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:
Area = 74.1 square units
Step-by-step explanation:
Area of the composite figure = Area of the rectangle + Area of the semicircle
Area o the rectangle = Length × Width
= 10 × 6
= 60 square units
Area of the semicircle = 
Here, r = radius of the semicircle
For the semicircle with radius = 
= 3 units
Area = 
= 4.5π
= 14.14 units²
Total area of the composite figure = 60 + 14.14
= 74.14 square units ≈ 74.1 square units
Answer:
1/9 is probably most likely the correct answer
Answer:
The answer is A.
Step-by-step explanation:
If you add both A and B then you will get 15 because 10 + 5 = 15
