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=
1 answer:
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Answer: There are 60 ways that they can travel to the concert.
Step-by-step explanation:
Since we have given that
Number of people want to go to a concert = 12
Number of cars = 3
Number of drivers in the group = 5
So, using the "Fundamental theorem of counting":
We get that
Hence, there are 60 ways that they can travel to the concert.
Answer:
(A)(12, 9)
Step-by-step explanation:
Given:
The beginning of the left edge of the stencil falls at (2, −1).
A point, say Q on the stencil is at (4, 1).
Point Q divides the stencil into the ratio 1:4.
We are required to find the end of the stencil.
Mathematically, Point Q divides the stencil internally in the ratio 1:4.
For internal division of a line with beginning point and end point
in the ratio m:n, we use the formula
,
, Q(x,y)=(4,1), m:n=1:4
Therefore:
The correct option is A.
Answer:
All three operations lead to polynomials.
See explanations below.
Step-by-step explanation:
Polynomial a =
Polynomial b =
Therefore:
a + b =
where we have combined all like terms. This is clearly another polynomial (of grade 2)
a - b (here we need to flip all signs inside the parenthesis when we remove this grouping symbol):
which is clearly another polynomial (but of grade 3)
a * b : (here we use distributive property to multiply each term of the first polynomial by each term of the second one, and then combine like terms)
which is indeed another polynomial (this time of grade 6)