\frac3{s+4}$

Apply the inverse Laplace transform with this formula:

$\mathcal{L}^(-1)[\frac1{s-a}]=e^(at)$

$y=3\mathcal{L}^(-1)[\frac1{s+4}]=3e^(-4t)$

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Which angles are congruent to each other?

Answers

Answer:

<8 and <6 are congruent to each other.

Step-by-step explanation:

A protractor was used to determine the answer. They both measured to 140 degrees.

Final answer:

Congruent angles are those that have the exact same degree measure – they are equal in size. The position of these angles does not impact their congruence.

Explanation:

In mathematics, two angles are described as congruent when they have the same measure, meaning that they are equal in degrees. For instance, if you have two angles each measuring 45 degrees, they are congruent. Even if these angles aren't located in the same position on a shape, or even on two different shapes entirely, they are considered congruent because they have the exact same degree measurement.

Congruency can also apply to other geometric elements like triangles and lines. However, in the context of your question, the concept is strictly applied to angles.

Learn more about Congruent Angles here:

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Simplify 12x7y3 divided by 6x3y

Answers

Answer:

12x7y3

----------- = 6x4y3

6x3y

Step-by-step explanation:

In dividing these numbers, you simply subtract 6x from 12x and subtract 3y from 7y because 6x and 3y are both in the denominator. 3 is left alone.

Evaluate a2 + b2 + c2 for a = -5, b = -2, and c = 3.

Answers

Step-by-step explanation:

(-5)² + (-2)² + 3²

= 25 + 4 + 9

= 38

Assume that the given procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean mu and standard deviation sigma. Also, use the range rule of thumb to find the minimum usual value mu minus 2 sigma and the maximum usual value mu plus 2 sigma. In an analysis of preliminary test results from a gender-selection method, 33 babies are born and it is assumed that 50% of babies are girls, so equals 33 and p equals 0.5.