In Exercise, use the differential equation for a leaking container, Eq. $\frac{d y}{d t}=-\frac{B \sqrt{2 g y}}{A(y)}$

At t=0, a conical tank of height 300 cm and top radius 100 cm [Figure] is filled with water. Water leaks through a hole in the bottom of area $B=3 \mathrm{~cm}^2$. Let y(t) be the water level at time t.

(a) Show that the tank's cross-sectional area at height y is $A(y)=\frac{\pi}{9} y^2$.

(b) Solve the differential equation satisfied by y(t)

(c) How long does it take for the tank to empty?

Consider which magma properties and rock-forming processes control the grain size, color, and specific gravity of an igneous rock. Which two of these properties have a common cause and are related to one another? Explain. (This connection will be helpful later when you are identifying igneous rocks.)

It is a short step from understanding how cooling rate affects grain size to deriving the basic rules of how magma and lava cool in nature. Three simple thought experiments will help you understand the cooling process.

Imagine you have two balls of pizza dough 20 cm in diameter. As shown in the figure on the right, one is rolled out to form a crust 1 cm thick and 50 cm in diameter. Both pieces of dough still have the same mass and volume, even though their shapes are very different. Both are baked in a $450^{\circ} \mathrm{F}$ oven for 20 minutes and removed. (i) Which will cool faster, the large cube or one of the small cubes? Why?

For each of the following shapes, determine which of the following descriptions apply.

S : simple closed curve

C : convex, simple closed curve

N: n-gon

Discuss the three modes of prenatal nutrition; what distinguishes the trophoblastic from the placental phases of nutrition; and the timetable on which these develop and overlap.

What is the most common prenatal infection?
a) Rubella
b) HIV
c) Cytomegalovirus
d) Albinism

If another student put shapes 2,4 , and 5 together because "they all have a right angle," at what van Hiele level is the student thinking?

The DNA nucleotide guanine (G) forms a complementary base-pair with which nucleotide?

A adenine (A)
B cytosine (C)
C thymine (T)
D guanine (G)
E uracil (U)

The figure below is an outcrop map of an area showing several different rock layers and their attitudes. Using the structural information available on the map and the stratigraphic column, draw a geologic map that shows the contacts between the rock units present. Note that in a few outcrop areas, a contact is visible.

Completing an Outcrop Map

A geologist has just finished mapping a few square kilometers. She has drawn the approximate shapes of outcrops, has plotted strike and dip measurements, and has located contacts where they were exposed. Complete the map by extrapolating contacts across the covered areas and by adding appropriate symbols for folds, if they are present. When you have completed the map, describe the basic structure of the map area in words using the space provided here.

Structural Description:

The truncated conical container shown here is full of strawberry milkshake which has a density of 0.8 $\mathrm{~g} / \mathrm{cm}^3$. As you can see, the container is $18 \mathrm{~cm}$ deep, $6 \mathrm{~cm}$ across at the base, and $9 \mathrm{~cm}$ across at the top (a standard size at Brigham's in Boston). The straw sticks up $3 \mathrm{~cm}$ above the top. About how much work does it take to suck up the milkshake through the straw (neglecting friction)?

Look carefully at the shapes you created in problem 5-85 that can be cut and rearranged into rectangles.

a. Circle those shapes. What are they called?

b. What lengths would you need to know to find the area of each rectangle? Where can you find those lengths on the parallelograms before you rearrange them into rectangles? Draw and label them on your circled sketches.

c. How is the area of each parallelogram that you circled related to the area of the two triangles that made it?

d. Darla created the shape at right out of two triangles and has measured and labeled some of the lengths. Which measurements should she use to find the area of the shaded triangle? What is the area of the shaded triangle?

e. Where else could you draw the height on Darla's shape?

A company manufactures and sells in-line skates. Its financial department has established the price demand function

$$p(x)=190-0.013(x-10)^2 \quad 10 \leq x \leq 100$$

where $p(x)$ is the price at which $x$ thousand pairs of in-line skates can be sold.

(A) Describe how the graph of function $p$ can be obtained from the graph of one of the basic functions in the given figure.

B) Sketch a graph of function $p$ using part (A) and a graphing calculator as aids.

The handrails for a steel staircase form a parallelogram ABCD. Additional bars are needed one third and two thirds of the way up the stairs. Explain why the additional bars must be the same length as the end bars.

The Koch snowflake is a fractal shape. At level 0, the shape is an equilateral triangle At level 1, each line segment is split into four equal parts, producing an equilateral bump in the middle of each segment. below Figure shows these shapes at levels 0, 1, and 2. At the top level, the script uses a function drawFractalLine to draw three fractal lines. Each line is specified by a given distance, direction (angle), and level. The initial angles are 0, 2120, and 120 degrees. The initial distance can be any size, such as 200 pixels. The function drawFractalLine is recursive. If the level is 0, then the turtle moves the given distance in the given direction. Otherwise, the function draws four fractal lines with one-third of the given distance, angles that produce the given effect, and the given level minus 1. Write a script that draws the Koch snowflake.

An electron (charge $-1.60 \times 10^{-19} \mathrm{C}$ ) moves at $2.20 \times 10^5 \mathrm{~m} / \mathrm{s}$ through a uniform 1.55 T magnetic field that points in the +y direction. The velocity of the electron lies in the xy-plane and is directed at $40.0^{\circ}$ to the +x axis and $50.0^{\circ}$ to the $+y$-axis. Find the direction of the magnetic force on the electron.