The Isosceles Triangle Angle Bisector to Congruent Sides Theorem states: "In an isosceles triangle, the angle bisectors to the congruent sides are congruent." Draw and label a diagram you can use to help you prove this theorem. State the "Given" and "Prove" statements.

Fill in each blank so that the resulting statement is true. The circumference, C, of a circle with radius r is given by the formula ____.

What is the physical significance of the Reynolds number? How is it defined for (a) flow in a circular pipe of inner diameter D and (b) flow in a rectangular duct of cross section $a imes b?$

Draw and label a diagram of the eastern horizon from northeast to southeast and label the rising point of the sun at the solstices and equinoxes.

Briefly explain the importance of each of the following. command economy

Compare exponential growth and exponential decay.

In an x-ray tube, if the energy with which the electrons strike the metal target is increased, the wavelengths of the characteristic x-rays do not change. Why not?

represent the complex number graphically. Then write the trigonometric form of the number. 2√2 - i

Find the x-coordinates of all local extrema. $f(x)=x^{5}-2 x^{2}+x$

(a) Calculate the potential energy of the interaction between two linear quadrupoles when they are collinear and their centres are separated by a distance r. (b) Calculate the potential energy of the interaction between two linear quadrupoles when they are parallel and separated by a distance r.

Which element would you expect to have the largest second ionization energy, $\mathrm{Na}, \mathrm{C}$, or $\mathrm{F}$ ? Why?

Bearcat Construction begins operations in March and has the following transactions.

$$\begin{array}{llllll} \text{March 1} & \text{Issue common stock for \$21,000.}\\ \text{March 5} & \text{Obtain \$9,000 loan from the bank by signing a note.}\\ \text{March 10} & \text{Purchase construction equipment for \$25,000 cash.}\\ \text{March 15} & \text{Purchase advertising for the current month for \$1,100 cash.}\\ \text{March 22} & \text{Provide construction services for \$18,000 on account.}\\ \text{March 27} & \text{Receive \$13,000 cash on account from March 22 services.}\\ \text{March 28} & \text{Pay salaries for the current month of \$6,000.}\\ \end{array}$$

Let F be the step function such that F(t)=n for $t \in[n, n+1)$, n an integer. Calculate (a) $\int_{0}^{6} x d F(x)$, (b) $\int_{0}^{3} x^{2} d F(x)$, (c) $\int_{1 / 4}^{\pi / 4} x^{2} d F(x)$.

Express each expression in simplest form with only positive exponents. $6 L^{-2}-4 C^{-1}$