X=a y=b x + y = k x – y = k ax = y –ax = y y=x2 x·y = k
Mth 86 Exam 3 Practice Franz Helfenstein NAME
Show your work. It must be neat and organized with answers simplified and boxed in for full credit. Use a ruler to draw straight lines. Label all axis. Put scales on all graphs. Use two decimal accuracy.
|1) (a) Graph: 6x + 5y = -12 |[pic] |
|(b) Graph: y = x + 8 | |
|(c) Give the lines' intersection ( , ) | |
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|(d) Graph y = | |
|(e) Give the y-intercept. y = | |
| | |
|(f) Give the max coordinates. ( , ) | |
2) There are 3 roots for y = 0.1x3 – 2x2 + 3. Find all three and give their coordinates.
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3) For #2, what value of x will give y = 5? x =
4) Give the slope of the line which passes through (-4.6 , 8.2) & (2.5 , -4.6).
5) Give the equation of the line (in slope-intercept form) that passes through (-10, 26) and (15, 11)
|6) Give the equation of this line in slope-intercept form. |[pic] |
|7) Give the equation of this line in slope-intercept form. |[pic] |
Graph the following two equations in the proscribed region. You graph must cross the boundary correctly.
|8) y = 0.5 x – 2750 |9) y = -9.45 x + 2740 |
|[pic] |[pic] |
|10) Consider the plot of Joe's Trip. |[pic] |
|(a) What are the units of the slope? | |
| | |
|(b) Give a short story that could produce this graph. | |
| |[pic] |
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|11) Consider the case where time is plotted on the x-axis and population numbers are plotted on the y-axis. | |
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|Give a narrative interpretation of: | |
(b) positive slope? (c) negative slope? (d) zero slope?
|12) Use your calculator's linear regression feature to find the "best fit" linear equation for this data in |x |y |
|slope-intercept form. |0 |20.3 |
| |10 |28.3 |
|a) y = |20 |32.2 |
| |30 |42.1 |
|b) Using the equation, what is the y-value when x is 100? y = |40 |45.6 |
| |50 |52.5 |
|c) Using the equation, what x-value will yield y = 0? x = | | |
13) This data represents mercury concentration found in the sea bottom of Lake Superior.
|Depth (cm) |0 |
d) Using your regression equation, give the sediment depth at which the mercury level drops to 10 ppb
See last page for graphing hints and answers.
Note: Problem 13 does not make sense as an exponential. It should be a quadratic. y = ax2 + bx + c
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|1) |[pic] |[pic] |[pic] |
| |enter equations |set window |graph |
| |[pic] |[pic] |[pic] |
| |modify window |graph |find intersection |
| | | |[2nd] [TRACE] 5:intersection |
| |[pic] |[pic] |[pic] |
| |enter new equation |set window |graph |
| |[pic] |[pic] | |
| |find y value at x = 0 |find maximum | |
| |[2nd] [TRACE] value |[2nd] [TRACE] 4:MAXIMUM | |
|2) |[pic] |[pic] |[pic] |
| |enter new equation |graph |modify window to see 3 roots |
|2) |[pic] |[pic] |[pic] |
| |graph |find roots |guess closest to desired root |
| | |[2nd] [TRACE] 2:zero |root at x ≈ 19.92 |
| | |bracket desired root | |
| |[pic] |[pic] |[pic] |
| |enter y = 5 |graph |find intersection |
|8) |[pic] |[pic] | |
| |set window |enter equation and graph | |
|9) |[pic] |[pic] | |
| |set window |enter equation and graph | |
|12) |[pic] |[pic] |[pic] |
| |enter data, run regression |modify window |we see both x = 100 and y = 0 |
| |graph | | |
| |[pic] |[pic] | |
| |[2nd] [TRACE] 1:value, X=100 |[2nd] [TRACE] 2:zero | |
|13) |[pic] | | |
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