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Nataly [62]
1 year ago
7

Use the laplace transform to solve the given initial-value problem. y' − 2y = (t − 4), y(0) = 0

Mathematics
1 answer:
yulyashka [42]1 year ago
4 0

Using the Laplace transform, the value o y' − 2y = (t − 4), y(0) = 0 is⇒y(t) = 0 e^-t + u(t -1)e^1-t

Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in  regions of physics, electrical engineering, control optics, arithmetic and sign processing.

y' − 2y = (t − 4),

y(0) = 0

Taking the Laplace transformation of the differential equation

⇒sY(s) - y (0) + Y(s) = e-s

⇒(s + 1)Y(s) = (0+ e^-s)/s + 1

⇒y(t) = L^-1{0/s+1} + {e ^-s/s + 1}

⇒y(t) = 0 e^-t + u(t -1)e^1-t

The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.

Learn more Laplace transformation here:-brainly.com/question/14487437

#SPJ4

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Derek has a white cube and a red cube.
cluponka [151]

Answer:

1/72

Step-by-step explanation:

Probability of getting a 4 on white cube is:

P(W) · P(4) = 1/2 × 1/6 = 1/12

P(R) · P(>4) = 1/2 × 2/6 = 1/6

multiply both probabilities:  1/12 × 1/6 = 1/72

3 0
2 years ago
The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation
aliina [53]

Answer:

a.  X~N(2,885, 651)

b.  0.086291

c.  0.00058

d.  3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting  the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

P(X

#substitute the given values in the formula to solve for P:

P(X

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058

Hence, the proportion of customers consuming over  5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09

Hence, the least amount of calories consumed to qualify for the award is 3213.10 calories.

8 0
3 years ago
Emily and Kylie are 140 miles apart, traveling towards each other. If Kylie travels 12 mph and Emily travels 8 mph how long unti
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Answer: 7 hr

Step-by-step explanation:

Given

Distance between Emily and Kylie is 140\ \text{miles}

Speed of Emily v_e=12\ mph

Speed of Kylie v_k=8\ mph

Distance traveled by Emily \Rightarrow d_e=12t

Distance traveled by Kylie \Rightarrow d_k=8t

\Rightarrow 12t+8t=140\\\Rightarrow 20t=140\\\Rightarrow t=7\ hr

They will meet after 7 hour.

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Step-by-step explanation:

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