Consider the curve given by the equation y^2 - 2x^2y = 3
a) Find dy/dx.
b) Write an equation for the line tangent to the curve at the point (1, -1).
c) Find the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal. d) Evaluate d 2y /dx2 at the point (1, -1).
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complete the following activities with these cricket chirp data.
Temperature (F degree) 69.7, 93.3, 84.3, 76.3, 88.6, 82.6, 71.6, 79.6
Chirp in 1 minute 882, 1188, 1104, 864, 1200, 1032, 960, 900
1. Find the regression models (linear and quadratic) for the above data
a. What is the equation for the line of best fit in y=mx+b form?
b. What is the equation for the best fitting quadratic model?
2. Use your models (not the actual data) and calculators to predict the number of chirps at each of the three temperatures.
| Linear | Quadratic | |
| 69.7 | ||
| 76.3 | ||
| 88.6 |
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Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Passing through ( −3,−4) and (2,6)
What is the equation of the line in point-slope form?
__
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
What is the equation of the line in slope-intercept form?
__
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
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A conical container of radius 10ft and height 40ft is filled to a height of 38 ft of a liquid weighing 62.4 lb/ft^3. How much work will it take to pump the contents to the rim? How much work will it take to pump the liquid to a level of 2 ft. above the cone's rim?
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| Let f (t) =
|
| (a) | f (t) can be written in the form g1(t) + g2(t)U(t − 2π) + g3(t)U(t − 4π) where U(t) is the Heaviside function. Enter the functions g1(t), g2(t), and g3(t), into the answer box below (in that order), separated with commas. |
| (b) | Compute the Laplace transform of
f (t). |
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Maximization by the simplex method
Solve the following linear programming problems using the simplex method.
1>.
Maximize z = x1 + 2x2 + 3x3
subject to x1 + x2 + x3 ≤ 12
2x1 + x2 + 3x3 ≤ 18
x1, x2, x3 ≥ 0
2>.
A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?
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diameter: 1.90, 3.30, 4.23, 6.04 and 6.60 and their corrosponding circumferences are 5.93, 10.45, 13.30, 18.45 and 21.20 respectively (Note: both are measured in centimeters). Now, use these data to obtain the following:
1. Plot c vs. d, obtain the equation of straight line and list the value of slope.
2. Perform the LINEST, and hence find the slope, the uncertainty in slope, y-intercept and the uncertainty in y-intercept.
3. Finally, find the % error in pi by comparing the slope from linest with the known value of pi (=3.14).
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How can you determine if two lines are parallel, perpendicular, or neither ?
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Test Review
Part I
In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-3x-9) + 1.
In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-3x+9) + 4
Part II
Convert the complex number from rectangular form to polar form.
Show all work for full credit.
z = -14 + 8i
Solve for all roots of the equation. Show all work for full
credit.
x3 + 216 = 0
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a.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=1/x, y=1/x, y=0, y=0, x=1, x=1, and x=3x=3 about the xx-axis.
b.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x^2 and y^2=x about the x-axis.
c.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves x= y - y^2 and x= 0 about the y-axis
d.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y^2= x and x = 2y about the y-axis
e.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y = x ,y= 0, x = 2, and x= 4 about the line x = 1
e.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y = x and y= sqrt(x)
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|
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Question : y'''+4y' =0 , y'''-2y''+4y'-8y=0 , y'''-3y''+3y'-y=0 , y^4 -4y'''+6y''-4y+y=0 , y^4+6y''+9y=0 , y^6+y'''=0
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| Two linearly independent solutions of the following
equation (1 − x) y″ + x y′ − y = 0 are y1(x) = 4ex and y2(x) = 8x. |
| (a) | Find the Wronskian W(y1, y2) of y1 and y2. |
| (b) | Using the method of variation of parameters, find a particular
solution of (1 − x) y″ + x y′ − y = 2(x − 1)2 e −x |
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