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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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What is the volume of the cone? What is the volume of the cylinder? What is the volume of the sphere? At the craft store discuss
KATRIN_1 [288]

Answer:

clay sphere gives more clay for less money

Step-by-step explanation:

Volume of cone=1/3πr^2h

=1/3*3.14*(9^2)*12

=1/3*3.14*81*12

=3,052.08/3

=1017.36 inches^3

Volume of a cyclinder=πr^2h

=3.14*(9^2)*12

=3.14*81*12

=3,052.08 inches^3

Volume of a sphere=4/3πr^3

=4/3*3.14*(9^3)

=4/3*3.14*(9^3)

=4/3*3.14*729

=9,156.24 / 3

=3,052.08 inches^3

Clay cone=$12

Clay cyclinder=$30

Clay sphere=$28

Which is the best to buy

Comparing volume

Volume of sphere=3,052.08 inches^3

Volume of cyclinder=3,052.08 inches^3

Volume of cone=1017.36 inches^3

Sphere and cyclinder both have the same volume which is 3 times more than volume of a cone

Clay sphere cost $28 which is cheaper than clay cyclinder at the same volume.

Therefore, clay sphere gives more clay for less money

4 0
2 years ago
I need help on #17 can someone please help me?
sashaice [31]

Answer:

t=2

Step-by-step explanation:

We are given the equation

h = -16t²+36t+1

Next, we are asked to find how long the ball was in the air (the time, in seconds) if Casey caught the ball 9 feet above the ground (9 feet is the height).

Therefore, as 9 is the height, we can plug that into our equation to get

9 = -16t²+36t+1

To make this a quadratic equation that is easy to factor, we can subtract 9 from both sides to get

-16t²+36t-8=0

To factor this, we need to find two values that add up to 36 and multiply to (-16)*(-8) = 128. With a little guess and check, I found the numbers 32 and 4 to work well. We can then make the equation

-16t²+32t+4t-8=0

-16t(t-2) + 4(t-2) = 0

(-16t+4)(t-2) = 0

Therefore, to solve for the equation being 0, or 9 = -16t²+36t+1, either (t-2) or (-16t+4) must equal 0

t-2 = 0

t=2

-16t+4 = 0

-16t = -4

t = 1/4

Therefore, t=1/4 and/or t=2. To figure out which one it is (or both!), we can take into account that the question states "on its way down". This means that the ball goes up and then down, and we want to find t when it is going down. Using the knowledge that a ball that is hit goes up and then down, as well as that -16t²+36t-8=0 is a quadratic equation with 2 solutions, we can say that the higher value of t (t=2) represents when the ball is going down

3 0
3 years ago
Which is the best example of natural selection?
Bas_tet [7]
A. Some insects in a population survive temperature changes and pass their traits on to their offspring
6 0
1 year ago
Write the expression √a3 - b3 without radicals, using only positive exponents
NikAS [45]
Having a root, is the same as having an exponent of 1/2

√a³, becomes a^3/2

a^(3/2) - b^3 is your answer

hope this helps


8 0
3 years ago
The solution to an inequality is given in interval notation as (2, oo). What is another way to represent this solution set?
andriy [413]

Assuming the variable is x, we can write (2, \infty) as x > 2

The given interval is from 2 onto infinity, basically describing everything larger than 2. We do not include 2 as part of the interval because of the curved parenthesis. If you had [2, \infty) then you would include 2 and you would say x \ge 2

In set builder notation, we can write \{x|x\in \mathbb{R}, \ x > 2\} which is basically a more long-winded way of saying x > 2. The fancy looking R indicates that x is a real number. So it's saying "we have a set of real numbers such that these numbers are greater than 2".

4 0
2 years ago
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