Underline the main clause in given sentence. Then circle the subordinate clause.
If the door is open, you can go right into the house.

Will two limp pieces of paper held a few inches apart come closer together or move farther apart if you blow between them? Explain.\s* Q31. A gust of wind blows sideways across an open outward-swinging door. Will the door slam shut or swing open as a result of this? Explain.

Manganese is available from its ore pyrolusite, which is manganese(IV) oxide, $\mathrm{MnO}_2$. Some manganese metal is prepared from $\mathrm{MnO}_2$ by reduction with aluminum metal. Write the balanced equation for this reduction.

In the half-reaction $\mathrm{NO}_{3}^{-} \rightarrow \mathrm{NH}_{4}^{+}$, on which side of the equation should electrons be added? Add the correct number of electrons to the side on which they are needed, and rewrite the equation.

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?

Knowing that d = 1.2 in., determine the torque T that causes a maximum shearing stress of $7.5\ \text{ksi}$ in the hollow shaft shown.

If you leave me refrigerator door open and the refrigerator runs continuously, does the kitchen get colder or warmer? Explain.

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.

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.

When the growth of a spherical cell depends on the flow of nutrients through the surface, it is reasonable to assume that the growth rate, $d V / d t$, is proportional to the surface area, S. Assume that for a particular cell $d V / d t=\dfrac{1}{3} \cdot S$. At what rate is its radius $r$ increasing?

Suppose that the force is applied perpendicular to the torque arm. Given: $\tau=35.7\ \mathrm{lb}\ \mathrm{ft}$ $r=0.0240 \mathrm{ft}$

$$F= ?$$

Garage door openers originally had a series of four on/off switches so that homeowners could personalize the frequencies that opened their garage doors. If all garage door openers were set at the same frequency, anyone with a garage door opener could open anyone else's garage door.

3. How many different positions are possible with 8 consecutive on/off switches?

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.

The table lists the measurements of a lot bounded by a stream and two straight roads that meet at right angles, where x and y are measured in feet.

Use the model in part (a) to estimate the area of the lot.