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Questions in mathematics

[Done] $\frac{6 x^6 y^4}{2 x^2 y^2} =$ F $3 x^4 y^2$ G $3 x^3 y^2$ H $4 x^3 y^2$ J $4 x^4 y^2$ K None of these

[Done] If [tex]$x$[/tex] satisfies the equation [tex]$\left(\int_0^1 \frac{d t}{t^2+2 t \cos \alpha+1}\right) x^2$ $-\left(\int_{-3}^3 \frac{t^2 \sin 2 t}{t^2+1} d t\right) x-2=0(0\ \textless \ \alpha\ \textless \ \pi)$[/tex], then the value of [tex]$x$[/tex] is (a) [tex]$\pm \sqrt{\frac{\alpha}{2 \sin \alpha}}$[/tex] (b) [tex]$\pm \sqrt{\frac{2 \sin \alpha}{\alpha}}$[/tex] (c) [tex]$\pm \sqrt{\frac{\alpha}{\sin \alpha}}$[/tex] (d) [tex]$\pm 2 \sqrt{\frac{\sin \alpha}{\alpha}}$[/tex]

[Done] Solve for $y: -5y + 6 = 16$

[Done] What is the period of the sinusoid given by [tex]y=-3 \cos \left(\frac{2 \pi}{5} x\right) ?[/tex]

[Done] Fill in the boxes to write $\frac{12}{7}$ as a mixed number. Improper fraction: $\frac{12}{7}$ Mixed number:

[Done] $\begin{array}{c}\left(x+3 x^{\prime}=0\right. \\ x=-9 \\ x=-1 \\ x=1 \\ x=6\end{array}$

[Done] Write the missing numbers in each number pattern. (a) 321, 323, 325, ____, 329, 331, ____ (b) 278, 275, 272, ____, 266, 263, ____ (c) 205, 207, 204, 206, 203, 205, 202, ____, 203, 200 (d) 101, 106, 102, 107, 103, 108, 104, ____, 110, ____, 111, 107

[Done] Solve the following: i. 345,678 + 123,456 - 98,765 ii. 765,432 - 234,567 + 456,789

[Done] [(1 + 5 × 6) - 6 + (8 × 9 ÷ 8)]

[Done] Find the LCM by using the factorization method. a. 12, 18, 27 b. 10, 12, 20