Simplify –3 – 1. A. –4 B. 2 C. 5 D.

Jonas builds a snow fort. He tells his friends it is 0.8 meters tall inside, but he rounded the height to the nearest tenth. Which could be the height of the snow fort before Jonas rounded it?

Check all options by rounding to the nearest tenth

A. 0.89 m

= 0.9 m

B. 0.74 m

= 0.7 m

C. 0.85

= 0.9 m

D. 0.77

= 0.8 m

Note: Digits 0 - 4 are rounded down while digits 5 - 9 are rounded up

Rounding to the nearest tenth means having one digits after the decimal point

5 0

3 years ago

Solve the given initial-value problem. x' = 1 2 0 1 − 1 2 x, x(0) = 2 7

Ilia_Sergeevich [38]

I'll go out on a limb and guess the system is

$\mathbf x'=\begin{bmatrix}\frac12&0\\1&-\frac12\end{bmatrix}\mathbf x$

with initial condition $\mathbf x(0)=\begin{bmatrix}2&7\end{bmatrix}^\top$ . The coefficient matrix has eigenvalues $\lambda$ such that

$\begin{vmatrix}\frac12-\lambda&0\\1&-\frac12-\lambda\end{vmatrix}=\lambda^2-\dfrac14=0\implies\lambda=\pm\dfrac12$

The corresponding eigenvectors $\eta$ are such that

$\lambda=\dfrac12\implies\begin{bmatrix}\frac12-\frac12&0\\1&-\frac12-\frac12\end{bmatrix}\eta=\begin{bmatrix}0&0\\1&-1\end{bmatrix}\eta=\begin{bmatrix}0\\0\end{bmatrix}$
$\implies\eta=\begin{bmatrix}1\\1\end{bmatrix}$

$\lambda=-\dfrac12\implies\begin{bmatrix}\frac12+\frac12&0\\1&-\frac12+\frac12\end{bmatrix}\eta=\begin{bmatrix}1&0\\1&0\end{bmatrix}\eta=\begin{bmatrix}0\\0\end{bmatrix}$
$\implies\eta=\begin{bmatrix}0\\1\end{bmatrix}$

So the characteristic solution to the ODE system is

$\mathbf x(t)=C_1\begin{bmatrix}1\\1\end{bmatrix}e^{t/2}+C_2\begin{bmatrix}0\\1\end{bmatrix}e^{-t/2}$

When $t=0$ , we have

$\begin{bmatrix}2\\7\end{bmatrix}=C_1\begin{bmatrix}1\\1\end{bmatrix}+C_2\begin{bmatrix}0\\1\end{bmatrix}=\begin{bmatrix}C_1\\C_1+C_2\end{bmatrix}$

from which it follows that $C_1=2$ and $C_2=5$ , making the particular solution to the IVP

$\mathbf x(t)=2\begin{bmatrix}1\\1\end{bmatrix}e^{t/2}+5\begin{bmatrix}0\\1\end{bmatrix}e^{-t/2}$

$\mathbf x(t)=\begin{bmatrix}2e^{t/2}\\2e^{t/2}+5e^{-t/2}\end{bmatrix}$

5 0

4 years ago

18. There are 56 fish in a tank, and each fish is yellow, blue, or black. There are six more yellow fish than blue fish, and fou

Alex73 [517]

Answer:

There are 24 yellow fish

Step-by-step explanation:

Blue: x

Yellow: x + 6

Black: x - 4

x + (x + 6) + (x - 4) = 56

3x + 2 = 56

3x = 54

x = 18

7 0

3 years ago

Simplify –3 – 1. A. –4 B. 2 C. 5 D. –2