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LenaWriter [7]
2 years ago
7

Estimate the sum of 1,256, 379 and 305,986 by first rounding each number to the nearest ten thousand.

Mathematics
1 answer:
KatRina [158]2 years ago
3 0

9514 1404 393

Answer:

  1,570,000

Step-by-step explanation:

The sum is approximately ...

  1,260,000 +310,000 = 1,570,000

_____

<em>Additional comment</em>

It is a good idea to estimate the error associated with an estimate. Here, both numbers are rounded up by about 4000 each, so the estimate is around 8000 high.

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A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2
andrey2020 [161]

Answer:

The required position of the particle at time t is: x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

Step-by-step explanation:

Consider the provided matrix.

v_1=\begin{bmatrix}-3\\1 \end{bmatrix}

v_2=\begin{bmatrix}-1\\1 \end{bmatrix}

\lambda_1=4, \lambda_2=2

The general solution of the equation x'=Ax

x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}

Substitute the respective values we get:

x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}

x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}

Substitute initial condition x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}

\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}

Reduce matrix to reduced row echelon form.

\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}

Therefore, c_1=2.5,c_2=1.5

Thus, the general solution of the equation x'=Ax

x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}

x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

The required position of the particle at time t is: x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

6 0
3 years ago
What is the substitution for 3x+4y^2 if x= -2 and y=3?
solniwko [45]

Answer:

<h2>30</h2>

Step-by-step explanation:

3x+4y^2\\\\\text{Substitute the value of x = -2 and y = 3 to the expression:}\\\\3(-2)+4(3^2)\qquad\text{use PEMDAS}\\\\=-6+4(9)=-6+36=30

5 0
3 years ago
2.1 in a decimal form
Allisa [31]

2.1 is already in a decimal form.

Hope I helped!

7 0
3 years ago
4 x equals negative 2x + negative 6
erastovalidia [21]
So x equals two if it is an exponent.9
7 0
3 years ago
Read 2 more answers
Roberto must make his costume for his school play. He needs a piece of fabric that is 2 2/3 yards long and 1 1/2 yards wide. Wha
erik [133]

Answer:

He will need 8.34 yards of fabric.

Step-by-step explanation:

Given that,

The length of the fabric, l = 2 2/3 yards = 8/3 yards

The width of the fabric, b = 1 1/2 yards = 3/2 yards

We need to find the piece of fabric Roberto needs. It is equal to the perimeter of the fabric such that,

P=2(l+b)\\\\P=2(\dfrac{8}{3}+\dfrac{3}{2})\\\\P=2\times \dfrac{25}{6}\\\\P=8.34\ \text{yards}

So, he will need 8.34 yards of fabric.

7 0
3 years ago
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