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spayn [35]
3 years ago
12

Use matrices and elementary row to solve the following system:

Mathematics
1 answer:
LiRa [457]3 years ago
5 0

I assume the first equation is supposed to be

5x-3y+2z=13

and not

5x-3x+2x=4x=13

As an augmented matrix, this system is given by

\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\4&-2&4&12\end{array}\right]

Multiply through row 3 by 1/2:

\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\2&-1&2&6\end{array}\right]

Add -1(row 2) to row 3:

\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&5&5\end{array}\right]

Multiply through row 3 by 1/5:

\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&1&1\end{array}\right]

Add -2(row 3) to row 1, and add 3(row 3) to row 2:

\left[\begin{array}{ccc|c}5&-3&0&11\\2&-1&0&4\\0&0&1&1\end{array}\right]

Add -3(row 2) to row 1:

\left[\begin{array}{ccc|c}-1&0&0&-1\\2&-1&0&4\\0&0&1&1\end{array}\right]

Multiply through row 1 by -1:

\left[\begin{array}{ccc|c}1&0&0&1\\2&-1&0&4\\0&0&1&1\end{array}\right]

Add -2(row 1) to row 2:

\left[\begin{array}{ccc|c}1&0&0&1\\0&-1&0&2\\0&0&1&1\end{array}\right]

Multipy through row 2 by -1:

\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&-2\\0&0&1&1\end{array}\right]

The solution to the system is then

\boxed{x=1,y=-2,z=1}

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14 a and b please and thank u
Murrr4er [49]

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7 0
3 years ago
Find the surface area of a cylinder with a base radius of 2 yd and a height of 3 yd.
kherson [118]

Answer:

20 π

Step-by-step explanation:

The surface area of a cylinder is made up of 2 circles and its side.

To find the circles' areas, use the area formula for a circle: A = πr^2.

Since our radius is 2 yd, we can substitute r = 2 into this formula.

A = π2^2 = 4π

Now remember, this is only the area of once circle. Multiply 4π by 2 to get the area of both circles: 8π.

Now we need to find the surface area of the side.

If we flatten it out, we can see that the side is actually a curled up rectangle.

The length is the circumference of the circle and the width is the height of the cylinder.

To find the circumference, use the circumference formula for a circle: C = 2πr.

Substitute r = 2 into the formula.

C = 2π2 = 4π

Now that we know that the length is 4π, we can multiply the length by the width to find the area of the cylinder's side.

l = 4π

w = 3

A = lw = 4π * 3 = 12π

Finally, we can add the areas of the circles and the side to get the total surface area.

8π + 12π  = 20π

And that is your answer!

Please mark as Brainliest! :)

3 0
3 years ago
PLEASE HELP,, MARKING BRAINLIEST!!!
Colt1911 [192]

Answer:

D.Triangles are not similar

5 0
2 years ago
Read 2 more answers
33 1/3% of 75<br><br>plz help​
Paraphin [41]

The answer is 25

x 33 1/3% = 75

75 / 33 1/3

0.3333

(75)(0.333) =  25

24.9999999 rounds to 25

Hope this helps, have a BLESSED day! :-)

6 0
3 years ago
The area of the region in the first quadrant between the graph of y = k*sin(x) and x-axis (where k &gt; 0 ) on the closed interv
astraxan [27]
Note that 0\le k\sin x\le k in the given closed interval, so the area is exactly given by the definite integral

\displaystyle\int_0^\pi k\sin x\,\mathrm dx

(no absolute values needed!)

Integrating gives

-k\cos x\bigg|_{x=0}^{x=\pi}=-k(\cos\pi-\cos0)=-k(-1-1)=2k
8 0
3 years ago
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