Jordon Haley
2022-05-09
Answered

Compute $$(-1914)\xf733$$.

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Kosyging1j7u

Answered 2022-05-10
Author has **14** answers

Divide $-1914$ by $33$.

$-58$

asked 2022-03-23

Given $\mathrm{cot}\left(b\right)=-2$ find $\mathrm{sin}\left(4b\right)$ and $\mathrm{cos}\left(4b\right)$

I made $\mathrm{sin}\left(4b\right)$ into a expanded form.

$4\mathrm{sin}\left(b\right){\mathrm{cos}}^{3}\left(b\right)-4{\mathrm{sin}}^{3}\left(b\right)\mathrm{cos}\left(b\right)$ And then I made a triangle using $\mathrm{cot}\left(b\right)=-2$for information.

I got from that triangle that, $\mathrm{sin}\left(b\right)=\frac{\sqrt{5}}{5}$ and that $\mathrm{cos}\left(b\right)=\frac{-2\sqrt{5}}{5}$

And from their I simplified.

But whenever I expand $\mathrm{cos}4b$ and plug in I get a bad answer, $\frac{353}{25}$ and I do not know if it is correct or wrong.

asked 2022-03-16

Assessing stability or instability of a system of equations with complex eigenvalues

Having this system , we get clearly two complex eigenvalues. If one has to assess the stability of the system at these eigenvalues, we have for the matrix A:

$\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$

that ${T}^{2}-4\mathrm{\Delta}\ge {\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\le {\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}=0$, where $T=a+c$, while $\mathrm{\Delta}=ad-bc=DetA$. But with complex eigenvalues $\pm 2i$, T which must be real, becomes complex and $\delta$ is always 0, when it would vary from greater than or lesser than zero for real eigenvalues. How do we solve this with complex eigenvalues?

asked 2022-03-27

Heat transfer between two fluids through a sandwiched solid (coupled problem):

Two fluids $({t}_{h},\text{}{t}_{c})$ flow opposite to each other on either side of a solid (T), while exchanging heat among themselves. In such a scenario, the conduction in the solid is governed by:

$x\in [0,1],y\in [0,1]$

1) $\kappa \frac{{\mathrm{d}}^{2}T}{\mathrm{d}{x}^{2}}+\mu {b}_{h}({t}_{h}-T)-\nu {b}_{c}(T-{t}_{c})=0$

with boundary condition as ${T}^{\prime}\left(0\right)={T}^{\prime}\left(1\right)=0$

The fluids are governed by the following equations:

2) $\frac{\mathrm{d}{t}_{h}}{\mathrm{d}x}+{b}_{h}({t}_{h}-T)=0$

3) $\frac{\mathrm{d}{t}_{c}}{\mathrm{d}x}+{b}_{c}(T-{t}_{c})=0$

The hot fluid initiates at $x=0$ and the cold fluid starts from $x=1$.

The boundary conditions are ${t}_{h}(x=0)=1$ and ${t}_{c}(x=1)=0$

Equation (1), (2) and (3) form a coupled system of ordinary differential equations.

It is pretty evident that using (2) and (3), Equation (1) can be re-written as:

4) $\kappa \frac{{\mathrm{d}}^{2}T}{\mathrm{d}{x}^{2}}-\mu \frac{\mathrm{d}{t}_{h}}{\mathrm{d}x}+\nu \frac{\mathrm{d}{t}_{c}}{\mathrm{d}x}=0$

However, I have not been able to proceed further.

Some parameter values are

${b}_{c}=12.38,\text{}{b}_{h}=25.32,\text{}\mu =1.143,\text{}\nu =1,\text{}\kappa =2.16$

asked 2022-03-30

asked 2022-04-17

find the Fourier transform of: f(t) = cos(3*pi*t)[u(t+4) - u(t-4)] :

a) using using the Fourier definition the integral identity

b) Finalize your answer using the *sinc* function

asked 2022-03-28

Write a quadratic equation in factored form that has solutions at 6 and -⅔

asked 2022-03-27

determine the lowest common multiple of the following 4x2y2, 6xy, 10xy2