Other Math Archive: Questions from October 03, 2023
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13. Compute a. \( 21^{\wedge}-1 \bmod 51 \) b. \( 79^{\wedge}-1 \bmod 101 \) c. \( 112^{\wedge}-1 \bmod 300 \) d. \( 33^{\wedge}-1 \bmod 83 \)2 answers -
Do problem 19
In Problems \( 11-20 \), solve the initial value problem. 11. \( y^{\prime \prime}+3 y^{\prime}=0 ; y(0)-3 y^{\prime}(0)=6 \) 12. \( y^{\prime \prime}+2 y^{\prime}=0 ; x(0)=6, y^{\prime}(0)=-2 \) 13.1 answer -
La derivada parcial de beta con respecto a la presión a temperatura constante es igual a menos la derivada parcial de kappa con respecto a la temperatura a presión constante.
93. Partiendo de que \( d V / V \) es una diferencial exacta, deducir la relación \[ \left(\frac{\partial \beta}{\partial P}\right)_{T}=-\left(\frac{\partial \kappa}{\partial T}\right)_{P} \]1 answer -
4. Determine la solución de la ecuación diferencial:
4. Determine la solución de la ecuación diferencial: \[ \left(3 x^{2} y+e^{y}\right) d x+\left(x^{3}+x e^{y}-2 y\right) d y=0 . \]1 answer -
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Investigate whether the following functions are quasi-concave or -convex.
(a) \( f(x, y)=y e^{-x} \) (b) \( f(x, y)=y e^{-x}, \operatorname{kun} x, y1 answer -
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Solve the following DE. in detail y' + y = -xy 3 ४
Solve the following DE. in detail \[ y^{\prime}+\frac{1}{x} y=-x y^{3} \]1 answer -
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7. Solve for \( y \) : \[ y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=\delta(x-5) ; \quad y(0)=y^{\prime}(0)=y^{\prime \prime}(0)=0 \]1 answer -
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(16\%) Differentiate each of the following functions: \[ \begin{array}{c} y=7 x(2 x-5)^{3} \\ y=\frac{(3 x-5)^{3}}{(2 x+3)} \\ y=\left(\frac{x+5}{2 x-8}\right)^{2} \\ y=\ln (9 x+2)^{4} \\ y=(6 x+1) e^1 answer