Describe a situation in real life that can be modeled by an algebraic equation or system of equations. How about one modeled by an inequality or system of inequalities? If it is a situation you read about or saw on television, please give the appropriate citation.
In: Math
The values of certain types of collectibles can often fluctuate greatly over time. Suppose that the value of a particular limited edition figurine is found to be able to be modeled by the function
?(?) = −0.01?4 + 0.47?3 − 7.96?2 + 49.18? + 65 for 0 ≤ ? ≤ 20 where ?(?) is in dollars, t is the number of years after the figurine was released, and ? = 0 corresponds to the year 1999.
a) What was the value of the figurine in the year 2009?
b) What was the value of the figurine in the year 2019?
c) What was the instantaneous rate of change of the value of the figurine in the year 2002?
d) What was the instantaneous rate of change of the value of the figurine in the year 2019?
e) Use your answers from parts a-d to estimate the value of the figurine in 2020.
In: Math
Suppose E and F are two mutually exclusive events in a sample space S with P(E) = 0.34 and P(F) = 0.46. Find the following probabilities.
| P(E ∪ F) | ||
| P(EC) | ||
| P(E ∩ F) | ||
| P((E ∪ F)C) | ||
| P(EC ∪ FC) |
In: Math
(1 point) At what
point does the normal to y=(−1)+2x2y=(−1)+2x2 at
(1,1)(1,1) intersect the parabola a second time?
(
equation editor
Equation Editor
,
equation editor
Equation Editor
)
Hint: The normal line is perpendicular to the tangent line. If two lines are perpendicular their slopes are negative reciprocals -- i.e. if the slope of the first line is mm then the slope of the second line is −1/m
In: Math
Suppose a company has fixed costs of $47,600 and variable cost per unit of 4/9x + 333 dollars,
where x is the total number of units produced. Suppose further that the selling price of its product is
1767 −5/9x dollars per unit.
(a) Find the break-even points. (Enter your answers as a
comma-separated list.)
x =
(b) Find the maximum revenue. (Round your answer to the nearest
cent.)
$
(c) Form the profit function P(x) from the cost
and revenue functions.
P(x) =
Find maximum profit.
$
(d) What price will maximize the profit? (Round your answer to the
nearest cent.)
$
In: Math
Julie recently drove to visit her parents who live 200200 miles away. On her way there her average speed was 99 miles per hour faster than on her way home (she ran into some bad weather). If Julie spent a total of 1010 hours driving, find the two rates.
In: Math
Writing Equations of Lines
Write the slope-intercept form of the equation of the line given the slope and y-intercept.
Slope = -5, y-intercept = -3
Write the slope-intercept form of the equation of the line given the slope and y-intercept.
Slope = -1, y-intercept = 5
Write the slope-intercept form of the equation of the line.
y – 5 = -10(x – 4)
Write the slope-intercept form of the equation of the line.
Write the slope-intercept form of the equation of the line through the given point with the given slope.
Through: (4,-4), slope = 2
Write the slope-intercept form of the equation of the line through the given point with the given slope.
Through: (-5,1), slope = undefined
Write the slope-intercept form of the equation of the line through the given points.
Through: (3,-3) and (4,0)
Write the slope-intercept form of the equation of the line through the given points.
Through: (3,5) and (0,1)
Write the standard form of the equation of the line given the slope and y-intercept.
Slope = -2, y-intercept = -2
Write the standard form of the equation of the line given the slope and y-intercept.
Through: (1,2), slope = 6
In: Math
Find the equation of the ellipse of the form Ax^2+Cy^2+Dx+Ey+F=0 with major axis of lenght 10 and foci have coordinates (8,2) and (0,2).
In: Math
Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume is now 25 ounces with 18 ounces of medicine and 7 ounces of water). How much water must now be added so that the mixture has the same proportion of medicine and water as the original mixture?
_________ ounces
In: Math
A, B, C, D are all matricies
A = 2x3
1 2 −3
−1 4 5
,
B = 2x3
3 0 −1
1 2 1
, C = 2x2
2 5
1 2
,
D = 3x3
1 −1 1
2 −1 2
4 −3 4
Find each of the following or explain why it does not exist.
1) A + B,
2) 2A − 3B,
3) A + C,
4) A − C,
5) AC,
6) CA,
7) AD,
8) DA,
9) C
10) D−1
.
11) Solve the matrix equation CX = B
In: Math
In: Math
Find the two scalars (in C) λ1 and λ2 so that A − λI is singular. For
A = [11 1 -1]
Use the fact that A − λI is singular iff det(A − λI) = 0.
For each λi find a basis for RS(A−λiI). Each basis will consist of a single vector, verify that the two vectors you found are orthogonal.
In: Math
In: Math
Match each table with its equation.
OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal
| Input | Output |
|---|---|
| -2 | -8 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal
| Input | Output |
|---|---|
| -2 | _ |
| -1 | _ |
| 0 | 0 |
| 1 | 1 |
| 4 | 2 |
| 9 | 3 |
OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal
| Input | Output |
|---|---|
| -2 | -0.5 |
| -1 | -1 |
| 0 | _ |
| 1 | 1 |
| 2 | 0.5 |
| 3 | 0.33 |
OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal
| Input | Output |
|---|---|
| -2 | 2 |
| -1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal
| Input | Output |
|---|---|
| -2 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal
| Input | Output |
|---|---|
| -2 | 4 |
| -1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
In: Math
1. Plot each point. Label them A,B,C , and D.
A. (2,-2) B. (-4,0 C. (1.5 5/2) D. ),5)
2. Find the x and Y intercepts of the gien equation and write answers in ordered pair form (x,y). Then graph the equation using these intercepts.
4x-3y=12
X-interceptis:______
Y-Intercepts is:_______
3. Find the slope of the line passing through the given points using the slope formula, then graph the line using the slope found. (3,5) and (-5,6)
m=_________
5. Find the slope and the y-intercept of the line with the given equation. Remember you must first solve this equation for y.
2x=3y=6
M=_________
6. Solve the system of equations by the elimination mehtod. If the lines intersect, identify the point of intersection, if the lines are parallel or coincindent, indicate the appropriate solution.
2x=11y=-10
5x=4y=22
7. Use the point-slope form of a linear equation y-y1=m(x-x1 ) to write the equation of the line with the given slope and point. Write your final answer in the slope-intercept form of a linear.equation y=mx+b.
Slopee=2 and passes through (3,5)
In: Math