Let er be the unit radial vector and r=x2+y2+z2−−−−−−−−−−√. Calculate the integral of F=e−rer over: (a) The upper-hemisphere of
x2+y2+z2=25 , outward-pointing normal (b) The region on the sphere of radius r=5 centered at the origin that lies inside the first octant x,y,z≥0 (a) ∬SF⋅dS=
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The linear function which represents the line given by the point-slope equation is (B) .
- The word linear function in mathematics refers to two distinct but related concepts.
- A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
To find the linear function which represents the line given by the point-slope equation:
Given:
Distribute the right side:
Adds 8 on both sides:
Convert to function notation:
Therefore, the linear function which represents the line given by the point-slope equation is (B) .
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The complete question is given below:
Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals start fraction one-half end fraction left-parenthesis x minus 4 right-parenthesis. (x – 4)?
A) F(x) = f(x) equals StartFraction one-half EndFraction x plus 4.X + 4
B) f(x) = f(x) equals StartFraction one-half EndFraction x plus 6.
C) X + 6 f(x) = f(x) equals StartFraction one-half EndFraction x minus 10.X –10
D) f(x) = f(x) equals StartFraction one-half EndFraction x minus 12.X – 12