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Reil [10]
3 years ago
6

Simplify. y 5 · y 3 ÷ y 2

Mathematics
1 answer:
Gnesinka [82]3 years ago
3 0
Y^5 x y^3 /y^2
y^8/y^2
y^4
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Please help me with the below question.
Snezhnost [94]

6a. By the convolution theorem,

L\{t^3\star e^{5t}\} = L\{t^3\} \times L\{e^{5t}\} = \dfrac6{s^4} \times \dfrac1{s-5} = \boxed{\dfrac5{s^4(s-5)}}

6b. Similarly,

L\{e^{3t}\star \cos(t)\} = L\{e^{3t}\} \times L\{\cos(t)\} = \dfrac1{s-3} \times \dfrac s{1+s^2} = \boxed{\dfrac s{(s-3)(s^2+1)}}

7. Take the Laplace transform of both sides, noting that the integral is the convolution of e^t and f(t).

\displaystyle f(t) = 3 - 4 \int_0^t e^\tau f(t - \tau) \, d\tau

\implies \displaystyle F(s) = \dfrac3s - 4 F(s) G(s)

where g(t) = e^t. Then G(s) = \frac1{s-1}, and

F(s) = \dfrac3s - \dfrac4{s-1} F(s) \implies F(s) = \dfrac{\frac3s}{\frac{s+3}{s-1}} = 3\dfrac{s-1}{s(s+3)}

We have the partial fraction decomposition,

\dfrac{s-1}{s(s+3)} = \dfrac13 \left(-\dfrac1s + \dfrac4{s+3}\right)

Then we can easily compute the inverse transform to solve for f(t) :

F(s) = -\dfrac1s + \dfrac4{s+3}

\implies \boxed{f(t) = -1 + 4e^{-3t}}

6 0
1 year ago
Discuss decline or growth of population of the settlement​
statuscvo [17]

Answer:

THE INCREASE AND DECLINE OF POPULATION

Step-by-step explanation:

Up until the beginning of the industrial revolution, global population grew very slowly. ... After about 1800 the growth rate accelerated to a peak of 2.1% annually in 1968; but since then, due to the world-wide collapse of the total fertility rate, it has declined to 1.1% today (2020).

5 0
2 years ago
What is the measure of angle A?
I am Lyosha [343]

First you have to find the angle B (check attachment)

B = 180^{\circ} - 137^{\circ} = 43^{\circ}\\

Then you can find the last angle inside the triangle, which I'll call C

C = 180^{\circ} - 102^{\circ} - 43^{\circ} = 35^{\circ}

Now you can find angle A

A = 180^{\circ} - C = 180^{\circ} - 35^{\circ} = 145^{\circ}

3 0
3 years ago
Translate each of the equations below into algebraic statements.
MrMuchimi

Answer:

a. 3 times the sum of a number and 3 equals 9

b. 5 less than the product of 4 times a number equals 11

Please Mark Brainliest If This Helped!

4 0
2 years ago
At a family reunion, a family friend brings 20 pounds of ice and 30 cups. Which expression shows the greatest common factor, usi
Eddi Din [679]

The expression for the greatest common factor of 20 and 30 using the distributive property is 10(2 + 3)

Pounds of ice = 20

Number of cups = 30

The relation for the distributive property :

a × (b + c)

Expand ;

a × (b + c) = (a × b) + (a × c) = ab + ac

Finding the greatest common factor of 20 and 30 ;

  • 20 = 2 × 10

  • 30 = 3 × 10

(2 × 10) + (3 × 10)

According to the distributive property

(2 × 10) + (3 × 10) = 10(2 + 3)

Therefore, the expression for the greatest common factor is 10(2 + 3)

Learn more :brainly.com/question/15263211

6 0
3 years ago
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