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fredd [130]
3 years ago
8

A. -4 <= x <= 0 b. y >= -3 c. all real numbers 4. {-4,0}

Mathematics
1 answer:
zimovet [89]3 years ago
8 0

Answer:

-4 <= x <= 0

Step-by-step explanation:

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Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?
TiliK225 [7]
Performing laplace transform of the equation.

sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)

Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
4 0
3 years ago
A lake polluted by bacteria is treated with an antibacterial chemical. Aftertdays, thenumber N of bacteria per milliliter of wat
jeyben [28]

Answer:

N(1)=50 is a minimum

N(15)=4391.7 is a maximum

Step-by-step explanation:

<u>Extrema values of functions </u>

If the first and second derivative of a function f exists, then f'(a)=0 will produce values for a called critical points. If a is a critical point and f''(a) is negative, then x=a is a local maximum, if f''(a) is positive, then x=a is a local minimum.  

We are given a function (corrected)

N(t) = 20(t^2-lnt^2)+ 30

N(t) = 20(t^2-2lnt)+ 30

(a)

First, we take its derivative

N'(t) = 20(2t-\frac{2}{t})

Solve N'(t)=0

20(2t-\frac{2}{t})=0

Simplifying

2t^2-2=0

Solving for t

t=1\ ,t=-1

Only t=1 belongs to the valid interval 1\leqslant t\leqslant 15

Taking the second derivative

N''(t) = 20(2+\frac{2}{t^2})

Which is always positive, so t=1 is a minimum

(b)

N(1)=20(1^2-2ln1)+ 30

N(1)=50 is a minimum

(c) Since no local maximum can be found, we test for the endpoints. t=1 was already determined as a minimum, we take t=15

(d)

N(15)=20(15^2-2ln15)+ 30

N(15)=4391.7 is a maximum

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3 years ago
Answer this please thank you
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73, 81, 89, 75, 89, 86, 84, 78, 91, 78. What is the MAD
ruslelena [56]
89 would be the correct answer
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In which order should the four different digits be arranged to obtain the largest 4-digit number?
Rashid [163]

9999

Is ur answer mate......

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3 years ago
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