For Exercises 49-51, an equation of a conic section (nondegenerative case) is given. a. Identify the type of conic section. b. Determine an acute angle of rotation to eliminate the x y term. c. Use a rotation of axes to eliminate the x y term in the equation. d. Sketch the graph. 47 x 2 + 34 3 x y + 13 y 2 − 64 = 0
For Exercises 49-51, an equation of a conic section (nondegenerative case) is given. a. Identify the type of conic section. b. Determine an acute angle of rotation to eliminate the x y term. c. Use a rotation of axes to eliminate the x y term in the equation. d. Sketch the graph. 47 x 2 + 34 3 x y + 13 y 2 − 64 = 0
Solution Summary: The author explains that the conic section is an equation of a hyperbola.
For Exercises 49-51, an equation of a conic section (nondegenerative case) is given.
a. Identify the type of conic section.
b. Determine an acute angle of rotation to eliminate the
x
y
term.
c. Use a rotation of axes to eliminate the
x
y
term in the equation.
d. Sketch the graph.
47
x
2
+
34
3
x
y
+
13
y
2
−
64
=
0
Curve that is obtained by the intersection of the surface of a cone with a plane. The three types of conic sections are parabolas, ellipses, and hyperbolas. The main features of conic sections are focus, eccentricity, and directrix. The other parameters are principal axis, linear eccentricity, latus rectum, focal parameter, and major and minor axis.
=
Q6 What will be the allowable bearing capacity of sand having p = 37° and ydry
19 kN/m³ for (i) 1.5 m strip foundation (ii) 1.5 m x 1.5 m square footing and
(iii)1.5m x 2m rectangular footing. The footings are placed at a depth of 1.5 m
below ground level. Assume F, = 2.5. Use Terzaghi's equations.
0
Ne
Na
Ny
35 57.8 41.4 42.4
40 95.7 81.3 100.4
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Elevation, m 0.5 2
2 6.5 9.5 13 18 25
No.of blows, N 11 15 29 32 30 44
0
estigate shear
12%
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Elementary Statistics: Picturing the World (7th Edition)
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