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3 years ago

Solve the following Simultaneous equationUsing any suitable method x+6y=2, 3x +2y =10

Mathematics

1 answer:

uranmaximum [27]3 years ago

5 0

Answer:

x = 0.5

y = -1/4 or -0.25

Step-by-step explanation:

x + 6y = 2

3x + 2y = 10

Multiply a number by any of the equations to get numbers of the same variable

3x + 18y = 6

3x + 2y = 10

3x - 3x = 0

NB: subtract evenly if u subtract down from top make sure u subtract down from top throughout

16y = -4

16y/16 = -4/16

y = -1/4 or -0.25

to find the x value, any where you see y u put in the y value(-0.25)

So u'll pick just one of the equations above

x + 6(0.25) = 2

x + 1.5 = 2

x = 1.5 + 2

x = 0.5

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Third leg.

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The wind has a speed of 35 mi/h and a direction S-10°-E.

We then can draw this as:

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$\begin{gathered} x=560\cdot\sin (20\degree)+35\cdot\sin (10\degree) \\ x\approx560\cdot0.342+35\cdot0.174 \\ x\approx191.53+6.08 \\ x\approx197.61 \end{gathered}$

and the y-coordinate (S-N axis) is:

$\begin{gathered} y=560\cdot\cos (20\degree)-35\cdot\cos (10\degree) \\ y\approx560\cdot0.940-35\cdot0.985 \\ y\approx526.23-34.47 \\ y\approx491.76 \end{gathered}$

Then, the actual speed vector is v3=(197.61, 491.76).

The starting location for the third leg is R2=(216.66, 167.67) [taken from the previous answer].

Then, we have to calculate the displacement in 20 minutes using the actual speed vector.

We can calculate the movement in each of the axis. For the x-axis:

$\begin{gathered} R_{3x}=R_{2x}+v_{3x}\cdot t \\ R_{3x}=216.66+197.61\cdot\frac{1}{3} \\ R_{3x}=216.66+65.87 \\ R_{3x}=282.53 \end{gathered}$

NOTE: 20 minutes represents 1/3 of an hour.

We can do the same with the y-coordinate:

$\begin{gathered} R_{3y}=R_{2y}+v_{3y}\cdot t \\ R_{3y}=167.67+491.76\cdot\frac{1}{3} \\ R_{3y}=167.67+163.92 \\ R_{3y}=331.59 \end{gathered}$

The final position is R3 = (282.53, 331.59).

To find the distance from the origin and direction, we transform the cartesian coordinates of R3 into polar coordinates:

The distance can be calculated as if it was a right triangle:

$\begin{gathered} d^2=x^2+y^2_{} \\ d^2=282.53^2+331.59^2 \\ d^2=79823.20+109951.93 \\ d^2=189775.13 \\ d=\sqrt[]{189775.13} \\ d\approx435.63 \end{gathered}$

The angle, from E to N, can be calculated as:

$\begin{gathered} \tan (\alpha)=\frac{y}{x} \\ \tan (\alpha)=\frac{331.59}{282.53} \\ \tan (\alpha)\approx1.1736 \\ \alpha=\arctan (1.1736) \\ \alpha=49.56\degree \end{gathered}$

If we want to express it from N to E, we substract the angle from 90°:

$\beta=90\degree-\alpha=90-49.56=40.44\degree$

Answer: the final location can be represented with the vector (282.53, 331.59).

1) The distance from the origin is 435.63 miles and

2) the direction is N-40°-E.

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3 years ago

Solve the following Simultaneous equationUsing any suitable method x+6y=2, 3x +2y =10​

Solve the following Simultaneous equationUsing any suitable method x+6y=2, 3x +2y =10