1. Cara monitors a snail in her aquarium. She notes that this morning it crawled 1” up the glass. A few hours later it crawled another 2” up the glass. Later, it crawled 4” down the glass. How far is the snail from where it started?
2. Henry starts the day with $30. He and his sister go to the fair. He pays for his own admission of $10,but fails to notice that $15 falls out of his wallet while he is paying. His sister lends him $10 so that he can still enjoy the fair. Write the equation that illustrates his day’s financial events.
3. Karen opens a credit account to purchase a new bed. She makes a down payment of $200 on a $1,000 bed. What is her financial situation?
4. Felicia owes her Dad $5.00. She earns $12.00 doing chores. How much did Felicia receive after her Dad took out what she owed him?
5. An elevator started at the first floor and went up 18 floors. It then came down 11 floors and went back up 16. At what floor was it stopped?
6. At midnight, the temperature was 30° F. By 6:00 a. m., it had dropped 5° and by noon, it had increased by 11°. What was the temperature at noon?
7. Some number added to 5 is equal to -11. Find the number.
8. From the top of a mountain to the floor of the valley below is 4,392 feet. If the valley is 93 feet below sea
level, what is the height of the mountain?
9. During one week, the stock market did the following: Monday rose 18 points, Tuesday rose 31 points, Wednesday dropped 5 points, Thursday rose 27 points and Friday dropped 38 points. If it started out at 1,196 on Monday, what did it end up on Friday?
10. An airplane started at 0 feet. It rose 21,000 feet at takeoff. It then descended 4,329 feet because of clouds. An oncoming plane was approaching, so it rose 6,333 feet. After the oncoming plane passed, it descended 8,453 feet, at what altitude was the plane flying?
11. Some number added to -11 is 37. Divide this number by -12. Then, multiply by -8. What is the final number?
12. Jim decided to go for a drive in his car. He started out at 0 miles per hour (mph). He then accelerated 20 mph down his street. Then, to get on the highway he accelerated another 35 miles per hour. A car was going slow in front of him so he slowed down 11 mph. He then go off the highway, so he slowed down another 7 mph. At what speed is he driving?

2

step-by-step explanation:

here we can see that the storage increases

at certain times of the year - during the

warmer months, when the gas is not much

used for heating and reserves can be

increased - and then decreases during the

colder months because the supply is being

used. it is possible to model this with a

relatively simple trigonometric graph, but

first we examine the simplest trig curves.

065/065.html

the basics

the simplest sine and cosine curves can be generated by plotting the trig-function values

against the angles used in each function. the values can be found in the chart below:

ø (˚) 0 30 45 60 90 120 135 150 180 210 225 240 270 300 315 330 360

sin ø

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0 1

2

2

2 3

2 1 3

2 2

2 1

2

0 − 1

2

− 2

2 − 3

2 − 1 − 3

2 − 2

2 − 1

2

0

cos ø

€

1 3

2 2

2 1

2 0 − 1

2

− 2

2 − 3

2 − 1 − 3

2 − 2

2 − 1

2

0 1

2 2

2 3

2 1

first we plot the sine data, letting the x-axis represent the angles and the y-axis the sine

values. the result is the scatter plot below.

based on just these 17 data points, we can see

that the function is following a straightforward

pattern - the sine values are increasing to 1,

decreasing through the same values to -1, then

returning to zero. when we connect the dots, we

get the periodic curve y = sin (x) below.

this “sine curve,” with equation

y = sin(x), is the simplest of trig

graphs. the curve rises and falls by

one unit from its “axis of

oscillation” - in this case, the x-axis

- and after we cycle through 360˚ it

appears we are ready to go through

the same y-values again. we can see

this same pattern in the cosine

function on the following page.

each sine and cosine curve has two basic characteristics:

amplitude - distance the curve rises above, and falls below, its axis of oscillation (marked by

the vertical arrows on the cosine graph). the formula is

€

amp = max− min

2 .

period - the length of one cycle (marked by the horizontal arrows on the cosine graph).

this can be calculated by measuring the distance between any successive maximum

points (or minimum points), or by doubling the horizontal distance between a

minimum and the next maximum.

for our first two curves, then, the amplitude is 1 and the period is 360˚ (or 2! if we are in radians).

adjusting the amplitude and frequency: y = a sin(bx), y = a cos(bx)

now that we have our “base” amplitude and frequency . . let’s change them. we can adjust both

characteristics by introducing the parameters a and b into the equations. the graph below shows the

curves y = a sin(x) for a = 1,2,3, and -0.5, with the original curve y = sin(x) being the thickest line.

clearly the amplitude of the curves has changed;

when a = 2, the amplitude is 2; when a = 3, the

amplitude is 3; and when a = -0.5 the amplitude is

0.5 (since amplitude, a distance, must be positive).

however, this last curve has also been flipped upside

down (or “reflected in the x-axis”). since the

amplitude must be positive even when a itself is

negative, we have the formula

amplitude = | a |.

the relationship between the b-value and the

period is not so straightforward. on the right

we have y = cos(bx) for b = 1,3, and 0.5. (the

thickest line is again our “base” curve.) when

b=3, the period decreases to 120˚; when

b=0.5, the period increases to 720˚ (so only

half the curve is shown here). we can describe

this reciprocal relationship with the formula

€

b = 360

period or

€

b = 2π

period ,

using the latter if we are working in radians.

shifting horizontally and vertically: y = sin(x-h) + k, y = cos(x-h) + k

to shift (or “translate”) a curve along either the x- or y-axis (or both), we introduce the parameters

h and k. below we have the graph of y = sin (x - 30) + 2 and y = sin(x). (note that we have returned

to an amplitude of 1 and period of 360˚). our original

curve y = sin(x) had its peak at the point (90,1); the

shifted curve has its corresponding peak at (120, 3). in

the same way, the original curve had a minimum value

at (270, -1); now the minimum is at (300,1). and

finally, the axis of oscillation has shifted vertically

from the line x = 0 to the line x =2. in other words, our

new curve has been created by shifting y = sin(x) right

30 and u p 2. and, in general, we can create the

following shifts:

horizontal shift = h (left if h < 0, right if h > 0)

vertical shift/new axis of oscillation = k.

modelling data: y = a sin[b(x-h)] + k, y = a cos[b(x-h)] + k

we have seen how the basic sine and cosine curves can be adjusted: by changing the amplitude

and period, and by shifting the curves horizontally and vertically. a summary is below.

amplitude = | a | vertical shift/axis of oscillation = k

period =

€

360

b

or

€

2π

b

c) the median for town a 30" is greater than the median for town b 25"

step-by-step explanation:

town a, median = q2 = 30

town b, median - q2 = 25

so the median for town a 30" is greater than the median for town b 25"