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Crank
3 years ago
10

John's age is 2 years more than twice as old as Mary. The sum of their ages is 32. How old is each? (pls include equation and so

lution thx)
Mathematics
2 answers:
svp [43]3 years ago
6 0
Mary would be 10 because 10 times 2 is 30 plus 2 more is 32 years.
nataly862011 [7]3 years ago
6 0
M = Mary
J = John

Equation:
J = 2M + 2
M = ( J - 2 ) / 2
J + M = 32

J = 22
M = 10

2 * 10 = 20 + 2 = 22 = Johns age

Sorry, I can't figure out an equation.  Just did trial and error
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Formulate the following problem as least squares problems. For each problem, give a matrixA and a vector b such that the problem
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c) A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]

x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]

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Step-by-step explanation:

a) considering the equation:

Minimize x_{1}^{2}  +2x_{2}x^{2}  +3x_{3}^{2}+(x_{1}   -x_{2} +x_{3} -1)^{2} +(-x_{1} -4x_{2} +2)^{2}

A=\left[\begin{array}{ccc}1&2&3\\1&-1&1\end{array}\right] (matrix A)

vector b

b=\left[\begin{array}{ccc}0\\1\end{array}\right]

b) If Pxn is matrix B and p-vector d, we have:

minimize (-6x_{2}+4)^{2}  +(-4x_{1} +3x_{2} -1)+(x_{1} +8x_{2} -3)^{2}

Ax=\left[\begin{array}{ccc}0&-6&0\\-4&3&0\\1&8&0\end{array}\right]

\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]

b=\left[\begin{array}{ccc}-4\\1\\3\end{array}\right]

Ax-b=\left[\begin{array}{ccc}-bx_{2}+4 \\-4x_{1}+3x_{2}-1  \\x_{1}+8x_{2}-3  \end{array}\right] =1

||Ax-b||^{2} =(-bx_{2}+4)^{2}  (-4x_{1} +3x_{2} -1)^{2} +(x_{1} +8x_{2} -3)^{2}

c) minimize 2(-bx_{2}+4)^{2}  +3(-4x_{1} +3x_{2} -1)^{2} +4(x_{1} -x_{2} -3)^{2} -(6\sqrt{2}x_{2}  +4\sqrt{2} )^{2} +(-4\sqrt{3} x_{1} +3\sqrt{3}x_{2}  -\sqrt{3})^{2}  +(2x_{1} -16x_{2} -6)^{2}

in matrix:

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x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]

b=\left[\begin{array}{ccc}-\sqrt{2} \\\sqrt{3} \\6\end{array}\right]

6 0
3 years ago
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