Find any domain restrictions on the given rational equation
2 answers:
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Answer:
a) (x, y, z) = (1, -1, 0)
b) a = 0; L = {t, t, 0}
c) a = 1 . . or . . a = 3
d) No
Step-by-step explanation:
a) The solution using row-reduction techniques is shown in the first attachment, part (a). The generic solution is shown evaluated for a=2, the result being (1, -1, 0).
You will note that the solution gives indeterminate values for a=1 and a=3, which make the denominators zero.
b) For this, we use the point solution of part (a) together with the cross product of the normal vectors of planes 1 and 2. Said cross product will be in the direction of their line of intersection. We substitute the parametric equation for that line into the equation for plane 3 and solve for <em>a</em>. The result is a = 0.
The simplification of the resulting equation also gives a=1 and a=3, but we treat those as extraneous solutions because the corresponding common point of intersection of the planes does not exist.
c) The values a = 1 and a = 3 were found in part (a). These are values of <em>a</em> that make the common point indeterminate.
d) Substituting the given values for (x, y, z) gives three equations for <em>a</em> that have 3 different solutions. Hence there cannot be a value of <em>a</em> that makes this be a common point of intersection.
e) The second attachment illustrates part (a), with <em>a</em>=2. The third attachment illustrates part (b) with <em>a</em>=0.
The fourth attachment illustrates part (c). The first picture has the triangular tunnel between the planes in a vertical orientation (<em>a</em>=1). The second picture has the triangular tunnel extending from lower front to upper back (<em>a</em>=3).
Answer:
Option D. 10,779 feet
Step-by-step explanation:
Given from the figure attached,
PT = OB = 7000 ft
PB = OT = x feet
and angle of elevation (∠POT) = 30°
By applying Tan rule in the triangle POT,
tan33° = =
tan33° =
x =
x = 10779 feet
Therefore, distance between the bird (B) and plane (P) is 10,779 feet.
Option D. will be the answer.
Answer:
B
Step-by-step explanation:
The range is the set of y-values for which the function is defined.
** Attached is the graph of the function
By looking at the graph, we can clearly see that there aren't any y-values that is not permitted in the graph. The function is defined for all y-values. Hence the range is set of all real numbers, or, the range is (-∞, +∞)
Answer choice B is right.
