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Lynna [10]
3 years ago
5

c{4}{3} = \frac{x}{6} " alt=" \frac{4}{3} = \frac{x}{6} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
timurjin [86]3 years ago
5 0

\bf \cfrac{4}{3}=\cfrac{x}{6}\implies \stackrel{\textit{cross-multiplying}}{(6)4=(3)x}\implies 24=3x\implies \cfrac{24}{3}=x\implies 8=x

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Find the area of the triangle
makkiz [27]

Answer:

84mm

Step-by-step explanation:

Formula of a triangle:

A =bh/2

A=14(12)/2

A=168/2

A=84mm

5 0
3 years ago
Which line segment is only a chord of F?
katen-ka-za [31]

Answer:

<h2>line AB is a chord</h2>

Step-by-step explanation:

Any line that segments a circle and joins two points at the circumference of a circle is called a chord.

line AB is a chord

While

line EC is a diameter

line DF is a radius

7 0
3 years ago
Write the linear system of differential equations in matrix form then solve the system.
zvonat [6]

In matrix form, the system is

\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}1&1\\4&1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}

First find the eigenvalues of the coefficient matrix (call it \mathbf A).

\det(\mathbf A-\lambda\mathbf I)=\begin{vmatrix}1-\lambda&1\\4&1-\lambda\end{vmatrix}=(1-\lambda)^2-4=0\implies\lambda^2-2\lambda-3=0

\implies\lambda_1=-1,\lambda_=3

Find the corresponding eigenvector for each eigenvalue:

\lambda_1=-1\implies(\mathbf A+\mathbf I)\vec\eta_1=\vec0\implies\begin{bmatrix}2&1\\4&2\end{bmatrix}\begin{bmatrix}\eta_{1,1}\\\eta_{1,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}

\lambda_2=3\implies(\mathbf A-3\mathbf I)\vec\eta_2=\vec0\implies\begin{bmatrix}-2&1\\4&-2\end{bmatrix}\begin{bmatrix}\eta_{2,1}\\\eta_{2,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}

\implies\vec\eta_1=\begin{bmatrix}1\\-2\end{bmatrix},\vec\eta_2=\begin{bmatrix}1\\2\end{bmatrix}

Then the system has general solution

\begin{bmatrix}x\\y\end{bmatrix}=C_1\vec\eta_1e^{\lambda_1t}+C_2\vec\eta_2e^{\lambda_2t}

or

\begin{cases}x(t)=C_1e^{-t}+C_2e^{3t}\\y(t)=-2C_1e^{-t}+2C_2e^{3t}\end{cases}

Given that x(0)=1 and y(0)=2, we have

\begin{cases}1=C_1+C_2\\2=-2C_1+2C_2\end{cases}\implies C_1=0,C_2=2

so that the system has particular solution

\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}e^{3t}\\2e^{3t}\end{bmatrix}

8 0
3 years ago
1 Construct the following triangles. You will need a ruler and a protractor.
Gwar [14]

Answer:

abcdefghijklmnopqrstuvwxy and z

Step-by-step explanation:

6 0
3 years ago
One-third of a number is 12. <br> Work out one-half of the number
Lana71 [14]
Since 1/3 of x is 12, it can also be expressed as x/3 = 12, and we can use multiplication to find x

12 x 3 = 36

1/2 of 36 is 18
4 0
3 years ago
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