Solve the given initial value problem (differential equation subject to a specified condition. $\frac{d x}{d t}=\frac{\sin (\sqrt{t})}{\sqrt{t}};$ x(0) = -1

Find the volume of a spherical beach ball wit h a diameter of

Draw angles in standard position such that the terminal side passes through the given point. (-4, -2)

If a system is described by transfer function $h(t)=2u(t)+2n(t-1)$, use the convolution to calculate the output (time domain) if the input is $(a)2u(t); \; (b)2te^{-2t}u(t)$.

Use the root test to show that $\Sigma k^{p} e^{-k}$ converges for any fixed positive real number p. What does this imply about the following improper integral?

$$\int_{1}^{\infty} x^{p} e^{-x} d x$$

How does the textbook's discussion of Anglo-American settlers in the Ohio Valley support or challenge each of the historians' arguments regarding British policy?

Explain when it is necessary to use a table showing z-scores and percentiles rather than the 68–95–99.7 Rule to determine the percentage of data items less than a given data item.

Fill in the blank in the sentence with the correct form of the passive tense of the verb using the infinitive in parentheses, then translate the sentence: Dico vos esse felices, qui a Hunis non _____. (capere)

The expansion of $(a+b)^3$ has 4 terms. a. How many terms are in the expansion of $(a+b+c)^3$? b. How many terms are in the expansion of $(a+b+c+d)^3$? c. Generalize these results.

Sketch the enclosed region and use the Shell Method to calculate the volume of rotation about the x-axis. x = y(4 - y),

$$x = ( y - 2 ) ^ { 2 }$$

Write two or three sentences to add more details to one of Walter Mitty's adventures in the story. Underline each complete subject once and each complete predicate twice.

State the meaning of each sentence if "or" is interpreted as the inclusive-or; then, state the meaning of each sentence if "o" is interpreted as the exclusive-or. In each case, which meaning do you think is intended.

To enter Utopia, you must possess a driver's license or a passport.

Use Separation of Variables to find the general solution.

$$\frac { d x } { d t } = ( t + 1 ) \left( x ^ { 2 } + 1 \right)$$

If $y=e^{2 t}$ is a solution to the differential equation $\frac{d^{2} y}{d t^{2}}-5 \frac{d y}{d t}+k y=0,$ find the value of the constant k and the general solution to this equation.