Transform the equation ${t(t - 1)y^{(4)} + e^{t}y'' + 4t^{2}y = 0}$ into an equivalent first order system.

Find each limit algebraically. $\lim _{x \rightarrow 1}\left(x^{2}+1\right)^{3}$

Solve the equation.

$$4 + \sqrt{4t - 4} = t$$

Two eighths of a circle equals what percent of a circle?

Assume that the flowrate. Q, of a gas from a smokestack is a function of the density of the ambient air,$\rho_{a}$, the density of the gas,$\rho_{g}$, within the stack, the acceleration of gravity, g, and the height and diameter of the stack, h and d, respectively. Use $\rho_{c}$, d, and g as repeating variables to develop a set of pi terms that could be used to describe this problem.

Solve the equation.

$$\ln (x-1)+\ln (x+1)=2 \ln \sqrt{12}$$

Solve the equation using square roots. $x^{2}-64=0$

For the given functions f and g, find the following. Also find the domain. $(f \cdot g)(x);f(x)=1+\frac{1}{x} ; g(x)=\frac{1}{x}$

Convert 0.42 kilometers to meters.

Determine whether the function has an inverse (is one-to-one). If so, find the inverse and graph both the function and its inverse. $f(x)=x^{4}-2 x-1$

What role did the policy of containment play in the involvement of the United States in wars in Korea and Vietnam?

A soda can in the shape of a cylinder is to hold 16 fluid ounces. Find the dimensions of the can that minimize the surface area of the can.

Coloca las cosas antiguas en una columna y las modernas en la otra. (Put the words in the correct column.)

Find the unique solution of least norm to the system of linear equations.

$$\begin{align*} x_1-2x_2+x_3&=3\\ -x_1+x_2+2x_3&=-1 \end{align*}$$