Write the general form of a second-order nonhomogeneous linear differential equation with constant coefficients.

Iris rolled a five-sided number cube numbered 1 through 5. Find the probability that a roll will result in each of the following. Write your answer using probability notation. P(odd). P(not odd). P(4). P(not 4).

use the method of variation of parameters to determine the general solution of the given differential equation. y'''−y'=t

Find the percent of the number. 70% of 70

Compute each. Assume the values of the variables are restricted so that the expressions are defined.

$$\frac { ( n - 1 ) ! } { ( n + 1 ) ! }$$

The solubility of

$$\mathrm { MnSO } _ { 4 } \cdot \mathrm { H } _ { 2 } \mathrm { O }$$

in water at

$$20 ^ { \circ } \mathrm { C }$$

is 70 g per 100 mL of water. Given a solution of

$$\mathrm { MnSO } _ { 4 } \cdot \mathrm { H } _ { 2 } \mathrm { O }$$

of unknown concentrati on, what experiment could you perform to determine whether the new solution is saturated, supersaturated, or unsaturated?

The most popular pizza at Pavone's Pizza is the 10-inch personal pizza with one topping. What is the area of a pizza with a diameter of 10 inches? Round your answer to the nearest hundredth.

Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why. A random sample of 15 college seniors is obtained, and the individuals selected are asked to state their ages.

Solve. If an equation has no real solution, say so.

$$2 \sqrt [ 3 ] { x } = \sqrt [ 3 ] { x ^ { 2 } }$$

Transform the given differential equation or system into an equivalent system of first-order differential equations.

$$x ^ { \prime \prime } = 3 x - y + 2 z , y ^ { \prime \prime } = x + y - 4 z , z ^ { \prime \prime } = 5 x - y - z$$

Transform the given differential equation or system into an equivalent system of first-order differential equations.

$$x ^ { \prime \prime } = ( 1 - y ) x , y ^ { \prime \prime } = ( 1 - x ) y$$

Three solutions of a second-order linear equation L[y] = g(t) are $\psi_{1}(t)=3 e^{t}+e^{t^{2}}, \psi_{2}(t)=7 e^{t}+e^{t^{2}}$ and $\psi_{3}(t)=5 e^{t}+e^{-t^{3}}+e^{t^{2}}.$ Find the solution of the initial-value problem $L[y]=g ; \quad y(0)=1, \quad y^{\prime}(0)=2.$

Tell whether the quotient is positive or negative without dividing. 5. 12 ÷ 4

Solve. 3y + 4y + 6 = 20