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grin007 [14]
3 years ago
5

JVU

Mathematics
1 answer:
pantera1 [17]3 years ago
6 0
The answer is 7 and negative 8 (C)
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In a regular triangle ABC with side 1, two squares MNKL, RKPT are drawn such that points M, L, R are on the side AC (the order o
Orlov [11]

Answer:

  • MN = (21 -6√3)/37 ≈ 0.286694
  • RK = (14√3 -12)/37 ≈ 0.331046

Step-by-step explanation:

In the attached figure, we have defined LM to be length x. Then the other lengths on side AC are ...

  AM = LR = x/√3

  RC = (2/√3)RK = (2/√3)(2/√3)x = 4/3x

Then the sum of lengths along AC is ...

  AC = AM +ML +LR +RC

  1 = x(1/√3 +1 +1/√3 +4/3) = x(7/3 +2/√3) = x(7√3 +6)/(3√3)

Then the value of x is ...

  x=\dfrac{3\sqrt{3}}{7\sqrt{3}+6}=\dfrac{3\sqrt{3}(7\sqrt{3}-6)}{(7\sqrt{3})^2-6^2}=\dfrac{3(21-6\sqrt{3})}{3(49-12)}\\\\\boxed{MN=\dfrac{21-6\sqrt{3}}{37}}\\\\RK=\dfrac{2\sqrt{3}}{3}MN\\\\\boxed{RK=\dfrac{14\sqrt{3}-12}{37}}

8 0
4 years ago
I need help :(:(:(:(
tigry1 [53]

The resulting matrix of the row operation is given as follows:

R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right]

<h3>How to find the resulting matrix?</h3>

We apply the row operation on the original matrix, given as follows:

A = \left[\begin{array}{ccc}4&3&0\\-6&-3&12\end{array}\right]

The operation is given by:

R_1 = R_1 - 0.5R_2

That is, applying to each element, we have that:

  • 4 - 0.5(-6) = 7.
  • 3 - 0.5(-3) = 4.5.
  • 0 - 0.5(12) = -6.

Hence the resulting matrix is:

R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right]

More can be learned about matrix operations at brainly.com/question/1821869

#SPJ1

3 0
2 years ago
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