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Korvikt [17]
2 years ago
12

What’s is the right answer choice to the picture.

Mathematics
2 answers:
Aleks04 [339]2 years ago
8 0

Answer:

B)  P (-4, 4) and R (2, 3)

Step-by-step explanation:

Q = (2, -4)

If ΔPQR is a right triangle, then

  • Missing point 1 will be on the x = 2 line
  • Missing point 2 will be on the y = -4 line

If PQ is 6 units, then

P = (2-6, -4) = (-4, -4) or

P = (2, -4+6) = (2, 2)

If QR is 7 units, then

R = (2-7, -4) = (-5, -4) or

R = (2, -4+7) = (2, 3)

Therefore, P (-4, 4) and R (2, 3)

ahrayia [7]2 years ago
7 0

Q has coordinates

  • (2,-4)

P is 6units left

  • P(2-6,-4)=(-4,-4)

R is 7units up

  • R(2,-4+7)
  • R(2,3)

Option B

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Consider the differential equation x2y′′ − 9xy′ + 24y = 0; x4, x6, (0, [infinity]). Verify that the given functions form a funda
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Step-by-step explanation:

Given equation is

x^2y'' - 9xy+24y=0

This Euler Cauchy type differential equation.

So, we can let

y=x^m

Differentiate with respect to x

y'= mx^{m-1}

Again differentiate with respect to x

y''= m(m-1)x^{m-2}

Putting the value of y, y' and y'' in the differential equation

x^2m(m-1) x^{m-2} - 9 x m x^{m-1}+24x^m=0

\Rightarrow m(m-1)x^m-9mx^m+24x^m=0

\Rightarrow m^2-m-9m+24=0

⇒m²-10m +24=0

⇒m²-6m -4m+24=0

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Therefore the auxiliary equation has two distinct and unequal root.

The general solution of this equation is

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and

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First we compute the Wronskian

W(x)= \left|\begin{array}{cc}y_1(x)&y_2(x)\\y'_1(x)&y'_2(x)\end{array}\right|

         = \left|\begin{array}{cc}x^4&x^6\\4x^3&6x^5\end{array}\right|

         =x⁴×6x⁵- x⁶×4x³    

        =6x⁹-4x⁹

        =2x⁹

       ≠0

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

y= c_1x^4+c_2x^6

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3 years ago
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