Let x and y be two positive numbers such that $x + y = 20$. Find the values of x and y for which xy is as large as possible.

Solve the given differential equation by undetermined coefficients. $y^{\prime \prime}+25 y=6 \sin x$

Differentiate each function in problem with respect to x. $f(x)=\frac{\sin x}{\left(x^{2}+1\right)^{10}}$

Integrate in problem. $\int 5 x^{4} d x$.

What reaction will take place at the cathode and the anode when each of the following is electrolyzed? molten KF

Evaluate the derivative of the following functions. $f(w)=w^{2}-\tan ^{-1} w^{2}$

The activation energy for some reaction

$$\mathrm{X}_{2}(g)+\mathrm{Y}_{2}(g) \longrightarrow 2 \mathrm{XY}(g)$$

is 167 kJ/mol, and $\Delta E$ for the reaction is 128 kJ/mol. What is the activation energy for the decomposition of XY?

Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by n = 1, by n = 2.

Answer the following questions in complete sentences. Cuánto tiempo hace que estudias en este colegio?

Solve the given differential equation by separation of variables. $d y-(y-1)^{2} d x=0$

Proceed as in Example 5 and find an explicit solution of the given initial-value problem. $\frac{d y}{d x}=y e^{-x^{2}}, \quad y(4)=1$

You work 40 hours per week at a candy store and earn $7.50 per hour. You also earn$7.00 per hour babysitting and can work as many hours as you want. You want to earn $370 a week. How many hours must you babysit?

Use computer software to obtain a direction field for the given differential equation. By hand, sketch an approximate solution curve passing through each of the given points. $\frac{d y}{d x}=\frac{1}{y}$ (a) y(0) = 1 (b) y( - 2) = -l

What observation about molecules compels us to consider the hybridization of atomic orbitals?