Math  /  Calculus

Questiona. Find zttz_{t t} for ztt=z(x,y,t)=cos(4+49t)sin(2x)sin(7y)z_{t t}=\quad z(x, y, t)=\cos (\sqrt{4+49 t}) \cdot \sin (2 x) \cdot \sin (7 y) aba^{b} sin(a)xf\sin (a) \quad \frac{\partial}{\partial x} f : \infty α\alpha Ω\Omega ? b. Does u=sin(53t)sin(2x)sin(7y)u=\sin (\sqrt{53} \cdot t) \cdot \sin (2 x) \cdot \sin (7 y) satisfy the membrane equation utt=uxx+uyy?u_{t t}=u_{x x}+u_{y y} ? Yes No

Studdy Solution
ztt=[cos(4+49t)24014(4+49t)+sin(4+49t)24014(4+49t)32]sin(2x)sin(7y)z_{tt} = \left[ -\cos(\sqrt{4 + 49t}) \cdot \frac{2401}{4(4 + 49t)} + \sin(\sqrt{4 + 49t}) \cdot \frac{2401}{4(4 + 49t)^{\frac{3}{2}}} \right] \sin(2x) \sin(7y).
The function uu *does* satisfy the membrane equation.

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