An architect is designing a very large square mall. Estimate the total area of the mall, if each side length is approximately 4890 feet.

For the differential equation

$$y''+\omega_0^2 y=0$$

with initial conditions $y(0)=y_0$ and $y'(0)=v_0 .$ a) Use the Laplace transfrom to show that is

$$y(t)=y_0\cos \omega_0 t +\frac{v_0}{\omega_0}\sin \omega_0 t$$

b) Show that the soluntion from (a) is equivalent with

$$y(t)=A\cos (\omega_0 t-\phi)$$

where is $\tan \phi=\frac{v_0}{y_0\omega_0}$ and $A=\sqrt{\frac{v_0^2}{\omega_0^2}+y_0^2}$ .

Is the statement in the following problem true or false? Give an explanation for your answer.

The function $f(t)=\cos (\pi t)+1$ has all of its zeros at odd integer values.

Describe one example of each of the scientific practices in the Hubbard Brook experiment

Find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line. $f(x)=x^{2}-2 x+3$ at (-1, 6)

Choose the correct answer.

Many famous (a) portico's, (b) porticoes, (c) porticos were designed by Spanish architect Antoni Gaudí.

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word.

Since Dirk thought that he was already headed for perdition, he...

(a) A favorable entropy change occurs when $\Delta S$ is positive. Does the order of the system increase or decrease when $\Delta S$ is positive?

(b) A favorable enthalpy change occurs when $\Delta H$ is negative. Does the system absorb heat or give off heat when $\Delta H$ is negative?

(c) Write the relation between $\Delta G, \Delta H$, and $\Delta S$. Use the results of parts (a) and (b) to state whether $\Delta G$ must be positive or negative for a spontaneous change.

Estimate each sum by clustering. 7.5 + 6.9 + 7.125

Is the statement in the following problem true or false? Give an explanation for your answer.

For all values of $\theta$ we have $e^{i \theta}=\cos \theta+i \sin \theta$.

Explain how to estimate the quotient of

$$4963 \div 39$$

.

Calculate the constants $A \text { and } \phi$ in terms of the initial conditions and thus verify equation (1.38) $A=\sqrt{\frac{\left(v_{0}+\zeta \omega_{n} x_{0}\right)^{2}+\left(x_{0} \omega_{d}\right)^{2}}{\omega_{d}^{2}}, \quad \phi=\tan ^{-1} \frac{x_{0} \omega_{d}}{v_{0}+\zeta \omega_{n} x_{0}}}$ for the underdamped case.

Rewrite the sentence adding details to make it more interesting and descriptive.

I've seen my favorite movie at least eight times.

Is the statement in the following problem true or false? Give an explanation for your answer.

The function $f(t)=3 \sin (2 \pi t)+4 \cos (2 \pi t)$ is sinusoidal.