Answer:
1).B
2).A
3).D
4).B
5).C
6).D
7).D
8).B
9).C
10). I believe it is A
Step-by-step explanation:
I'm sorry, i do not know how to explain this, I hope I helped you in some way and I hope these answers work for you :)
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.
Answer:
The triangle with those measures will be unique.
Step-by-step explanation:
The triangle described is an isosceles right triangle with side lengths 10 cm. All such triangles are congruent (it is unique).
0.985 is the median.
I hope this helped
Answer:
Step-by-step explanation:
