6z to the 4th power - 2z to the 3rd power
Answer:
Step-by-step explanation:
This equation can simply be solved by adding 15 to both sides.
To graph, draw a closed point at the center of the line and darken the area to the right of it.
The answer is 160 because 312÷2 equals 156 and 156 is closer to 160 than 150
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.
$30 because you are taking away 20% of $30 and then adding back that 20%.
