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3 years ago

Aaron estimated that 148% of 333 is 495

Mathematics

2 answers:

maksim [4K]3 years ago

7 0

Answer:

492.84

Step-by-step explanation:

333 x 148÷100

= 492.84

Eva8 [605]3 years ago

3 0

Answer: Yes, because his calculation should be 150% of 330.

Step-by-step explanation:

150×330 = 495

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Use the laplace transform to solve the given system of differential equations. dx dt + 3x + dy dt = 1 dx dt − x + dy dt − y = et

blagie [28]

Let $X(s)$ and $Y(s)$ denote the Laplace transforms of $x(t)$ and $y(t)$ .

Taking the Laplace transform of both sides of both equations, we have

$\dfrac{dx}{dt} + 3x + \dfrac{dy}{dt} = 1 \implies \left(sX(s) - x(0)\right) + 3X(s) + \left(sY(s) - y(0)\right) = \dfrac1s \\\\ \implies (s+3) X(s) + s Y(s) = \dfrac1s$

$\dfrac{dx}{dt} - x + \dfrac{dy}{dt} = e^t \implies \left(sX(s) - x(0)\right) - X(s) + \left(sY(s) - y(0)\right) = \dfrac1{s-1} \\\\ \implies (s-1) X(s) + s Y(s) = \dfrac1{s-1}$

Eliminating $Y(s)$ , we get

$\left((s+3) X(s) + s Y(s)\right) - \left((s-1) X(s) + s Y(s)\right) = \dfrac1s - \dfrac1{s-1} \\\\ \implies X(s) = \dfrac14 \left(\dfrac1s - \dfrac1{s-1}\right)$

Take the inverse transform of both sides to solve for $x(t)$ .

$\boxed{x(t) = \dfrac14 (1 - e^t)}$

Solve for $Y(s)$ .

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$\boxed{y(t) = e^t - 1 + \dfrac14 t}$

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1 year ago

What is the value of the expression i^0 x i^1 x i^2xi^3xi^4

monitta

Answer: The answer is - 1.

Step-by-step explanation: We are given to find the value of the given expression

$E_c=i^0\times i^1\times i^2\times i^3\times i^4.$

We know that 'i' is an imaginary unit and its value is √-1. So, we have

$i^0=(\sqrt{-1})^0=1,\\\\i^1=i=\sqrt{-1},\\\\i^2=(\sqrt{-1})^2=-1,\\\\i^3=i^2.I=(-1)i=-\sqrt{-1},\\\\i^4=(i^2)^2=(-1)^2=1.$

Therefore, the given expression becomes

$E_c\\\\=i^0\times i^1\times i^2\times i^3\times i^4\\\\=1\times \sqrt{-1}\times(-1)\times({-\sqrt{-1}})\times 1\\\\=1\times (-1)\\\\=-1.$ .

Thus, the answer is - 1.

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Step-by-step explanation:

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