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2 years ago

HELP HELP HELP HELP HELP HELP HELP PLEASEEEEEEEEEEEEEEES

Mathematics

1 answer:

Akimi4 [234]2 years ago

4 0

Answer:

600

Step-by-step explanation:

6 x 6 x 10 = 360

6 x 4 x 10 = 240

360 + 240 = 600

Multiply base times height for area of triangle, multiply that by the depth (10m)

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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

2 years ago

Simplify the following math expression: 5+4(6-3)+4/2

lesantik [10]

Answer:

you have to solve the brackets first(6-3=3)

Then solve the division (4/2=2)

lastly the addition (5+4=9)

so we have 9×3=27

27+2=29.

3 0

1 year ago

Read 2 more answers

given the equation y-5=5x determine whether the points (2,12) and (-2,-5) are a solution on the graph

Flura [38]

(x,y)
sub points to see if we get true statemtn

(2,12)
x=2 and y=12

12-5=5(2)
7=10
false
no, (2,12) is not a point

(-2,-5)
x=-2
y=-5

-5-5=5(-2)
-10=-10
true
(-2,-5) is a soltuion

(-2,-5) is the only solution given that works

6 0

2 years ago

HELP PLSSSSSSSSSSSSSSSSSSSSS

vredina [299]

C because the the negative always is turned into a positive if you leave a braniest answer that would mean a lot of it helped thanks!!!

8 0

2 years ago

Read 2 more answers

Please help, I am super stuck and I cant lose points<br><br> this homework is 16 points total

bekas [8.4K]

Hello,

7) A∪C={1,2,3,4,5,7,9}

8) A∩B={2,4}

C'= complement of C ={2,4,6}

9) A∪B∩C'={1,2,3,4,6,8}∩{2,4,6}={2,4,6}

10) A∪(B∩C')={1,2,3,4}∩{2,4,6}={1,2,3,4,6}

Are you blind?

4 0

2 years ago