Building Quadrilaterals Now use strands of spaghetti to conduct this quadrilateral-building experiment at least three times. Keep a record of your findings, including sketches of the shapes you make.

• Mark any three points along the length of a strand of spaghetti and break the spaghetti at those three points.
• Try to build a quadrilateral with the pieces end-to-end.
• If a quadrilateral can be built, try to build another, differently shaped quadrilateral with the same side lengths.

a. Was it possible to build a quadrilateral in each case? If a quadrilateral could be built, could you build a differently shaped quadrilateral using the same four segments? Compare your findings with those of others.

b. If a quadrilateral can be built from four side lengths, how are the side lengths related? Use a ruler and compass to test your conjecture for segments of length $3 \mathrm{~cm}, 5 \mathrm{~cm}, 8 \mathrm{~cm}$, and $10 \mathrm{~cm}$. For segments of length $4 \mathrm{~cm}, 4 \mathrm{~cm}, 7 \mathrm{~cm}$, and $15 \mathrm{~cm}$. For segments of length $2 \mathrm{~cm}, 4 \mathrm{~cm}, 8 \mathrm{~cm}$, and $16 \mathrm{~cm}$.

c. Suppose $a, b, c$, and $d$ are consecutive side lengths of any quadrilateral. Write an equation or inequality relating $a, b, c$, and $d$. How many different equations or inequalities can you write relating $a, b, c$, and $d$ ?

d. Write in words the relationship that must be satisfied by the four side lengths of any quadrilateral (do not use letters to name side lengths).

Special Quadrilaterals Quadrilaterals are more complicated than triangles. They bremore sides and more angles you discovered that using the ume four side lengths of a quadrilateral, you could build quite different shapes. Qudriaterals are classified as convex - as in the case of the quadrilateral below on thlefi-or nonconvex-as in the case of the quadrilateral on the right.

The A-36 steel bolt is tightened within a hole so that the reactive torque on the shank AB can be expressed by the equation

$$t = (kx^{2/3}) N · m/m,$$

where x is in meters. If a torque of T = 50 N · m is applied to the bolt head, determine the constant k and the amount of twist in the 50-mm length of the shank. Assume the shank has a constant radius of 4 mm.

An FM radio station broadcasts at a frequency of 98.1 MHz. The power radiated from the antenna is

$$5.0 \times 10 ^ { 4 } \mathrm { W }$$

How many photons per second does the antenna emit?

Using conversion factors, solve the following clinical problem: A nurse practitioner prepares 500. mL of an IV of normal saline solution to be delivered at a rate of 80. mL/h. What is the infusion time, in hours, to deliver 500. mL?

Getting into a car involves these steps. Open the car door. Sit down. Close the door. Buckle the seat belt. Describe the steps you take in getting out of a car. How are they related to the steps involved in getting into a car?

A flow calorimeter is a device used to measure the specific heat of a liquid. Energy is added as heat at a known rate to a stream of the liquid as it passes through the calorimeter at a known rate. Measurement of the resulting temperature difference between the inflow and the outflow points of the liquid stream enables us to compute the specific heat of the liquid. Suppose a liquid of density $0.85 \mathrm{~g} / \mathrm{cm}^3$ flows through a calorimeter at the rate of $8.0 \mathrm{~cm}^3 / \mathrm{s}$. When energy is added at the rate of $250 \mathrm{~W}$ by means of an electric heating coil, a temperature difference of $15 \mathrm{C}^{\circ}$ is established in steady-state conditions between the inflow and the outflow points. What is the specific heat of the liquid?

Predict whether loss of the following E. coli genes would be lethal or not: (a) $dnaB$ (which encodes DnaB), (b) $polA$ (which encodes Pol I), (c) $s s b$, (d) $recA$.

If the competitor leans slightly farther back (increasing the angle between his body and the vertical) but remains stationary in this new position, which statement is true? Assume that the rope remains horizontal.
A. The difference between $T_1$ and $T_2$ increases, balancing the increased torque about his feet that his weight produces when he leans farther back.
B. The difference between $T_1$ and $T_2$ decreases, balancing the increased torque about his feet that his weight produces when he leans farther back.
C. Neither $T_1$ nor $T_2$ changes because no other forces are changing.
D. Both $T_1$ and $T_2$ change, but the difference between them remains the same.

Solve previous problem for the case where the assembly starts from rest with an initial angular acceleration $\alpha=900 \mathrm{rad} / \mathrm{s}^{2}$ as a result of a starting torque (couple) M applied to the shaft in the same sense as N. Neglect the moment of inertia of the shaft about its z-axis and calculate M.

A 5-cm-diameter horizontal jet of water with a velocity of 40 m/s relative to the ground strikes a flat plate that is moving in the same direction as the jet at a velocity of 10 m/s. The water splatters in all directions in the plane of the plate. How much force does the water stream exert on the plate?

Write a balanced equation describing each of the following chemical reactions. (a) Solid potassium chlorate, $\mathrm{KClO}_3$, decomposes to form solid potassium chloride and diatomic oxygen gas. (b) Solid aluminum metal reacts with solid diatomic iodine to form solid $\mathrm{Al}_2 \mathrm{I}_6$. (c) When solid sodium chloride is added to aqueous sulfuric acid, hydrogen chloride gas and aqueous sodium sulfate are produced. (d) Aqueous solutions of phosphoric acid and potassium hydroxide react to produce aqueous potassium dihydrogen phosphate and liquid water.

As you drive by an AM radio station, you notice a sign saying that its antenna is 112 m high. If this height represents one-quarter of the wavelength of its signal, what is the frequency of the station?

Is a student identification number an example of a permutation or a combination?

A soccer player $20.0 \mathrm{~m}$ from the goal stands ready to score. In the way stands a goalkeeper, $1.70 \mathrm{~m}$ tall and $5.00 \mathrm{~m}$ out from the goal, whose crossbar is at $2.44 \mathrm{~m}$ high. The striker kicks the ball toward the goal at $18 \mathrm{~m} / \mathrm{s}$. Determine whether the ball makes it over the goalkeeper and/or over the goal for each of the following launch angles (above the horizontal): (c) $30^{\circ}$.