5. Find the two sets of coordinates of the intersection of the straight line y = mx + b, where m= 5 and b = 50, with the parabola y = ax² + bx + c, where a = 1.1, b = -2.3 and c = -30.5. Make a chart of the two series to show the intersections.
5. Find the two sets of coordinates of the intersection of the straight line y = mx + b, where m= 5 and b = 50, with the parabola y = ax² + bx + c, where a = 1.1, b = -2.3 and c = -30.5. Make a chart of the two series to show the intersections.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![5. Find the two sets of coordinates of the intersection of the straight line y = mx
+ b, where m= 5 and b = 50, with the parabola y = ax² + bx + c, where a =
1.1, b = -2.3 and c = -30.5. Make a chart of the two series to show the
intersections.
6. Find the two sets of coordinates of the intersection of the straight line with y
= h and the circle of radius r (the equation of a circle is x² + y² = r; thus
y = √√√1-x²). For example, user = 1 and h = some value between 0 and 1.
The intersections will be at x, y = h and -x, y = h. Make a chart to show the
circle (values of x from -1 to 1 and calculated values of y, also same values
of x and -y).
7. Having solved problem #8, and having created the chart, use the values of the
intersections to create a chart series that shows the circumscribed rectangle
(four sets of coordinates: x, y = h; -x, y = h; x, y = -h; -x, y = -h). Use any
suitable method to find the coordinates of the circumscribed square.
8. For the chemical reaction
2A B + 2C
the equilibrium constant expression is
K =
[B][C]²
For this reaction, the value of the equilibrium constant K at a certain
temperature is 0.288 mol L-¹.
A reaction mixture is prepared in which the initial concentrations are [A] = 1,
[B] = 0, [C] = 0 mol L. From mass balance and stoichiometry, the
concentrations at equilibrium are [A] = 1 − 2x, [B] = x, [C] = 2x mol L−¹,
4x3
from which the expression for K is
Find the value of x that
1-4x-4x²
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Transcribed Image Text:5. Find the two sets of coordinates of the intersection of the straight line y = mx
+ b, where m= 5 and b = 50, with the parabola y = ax² + bx + c, where a =
1.1, b = -2.3 and c = -30.5. Make a chart of the two series to show the
intersections.
6. Find the two sets of coordinates of the intersection of the straight line with y
= h and the circle of radius r (the equation of a circle is x² + y² = r; thus
y = √√√1-x²). For example, user = 1 and h = some value between 0 and 1.
The intersections will be at x, y = h and -x, y = h. Make a chart to show the
circle (values of x from -1 to 1 and calculated values of y, also same values
of x and -y).
7. Having solved problem #8, and having created the chart, use the values of the
intersections to create a chart series that shows the circumscribed rectangle
(four sets of coordinates: x, y = h; -x, y = h; x, y = -h; -x, y = -h). Use any
suitable method to find the coordinates of the circumscribed square.
8. For the chemical reaction
2A B + 2C
the equilibrium constant expression is
K =
[B][C]²
For this reaction, the value of the equilibrium constant K at a certain
temperature is 0.288 mol L-¹.
A reaction mixture is prepared in which the initial concentrations are [A] = 1,
[B] = 0, [C] = 0 mol L. From mass balance and stoichiometry, the
concentrations at equilibrium are [A] = 1 − 2x, [B] = x, [C] = 2x mol L−¹,
4x3
from which the expression for K is
Find the value of x that
1-4x-4x²
.
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