$$\begin{aligned} \text { Show that there is no Hamiltonian path in } \\ & \operatorname { Cay } \left( \{ ( 1,0 ) , ( 0,1 ) \} : Z _ { 3 } \oplus Z _ { 2 } \right) \\ \text { from } ( 0,0 ) \text { to } ( 2,0 ) \end{aligned}$$

The weight $W_{t}$ grams of radioactive substance remaining after t years is given by $W_{t}=1000 \times 2^{-0.03 t}$ grams. Write an expression for the amount of substance that has decayed after t years.

Make a table of values of the equation if the replacement set is {-2, -1, 0, 1, 2}. 4.2x - 1.6 = y

Use Green’s theorem to evaluate $\oint_{C} \mathbf{F} \cdot d R.$ All closed curves are oriented positively. $\mathbf{F}=8 x y^{2} \mathbf{j} ,$ and C is the circle of radius 4 about the origin.

What might be the consequences of feudal lords'appointing Church officials instead of the Church?

These squirrels glide from tree to tree at a constant speed, moving in a straight line tipped below the vertical and steadily losing altitude as they move forward. Short and long glides have different profiles. A squirrel in a typical long glide covers a horizontal distance of 16 m while losing 8.0 m of elevation. During this glide, a. What is the angle of the squirrel's path below the horizontal? b. What is the total distance covered by the squirrel?

Write the fraction in simplest form.

$$\frac { 6 } { 26 }$$

Give the transfer function of a second-order bandpass filter with a center frequency of $10^{5} \mathrm{rad} / \mathrm{s},$ a center-frequency gain of 10, and a 3-dB bandwidth of $10^{3}\ \mathrm{rad} / \mathrm{s}.$

Find the slope of the line through each pair of points. $\left(\frac{1}{6}, \frac{1}{2}\right)$ and $\left(\frac{5}{6}, \frac{9}{2}\right)$

The sum of the squares of two consecutive even integers is 1252. Find the integers.

Use the slope–intercept form to write an equation of the line that has the given slope and passes through the given point. Slope 7; passes through (-7, 5)

¿Quien es? A.Complete the sentences below with the correct family relationships
Mis... son los hijos de mis padres.

Solve by graphing. State the solutions. $y=\frac{1}{4} x^{2}-4 ; x^{2}+y^{2}=16$

Solve each inequality. $30\geq t+45$