Answer:
The answer is x=1
Step-by-step explanation:
-4(3x+6)+6=-30
-12x-24+6=-30
-12x-18=-30
-12x-18+18=-30+18
-12x=-12
-12x/-12=-12/-12
x=1
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.
Step-by-step explanation:
Add 8n to both sides to get
8n-67 = 5
then add 67
8n = 5+67 = 72
divide by 8
n = 9
If that is the position function, velocity is the derivative of it.
v(t)=-14
Since velocity is a constant -14, the value of t has no bearing on the result. The instantaneous velocity is always -14.
