Answer:
P ( -1, -3)
Step-by-step explanation:
Given ratio is AP : PB = 3 : 2 = m : n and points A(5,6) B(-5,-9)
We will calculate coordinates of the point P which divides line segment AB in the following way:
xp = (n · xa + m · xb) / (m+n) = (2 · 5 + 3 · (-5)) / (3+2) = (10-15) / 5 = -5/5 = -1
xp = -1
yp = (n · ya + m · yb) / (m+n) = (2 · 6 + 3 · (-9)) / (3+2) = (12-27) / 5 = -15/5 = -3
yp = -3
Point P( -1, -3)
Answer:
5.4.
Step-by-step explanation:
If we divide 2 by 5 we get 0.4
So 5 and 2/5 = 5.4
Answer:
1) False
2) False
3) True
4) False
Step-by-step explanation:
1) Flase, {v1,v2,v3, ..., vp} is a base for H when they span H and also they are linearly independent.
2) False. A single nonzero vector is linearly independent , not dependent. There is not null linear combination that gives 0 as a result involving that vector.
3) True, if the columns werent linearly independent, we could triangulate the matrix and obtain 0, so the matrix wouldnt be invertible. This means that the columns should be linearly independent for the matrix to be invertible and as a consecuence, they will spam a subspace of R^n of dimension n, which means that they will spam all R^n and therefore, they form a basis of R^n.
4) False. A basis is a spanning set that is as small as possible. Larger spanning sets will have extra elements apart from those who can form a base toguether. Those elements will make the set linearly dependent.
-6 minus 6=0 i think it is correct
Answer:
3040000mm³
Step-by-step explanation:
Volume of a cube = a³ ; a = size of edge
Volume of cubical tank = 12³ = 12 * 12 * 12 = 1728 cm³
Half filled cube = 1728 / 2 = 864 cm³
Volume is f rectangular tank :
V = length * width * height
V = 10 * 8 * 7 = 560 cm³
Volume of water left in cubical tank :
(864 - 560) = 304cm³
1cm³ = 1000mm³
304cm³ = 304 * 1000 = 3040000mm³
