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pishuonlain [190]
3 years ago
14

Suppose a certain forest fire doubles in size every 12 hours. If the initial size of the fire was 1 acre, how many acres will th

e fire cover in 2 days?
Mathematics
1 answer:
sineoko [7]3 years ago
8 0
The forest fire will be 4 acres
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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
( 100 POINTS FOR EVERYTHING )
Lina20 [59]

Answer:

3. x+8

4. 6y

5. 1/2m

6. 50/h

7. 7-n

8. 15+x

9. 2t/12

10. p² -3

11. 2k-7

12. 3(w+5)

13. C

14. The error was it was written that you would subtract the pages read by pages in the article which is incorrect. You would subtract pages total (5) by pages read (p). So it is 5-p.

15. 4v

16. 16/p

17. 2.97/p

18. 20+j

19. 7-d

20. m/60

21. y/12

22. unit rate-8

23. unit rate-1.5

24. unit rate-2.4

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3 0
2 years ago
In the accompanying diagram of ABC ca is extended to D, m∠ABC = 70 and m∠BCA =50 Find m∠DAB
zvonat [6]

Answer:

<em>120 degrees</em>

Step-by-step explanation:

Find the diagram attached.

From the diagram;

Interior angles are m∠BCA and m∠ABC

Exterior angle is m∠DAB

The sum of interior angle of the triangle is equal to exterior

m∠BCA +m∠ABC =m∠DAB

Given

m∠ABC = 70

m∠BCA =50

m∠DAB = 70 + 50

m∠DAB = 120 degrees

<em>Hence the measure of m∠DAB is 120 degrees</em>

6 0
3 years ago
A spinner has three unusual sections: red, yellow, and blue.. The table shows the results of Nolan’s spins. Find the probability
Anika [276]

Answers:

  • Red = 1/3
  • Yellow = 7/15
  • Blue = 1/5

====================================================

Explanation:

Add up all the frequencies in the table to see that there are 120+168+72 = 360 spins total.

  • Of those 360 spins, 120 of them land on red. The probability of landing on red is 120/360 = (120*1)/(120*3) = 1/3
  • Since 168 land on yellow, this means the probability of landing on yellow is 168/360 = (24*7)/(24*15) = 7/15
  • Lastly, we have 72 occurrences of blue out of 360 total spins. The probability of landing on blue is 72/360 = (72*1)/(72*5) = 1/5
4 0
3 years ago
What type of polynomial is this
Crank

Answer:

trinomial..............

5 0
2 years ago
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