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2 years ago

2.

Mathematics

1 answer:

OLEGan [10]2 years ago

4 0

Answer:

It takes four hours because the little bro is alone and only one lawn mower is used

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A new test is developed to test for a certain allergy, giving "positive" or "negative" results to indicate that a person does or

notsponge [240]

Answer:

the first blank is 82, the second blank is 8,910. I got that third blank wrong and it should be 7.1 I think. and the last block is should not. to find the third box all you need to do is:
82+990=1,072 then divide 82 by 1,072 and round to the nearest tenth

5 0

2 years ago

susan is arranging coffee mugs on shelves in her shop. she wanta each shelf to have the same number of mugs.she only wants one c

m_a_m_a [10]

This question belongs to greatest common factor.

49 = 7*7

56 = 7*8

So Greatest common factor = 7

Hence Susan can arrange 7 mugs on one shelf.

For 49 blue mugs, Susan can arrange 7 mugs in 7 shelves.

For 56 red mugs, Susan can arrange 7 mugs on 8 shelves.

Hence, 7 shelves are needed for BLUE mugs and 8 shelves are needed for RED mugs.

8 0

3 years ago

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 density of the oak board, it's 5.5 inches wide, 1.5 inches thick , 3 feet long and weighs 8.05 lbs? Please show work

laiz [17]

Answer:

37 - 56 lb / ft3

0.6 - 0.9 103 kg / m3

Step-by-step explanation:

The density or hardness of wood varies by species, and the value is necessary to approximate the weight of lumber by volume. In this table, the density of different species of wood is expressed as weight in pounds per cubic foot and kilograms per cubic meter. The density will vary based on the moisture content of the wood.

8 0

3 years ago

The rectangles in the figure below are similar. Find the value of x

V125BC [204]

Answer:

C. 6

Step-by-step explanation:

It is given that the rectangles in the figure are similar.

<em>Thus, the corresponding sides of the two rectangles will be equal.</em>

So, we get,

$\frac{3}{x}=\frac{5}{x+4}$