Answer:
64
Step-by-step explanation:
We can use the product rule of counting to answer this:
There are 4 possibilities for the 1st digit
There are 4 possibilities for the 2nd digit
There are 4 possibilities for the 3rd digit
So we use the product rule of counting to give us:
4×4×4=64
Answer:
Point U' (-2, 1)
Step-by-step explanation:
When moving up and down on a graph, this affects the y coordinate only.
Since it is moving up 1 unit, we have to add 1 to the y coordinate. So U' will end up being (-2, 1).
Answer:
b = 
Step-by-step explanation:
Given
k = 
← multiply both sides by (v - b)
k(v - b) = brt ← distribute left side
kv - kb = brt ( subtract brt from both sides )
kv - kb - brt = 0 ( subtract kv from both sides )
- kb - brt = - kv ( multiply through by - 1 to clear the negatives )
kb + brt = kv ← factor out b from each term on the left
b(k + rt ) = kv ← divide both sides by (k + rt )
b =
Y=3x+30
because if you look she automatically makes $30, and her salary goes up every time cone by 3<span />
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
