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Gekata [30.6K]
3 years ago
6

(1 point) Write the given second order equation as its equivalent system of first order equations. u′′+6.5u′−1.5u=8sin(3t),u(1)=

−3,u′(1)=−1.5 Use v to represent the "velocity function", i.e. v=u′(t). Use u and v for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are OK.)
Mathematics
1 answer:
Over [174]3 years ago
6 0

Answer:

v' + 6.5\cdot v = 1.5\cdot u + 8\cdot \sin 3t

Step-by-step explanation:

The differential equation is:

v' + 6.5 \cdot v -1.5\cdot u = 8 \cdot \sin 3t

v' + 6.5\cdot v = 1.5\cdot u + 8\cdot \sin 3t

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Three sevenths of a children's choir are boys. If there are 12 boys in the choir, how many children, c, total are in the choir?
ruslelena [56]

Answer:

Here c represents the total number of children  in choir.

As per the statement:

Total number of boys in choir = 12

It is also given that: Three sevenths of a children's choir are boys.

⇒ Total number of boys = \frac{3}{7} c

or

12 = \frac{3}{7}c

By cross multiply we have;

84 = 3c

Divide both sides by 3 we have;

c = 28

Therefore, the total number of children in choir is 28 children


6 0
3 years ago
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Lines a and b are parallel.
Andreyy89

Answer:

∠s = 22°

Step-by-step explanation:

∠t = 158° ( corresponding angles )

∠s = 180° - ∠t ( straight angle )

    = 180° - 158° = 22°

 

7 0
3 years ago
Is it pp PP pP or coc
ddd [48]

Answer:

its Pp or it could also be nonexistent

8 0
3 years ago
What is another way to express 12/12
Readme [11.4K]
The answer is 6/6 so does that help you today and it can also be one whole
3 0
3 years ago
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In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample. To determine
zimovet [89]

Answer:

(a)  0.2650

(b)  0.0111

(c)  0.0105

(d)  0.0006

Step-by-step explanation:

Given that:

In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample.

Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with mean μ = 15.       &;

If the area of the agar plate is 75cm²;

what is the probability  of observing fewer than 4 CFUs in a 25 cm² area of the plate.

We can determine the mean number of CFUs that appear on a 25cm² area of the plate as follows;

75cm²/25cm² = 3

Since;

mean  μ = 15  

mean number of CFUs that appear on a 25cm² = 15/3 = 5 CFUs

Thus ; the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate is estimated as:

= P(X < 4)

Using the EXCEL FUNCTION ( = poisson.dist(3, 5, TRUE) )

we have ;

P(X < 4) = 0.2650

b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs?

Given that the total number of CFUs = 5 plates; then the mean number of CFUs in 5 plates =  15×5 = 75 CFUs

The probability is therefore = P( X > 95 )

= 1 - P(X ≤ 95)

= 1 - poisson.dist(95,75,TRUE) ( by using the excel function)

= 0.0111

c) Repeat the probability calculation in part (b) but now use the normal approximation.

Let assume that the mean and the variance of the poisson distribution are equal

Then;

X \sim N (\mu = 75 , \sigma^2 = 75)

We are to repeated the probability calculation in part (b) from above;

So:

P( X > 95 )

use the normal approximation

From standard normal variable table:

P(Z > 2.3094)

Using normal table

P(Z > 2.3094) = 0.0105

(d)  Find the difference between this value and your answer in part (b).

So;

the difference between the value in part c and part b is;

=  0.0111 - 0.0105

= 6*10^{-4}

= 0.0006 to four decimal places

5 0
3 years ago
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