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3 years ago

The function h(t) = −5t2 + 25t shown in the graph models an architectural arch:

Mathematics

1 answer:

alukav5142 [94]3 years ago

6 0

Answer:

the answer is actually 0 ≤ x ≤ 5

Step-by-step explanation:

i got it right

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

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2 years ago

Mental Math A typical tip in a restaurant is 15% of the total bill. If the bill is $110, what would the

Katarina [22]

Answer:

$16.50

Step-by-step explanation:

15/100*110

15/10*11

3/2*11

33/3

16.50

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2 years ago

What is the slope of the line shown on the graph

kvasek [131]

Answer: The best and most correct answer among the choices provided by your question is the the first choice. We can conclude from the figure you specified that the "Points are graphed at negative 3 comma 2 and negative 1 comma negative 1". I hope my answer has come to your help. God bless and have a nice day ahead.

Step-by-step explanation:

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3 years ago

The segments shown below could form a triangle.

-BARSIC- [3]

Answer:

True. It could. Sorry my answer just has to be 20 characters long

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2 years ago

Im trying to pass the hardest quiz in the world(will give brainliest) the first question is

Ymorist [56]

Whatever your color eyes are

hope this helps