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3 years ago

ANSWER ASAP PLZ

Mathematics

1 answer:

IRISSAK [1]3 years ago

7 0

Answer:

BC=QR

Step-by-step explanation:

conditions to be congruent, SSS, SAS, or ASA

Here, one side and one angle are already congruent, so another side including the angle should be same, to satisfy SAS

thus, BC=QR

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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

C = d where C is the circumference of a circle, is about 3.14, and d is the diameter.

Rzqust [24]

Answer:

Formula for Circumference of a Circle

Circumference is given by the formula C = πd where π = 3.14 and d is the diameter of the circle. Circumference is given by the formula C = 2πr where π = 3.14 and r is the radius of the circle.

Hope it's helpful to you

3 0

4 years ago

Cassie paid $276.45 for 5 months of cell phone service. At that rate, how much will Cassie pay for a full year of cell phone ser

irinina [24]

It’s 663.48 because if you divide 276.45 by 5 than you get 55.19 and multiply that by 12 and it’s 663.48

3 0

3 years ago

To win the carnival game Ring Ding, you must toss a wooden ring onto a grid of rectangles so that it lands without touching any

guapka [62]

Answer:

5in x 10in

Step-by-step explanation:

Solution:

1. You have to assume that the ring will land on the board and as a result, just focus on one rectangle of the board since they are all the same size.

2. For the ring to land entirely inside the rectangle, the center of the ring needs to be 1.5 inches inside the border (radius is 1.5 inches), so the "winning rectangle" will have dimensions:

L = (x - 2(1.5)) = x - 3

w = (2x - 2(1.5)) = 2x-3.

3. Now, we will set up and solve our geometric probability equation. The winning rectangle's area of (x-3)*(2x-3) divided by the total rectangle's area of x*(2x) = 28%

(2x-3)*(x-3)/(2x^2) = .28

2x^2 - 9x + 9 = .56x^2

1.44x^2 - 9x + 9 = 0

4 . Now you can plug that in the quadratic formula and get the solutions x = 1.25 or 5. However, it cannot by 1.25 because that is too small of a dimension for the the circle with diameter of 3 to fit in, the answers has to be 5.

5. As a result, the dimensions of the rectangles are 5in x 10in.

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3 years ago

Need help fast please

Ray Of Light [21]

Answer:

Step-by-step explanation:

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4 years ago