A drawer contains 4 blue socks, 8 black socks, and 10 white

Are heart rate and age proportional or non proportional for each method

sp2606 [1]

Answer:

Yes

Step-by-step explanation:

For example

Doctors have two methods of calculating maximum heart rate. With the first method, maximum heart rate, y, in beats per minute is y=220−x, where x is the person’s age.

5 0

2 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

Assuming the lines are parallel angel 4 corresponds with angle ___

Soloha48 [4]

Answer:

∠ 2

Step-by-step explanation:

∠ 2 corresponds to ∠ 4 because each is in the same position, the upper right- hand corner, in its group of 4 angles.

6 0

3 years ago

Read 2 more answers

Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plu

Lostsunrise [7]

The domain of the composite function is given as follows:

[–3, 6) ∪ (6, ∞)

<h3>What is the composite function of f(x) and g(x)?</h3>

The composite function of f(x) and g(x) is given as follows:

$(f \circ g)(x) = f(g(x))$

In this problem, the functions are:

$f(x) = \frac{1}{x - 3}$ .

$g(x) = \sqrt{x + 3}$

The composite function is of the given functions f(x) and g(x) is:

$f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}$

The square root has to be non-negative, hence the restriction relative to the square root is found as follows:

$x + 3 \geq 0$

$x \geq -3$

The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:

$\sqrt{x + 3} - 3 \neq 0$

$\sqrt{x + 3} \neq 3$

$(\sqrt{x + 3})^2 \neq 3^2$

$x + 3 \neq 9$

$x \neq 6$

Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:

[–3, 6) ∪ (6, ∞)

More can be learned about composite functions at brainly.com/question/13502804

#SPJ1

7 0

1 year ago

How many centimeters is in 2 inches

Ilya [14]

2 inches is equal to 5.08 centimeters

Hope this helps you. :-)

5 0

3 years ago

Read 2 more answers